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Recover signal from single-sided spectrum using ifft

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Hans
Hans 2024 年 4 月 23 日
コメント済み: Star Strider 2024 年 4 月 23 日
I am trying to recover a signal by inverse Fourier-transforming the single-sided spectrum, but I am getting the wrong result. I do successfully transform the single-sided spectrum back to double-sided spectrum but from there I get lost. What am I doing wrong here? In fact, how can I recover the full information after doing abs(), isn't there lost info there?
Fs = 1000; % Sampling frequency
T = 1/Fs; % Sampling period
L = 1500; % Length of signal
t = (0:L-1)*T; % Time vector
S = 0.7*sin(2*pi*50*t) + sin(2*pi*120*t);
X = S + 2*randn(size(t));
figure(1)
plot(1000*t(1:50),X(1:50))
title("Signal Corrupted with Zero-Mean Random Noise")
xlabel("t (milliseconds)")
ylabel("X(t)")
Y = fft(X);
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);
f = Fs*(0:(L/2))/L;
figure(2)
plot(f,P1)
title("Single-Sided Amplitude Spectrum of X(t)")
xlabel("f (Hz)")
ylabel("|P1(f)|")
X2=ifft(Y);
figure(3)
plot(X2(1:50))
Y2 = 2*[P1(1) P1(2:end)/2 fliplr(conj(P1(2:end)))/2];
X3 = ifft(L*Y2);
figure(4)
plot(Y2)
figure(5)
plot(X3(1:50))

回答 (1 件)

Star Strider
Star Strider 2024 年 4 月 23 日
The problem appears (to me) that you are using the absolute value (‘P2’) of the fft result. This essentially discards the phase information.
If you also calculate the phase, for example using:
Q1 = angle(Y);
and then reconstitute it using:
Y2 = P1 * exp(1i*Q1);
you will likely get the original signal and can then take its inverse Fourier transform.
I included an example of this at the end after ‘Illustrating —’.
Fs = 1000; % Sampling frequency
T = 1/Fs; % Sampling period
L = 1500; % Length of signal
t = (0:L-1)*T; % Time vector
S = 0.7*sin(2*pi*50*t) + sin(2*pi*120*t);
X = S + 2*randn(size(t));
figure(1)
plot(1000*t(1:50),X(1:50))
title("Signal Corrupted with Zero-Mean Random Noise")
xlabel("t (milliseconds)")
ylabel("X(t)")
Y = fft(X);
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);
f = Fs*(0:(L/2))/L;
figure(2)
plot(f,P1)
title("Single-Sided Amplitude Spectrum of X(t)")
xlabel("f (Hz)")
ylabel("|P1(f)|")
X2=ifft(Y);
figure(3)
plot(X2(1:50))
Y2 = 2*[P1(1) P1(2:end)/2 fliplr(conj(P1(2:end)))/2];
X3 = ifft(L*Y2);
figure(4)
plot(Y2)
figure(5)
plot(X3(1:50))
% Illustrating —
Y = fft(X); % Re-Calculate 'Y'
P2 = abs(Y); % Magnitude (AADDED)
Q2 = angle(Y); % Phase (ADDED)
Y2 = P2 .* exp(1i*Q2); % Re-Constitute Complex Vector (ADDED)
Compare_Vectors = [Y2; Y]
Compare_Vectors =
1.0e+02 * Columns 1 through 9 -1.6495 + 0.0000i 0.0636 + 0.3138i -0.7084 - 0.6529i -0.1453 + 0.6065i 0.2842 + 0.5790i -0.4591 - 0.4035i 0.1982 - 0.3913i -0.8853 - 0.5686i 0.3824 + 0.4446i -1.6495 + 0.0000i 0.0636 + 0.3138i -0.7084 - 0.6529i -0.1453 + 0.6065i 0.2842 + 0.5790i -0.4591 - 0.4035i 0.1982 - 0.3913i -0.8853 - 0.5686i 0.3824 + 0.4446i Columns 10 through 18 0.3847 + 0.9388i -0.4213 - 0.0597i -0.4659 - 0.1204i 0.2474 - 0.8358i -0.0197 - 0.7281i -0.3869 - 0.2937i 0.1777 + 1.1340i 0.4714 + 0.4394i -0.4998 + 0.2883i 0.3847 + 0.9388i -0.4213 - 0.0597i -0.4659 - 0.1204i 0.2474 - 0.8358i -0.0197 - 0.7281i -0.3869 - 0.2937i 0.1777 + 1.1340i 0.4714 + 0.4394i -0.4998 + 0.2883i Columns 19 through 27 -0.7508 + 0.6036i 1.1517 + 0.5441i 0.1629 + 0.2781i 0.2784 - 0.3317i -0.0407 + 0.5985i -0.0831 - 0.2014i 0.4370 - 0.1637i 0.2233 + 0.2844i -0.0706 - 0.0055i -0.7508 + 0.6036i 1.1517 + 0.5441i 0.1629 + 0.2781i 0.2784 - 0.3317i -0.0407 + 0.5985i -0.0831 - 0.2014i 0.4370 - 0.1637i 0.2233 + 0.2844i -0.0706 - 0.0055i Columns 28 through 36 -0.6118 + 0.0098i -0.2174 + 0.0561i -0.4367 + 0.2627i -0.9185 + 0.7952i -0.5498 - 0.6233i 0.5755 + 0.6548i 1.1869 - 0.8200i -0.5308 - 0.4921i 0.6911 - 0.2684i -0.6118 + 0.0098i -0.2174 + 0.0561i -0.4367 + 0.2627i -0.9185 + 0.7952i -0.5498 - 0.6233i 0.5755 + 0.6548i 1.1869 - 0.8200i -0.5308 - 0.4921i 0.6911 - 0.2684i Columns 37 through 45 0.0699 - 0.2685i 0.6454 + 0.1652i -0.3822 - 0.1407i -0.4427 + 0.2446i 0.3121 - 0.1513i 0.1962 + 0.2082i 0.4753 - 0.2914i 0.5978 + 0.9724i 0.6307 + 1.0644i 0.0699 - 0.2685i 0.6454 + 0.1652i -0.3822 - 0.1407i -0.4427 + 0.2446i 0.3121 - 0.1513i 0.1962 + 0.2082i 0.4753 - 0.2914i 0.5978 + 0.9724i 0.6307 + 1.0644i Columns 46 through 54 -0.4908 - 0.2029i -1.2722 - 0.2366i 0.1695 + 1.1441i -0.4380 + 0.5496i 1.1572 + 0.1984i 1.1418 - 0.4241i 0.0334 - 0.2270i -0.2531 - 0.3224i 0.5920 + 0.7406i -0.4908 - 0.2029i -1.2722 - 0.2366i 0.1695 + 1.1441i -0.4380 + 0.5496i 1.1572 + 0.1984i 1.1418 - 0.4241i 0.0334 - 0.2270i -0.2531 - 0.3224i 0.5920 + 0.7406i Columns 55 through 63 -0.7116 - 0.3801i -0.4229 - 0.1297i -0.3772 - 0.5141i 0.0947 - 0.4745i 1.2963 - 1.0287i 0.7329 + 0.0296i -0.7902 - 0.1437i 0.0081 + 0.4450i -1.0926 + 0.3091i -0.7116 - 0.3801i -0.4229 - 0.1297i -0.3772 - 0.5141i 0.0947 - 0.4745i 1.2963 - 1.0287i 0.7329 + 0.0296i -0.7902 - 0.1437i 0.0081 + 0.4450i -1.0926 + 0.3091i Columns 64 through 72 -1.0494 + 0.0730i -0.0349 + 0.0508i 1.1594 + 0.4242i -0.0179 - 0.1750i 0.4145 - 0.6600i 0.5036 - 0.1983i -0.4228 - 0.7471i 0.4557 + 1.0042i -0.0356 - 0.7771i -1.0494 + 0.0730i -0.0349 + 0.0508i 1.1594 + 0.4242i -0.0179 - 0.1750i 0.4145 - 0.6600i 0.5036 - 0.1983i -0.4228 - 0.7471i 0.4557 + 1.0042i -0.0356 - 0.7771i Columns 73 through 81 -0.6484 - 0.6162i 0.0521 - 0.5187i -0.0380 - 0.0127i 0.0116 - 4.8502i 0.6240 - 0.3417i -0.1614 + 0.5115i 0.0720 - 0.2640i -0.3245 + 0.8793i 0.7014 - 0.1698i -0.6484 - 0.6162i 0.0521 - 0.5187i -0.0380 - 0.0127i 0.0116 - 4.8502i 0.6240 - 0.3417i -0.1614 + 0.5115i 0.0720 - 0.2640i -0.3245 + 0.8793i 0.7014 - 0.1698i Columns 82 through 90 -0.3172 - 1.0701i 0.5448 + 0.2742i -0.3844 - 0.0006i -1.4325 - 0.2173i 0.8034 + 1.2062i 0.0616 + 1.0753i 0.2828 + 0.5478i -0.4365 + 1.3117i -0.2350 - 0.6952i -0.3172 - 1.0701i 0.5448 + 0.2742i -0.3844 - 0.0006i -1.4325 - 0.2173i 0.8034 + 1.2062i 0.0616 + 1.0753i 0.2828 + 0.5478i -0.4365 + 1.3117i -0.2350 - 0.6952i Columns 91 through 99 0.3908 - 0.0085i -0.8230 + 0.5935i -1.0381 + 0.3321i -0.2965 - 0.2791i 0.1413 - 0.0593i 0.0930 + 0.0471i -0.0937 + 0.7034i 0.4884 - 0.7478i -0.2526 - 0.3082i 0.3908 - 0.0085i -0.8230 + 0.5935i -1.0381 + 0.3321i -0.2965 - 0.2791i 0.1413 - 0.0593i 0.0930 + 0.0471i -0.0937 + 0.7034i 0.4884 - 0.7478i -0.2526 - 0.3082i Columns 100 through 108 1.0403 - 0.3113i 0.0056 - 0.3621i -0.0717 + 0.2884i -0.2407 + 0.7200i -0.6191 + 0.5376i -0.2563 + 1.0383i -0.7267 - 0.0082i -1.4226 - 0.5561i 0.3785 - 0.0404i 1.0403 - 0.3113i 0.0056 - 0.3621i -0.0717 + 0.2884i -0.2407 + 0.7200i -0.6191 + 0.5376i -0.2563 + 1.0383i -0.7267 - 0.0082i -1.4226 - 0.5561i 0.3785 - 0.0404i Columns 109 through 117 0.2321 + 0.1331i -1.1329 - 0.6168i 0.1724 - 0.1895i -0.5240 - 0.1372i 0.4782 - 0.5115i -0.2460 - 0.0912i 0.1189 - 0.0140i -0.3413 - 0.0441i -0.5216 + 0.0401i 0.2321 + 0.1331i -1.1329 - 0.6168i 0.1724 - 0.1895i -0.5240 - 0.1372i 0.4782 - 0.5115i -0.2460 - 0.0912i 0.1189 - 0.0140i -0.3413 - 0.0441i -0.5216 + 0.0401i Columns 118 through 126 -0.4048 - 0.2312i 0.3573 + 0.1634i -0.1133 + 0.5948i -0.4247 + 0.1653i -0.0694 + 0.4570i 1.2645 + 0.0069i -0.3881 - 0.3684i -0.0903 - 0.1492i 0.8721 - 0.0891i -0.4048 - 0.2312i 0.3573 + 0.1634i -0.1133 + 0.5948i -0.4247 + 0.1653i -0.0694 + 0.4570i 1.2645 + 0.0069i -0.3881 - 0.3684i -0.0903 - 0.1492i 0.8721 - 0.0891i Columns 127 through 135 -0.6007 - 0.4403i 0.0176 + 0.8373i -1.0955 - 0.5859i 0.3709 - 0.1030i 0.1394 - 1.0061i 0.2802 - 0.0788i 0.6192 - 0.4147i 0.5028 - 0.2895i 0.7401 - 0.8717i -0.6007 - 0.4403i 0.0176 + 0.8373i -1.0955 - 0.5859i 0.3709 - 0.1030i 0.1394 - 1.0061i 0.2802 - 0.0788i 0.6192 - 0.4147i 0.5028 - 0.2895i 0.7401 - 0.8717i Columns 136 through 144 -0.1150 + 0.4904i 0.1225 + 0.3840i -0.4262 - 0.4046i 0.2982 + 0.5171i 0.3437 - 0.5529i -0.0523 - 0.9016i -0.2675 + 0.0827i -0.8393 - 0.3414i 0.3762 - 0.8680i -0.1150 + 0.4904i 0.1225 + 0.3840i -0.4262 - 0.4046i 0.2982 + 0.5171i 0.3437 - 0.5529i -0.0523 - 0.9016i -0.2675 + 0.0827i -0.8393 - 0.3414i 0.3762 - 0.8680i Columns 145 through 153 -0.5292 - 0.3840i -0.3131 + 0.7414i 0.5552 - 0.0869i -0.2124 - 0.0304i -0.4114 - 0.5704i 0.5837 - 0.1399i 0.3015 + 0.0115i 0.4825 + 0.7799i 0.7568 + 0.3328i -0.5292 - 0.3840i -0.3131 + 0.7414i 0.5552 - 0.0869i -0.2124 - 0.0304i -0.4114 - 0.5704i 0.5837 - 0.1399i 0.3015 + 0.0115i 0.4825 + 0.7799i 0.7568 + 0.3328i Columns 154 through 162 0.0152 + 0.9018i 0.3461 + 0.5462i 0.6739 - 0.0151i -0.1597 + 0.6976i -0.6455 - 0.1014i 0.1260 + 0.1731i 0.0690 + 0.1772i 0.0010 + 0.7462i 0.9948 + 0.6923i 0.0152 + 0.9018i 0.3461 + 0.5462i 0.6739 - 0.0151i -0.1597 + 0.6976i -0.6455 - 0.1014i 0.1260 + 0.1731i 0.0690 + 0.1772i 0.0010 + 0.7462i 0.9948 + 0.6923i Columns 163 through 171 -0.4921 - 0.3886i -0.3491 + 1.0137i -0.0470 - 1.1353i 0.5456 + 0.1951i -0.2399 - 0.7713i 0.7301 + 0.0446i 0.9579 + 0.1152i -0.2644 - 0.8495i 0.4746 + 0.7109i -0.4921 - 0.3886i -0.3491 + 1.0137i -0.0470 - 1.1353i 0.5456 + 0.1951i -0.2399 - 0.7713i 0.7301 + 0.0446i 0.9579 + 0.1152i -0.2644 - 0.8495i 0.4746 + 0.7109i Columns 172 through 180 0.3008 + 0.1699i -0.2666 - 0.0575i -0.3975 - 0.1010i -0.2408 + 1.0441i 0.2559 + 0.1707i 0.4452 - 0.1542i -0.0044 + 0.0164i 0.4336 + 0.5456i -0.1661 - 0.4108i 0.3008 + 0.1699i -0.2666 - 0.0575i -0.3975 - 0.1010i -0.2408 + 1.0441i 0.2559 + 0.1707i 0.4452 - 0.1542i -0.0044 + 0.0164i 0.4336 + 0.5456i -0.1661 - 0.4108i Columns 181 through 189 -0.6500 - 8.2004i -0.7628 + 1.0036i 0.2372 - 0.2108i -0.4279 + 0.4167i 0.3415 - 0.2017i 0.4215 + 0.4795i 1.1586 - 0.6749i -0.2858 - 1.1116i 0.5812 + 0.0800i -0.6500 - 8.2004i -0.7628 + 1.0036i 0.2372 - 0.2108i -0.4279 + 0.4167i 0.3415 - 0.2017i 0.4215 + 0.4795i 1.1586 - 0.6749i -0.2858 - 1.1116i 0.5812 + 0.0800i Columns 190 through 198 0.3339 - 0.1278i 0.2267 - 0.2742i -0.3947 + 0.5681i 0.0817 + 0.3077i -1.0817 + 0.6393i 0.3551 - 0.2029i 0.5936 + 0.0054i -0.3304 + 0.2679i -0.2886 - 0.6429i 0.3339 - 0.1278i 0.2267 - 0.2742i -0.3947 + 0.5681i 0.0817 + 0.3077i -1.0817 + 0.6393i 0.3551 - 0.2029i 0.5936 + 0.0054i -0.3304 + 0.2679i -0.2886 - 0.6429i Columns 199 through 207 0.0325 - 0.3917i -0.6070 - 0.5261i 0.5528 + 0.2621i 0.1149 + 0.6497i 0.4999 - 0.2880i 0.2673 + 0.2757i -0.7946 - 0.7938i -0.2020 + 0.0353i -0.1162 - 0.2140i 0.0325 - 0.3917i -0.6070 - 0.5261i 0.5528 + 0.2621i 0.1149 + 0.6497i 0.4999 - 0.2880i 0.2673 + 0.2757i -0.7946 - 0.7938i -0.2020 + 0.0353i -0.1162 - 0.2140i Columns 208 through 216 0.3383 + 0.7181i -0.3692 - 0.2421i -0.2614 - 0.7167i 0.5738 + 0.1032i 0.0267 - 0.6131i -0.2450 - 0.2149i 0.2642 - 0.3165i 0.7659 + 0.0776i -0.0542 - 0.7347i 0.3383 + 0.7181i -0.3692 - 0.2421i -0.2614 - 0.7167i 0.5738 + 0.1032i 0.0267 - 0.6131i -0.2450 - 0.2149i 0.2642 - 0.3165i 0.7659 + 0.0776i -0.0542 - 0.7347i Columns 217 through 225 -1.0355 - 0.3260i -0.7604 - 0.5047i 0.7289 + 0.5857i 0.7437 - 0.1794i -0.5514 + 0.6977i 0.5035 - 0.3027i -0.2240 + 1.1389i 0.5703 + 0.0951i 0.5139 - 0.9623i -1.0355 - 0.3260i -0.7604 - 0.5047i 0.7289 + 0.5857i 0.7437 - 0.1794i -0.5514 + 0.6977i 0.5035 - 0.3027i -0.2240 + 1.1389i 0.5703 + 0.0951i 0.5139 - 0.9623i Columns 226 through 234 0.2852 + 0.0469i -0.1238 - 0.2206i -1.1941 + 0.5176i -0.7173 + 0.3920i -0.7207 - 0.0128i 0.7631 + 0.1957i -0.7018 - 0.3729i -1.0055 - 0.8167i -0.1148 + 0.5457i 0.2852 + 0.0469i -0.1238 - 0.2206i -1.1941 + 0.5176i -0.7173 + 0.3920i -0.7207 - 0.0128i 0.7631 + 0.1957i -0.7018 - 0.3729i -1.0055 - 0.8167i -0.1148 + 0.5457i Columns 235 through 243 0.4747 - 0.2068i -0.5685 + 0.8472i 0.3503 - 0.3557i -1.2736 + 0.6638i -0.0431 + 0.1637i -0.1696 + 0.9134i -0.8260 + 0.9899i 0.2546 - 0.1646i 0.0880 - 0.1137i 0.4747 - 0.2068i -0.5685 + 0.8472i 0.3503 - 0.3557i -1.2736 + 0.6638i -0.0431 + 0.1637i -0.1696 + 0.9134i -0.8260 + 0.9899i 0.2546 - 0.1646i 0.0880 - 0.1137i Columns 244 through 252 0.7069 + 0.4829i 0.0789 + 1.1149i -0.5080 - 0.4167i 0.7918 + 0.2849i 0.8757 - 0.0262i -0.5772 + 1.0660i 0.0363 - 0.4289i 0.8619 + 0.1361i -0.1532 + 0.7543i 0.7069 + 0.4829i 0.0789 + 1.1149i -0.5080 - 0.4167i 0.7918 + 0.2849i 0.8757 - 0.0262i -0.5772 + 1.0660i 0.0363 - 0.4289i 0.8619 + 0.1361i -0.1532 + 0.7543i Columns 253 through 261 -0.9435 - 0.3907i 0.5628 + 0.6835i -0.3612 + 0.2098i 1.7876 - 0.3532i 1.1799 - 0.3571i 0.7301 - 0.9061i 0.9741 - 0.4876i -0.2978 + 0.2519i -0.5288 + 0.6553i -0.9435 - 0.3907i 0.5628 + 0.6835i -0.3612 + 0.2098i 1.7876 - 0.3532i 1.1799 - 0.3571i 0.7301 - 0.9061i 0.9741 - 0.4876i -0.2978 + 0.2519i -0.5288 + 0.6553i Columns 262 through 270 -0.8649 - 0.2182i -0.1560 - 0.7638i 0.3961 - 0.4284i -0.0402 + 0.1522i -0.0205 + 0.4709i 0.5572 + 0.7762i -0.4071 - 0.1296i -0.2415 + 0.2783i -0.2127 - 0.2738i -0.8649 - 0.2182i -0.1560 - 0.7638i 0.3961 - 0.4284i -0.0402 + 0.1522i -0.0205 + 0.4709i 0.5572 + 0.7762i -0.4071 - 0.1296i -0.2415 + 0.2783i -0.2127 - 0.2738i Columns 271 through 279 0.3983 + 0.5766i 0.2075 - 0.4511i -0.4918 - 0.1792i -0.0749 - 0.3175i -0.4273 + 0.0288i 0.4790 + 0.1400i -0.7034 - 1.1767i -0.3115 - 0.3772i -0.7359 - 0.6149i 0.3983 + 0.5766i 0.2075 - 0.4511i -0.4918 - 0.1792i -0.0749 - 0.3175i -0.4273 + 0.0288i 0.4790 + 0.1400i -0.7034 - 1.1767i -0.3115 - 0.3772i -0.7359 - 0.6149i Columns 280 through 288 -0.4719 + 0.3285i -0.3265 - 0.0701i 0.4566 + 0.1158i -0.1529 - 0.1524i -0.1434 - 0.0745i 0.0339 - 0.4610i 0.9427 - 0.2290i -0.4111 + 0.1534i -0.3541 + 0.3956i -0.4719 + 0.3285i -0.3265 - 0.0701i 0.4566 + 0.1158i -0.1529 - 0.1524i -0.1434 - 0.0745i 0.0339 - 0.4610i 0.9427 - 0.2290i -0.4111 + 0.1534i -0.3541 + 0.3956i Columns 289 through 297 0.2143 - 1.6187i -0.5697 - 0.1176i -0.5023 + 0.0290i -0.4719 - 0.1788i -0.5160 + 0.0430i -0.1601 + 0.3006i 0.0933 + 0.0916i -0.1956 + 0.1846i -0.7991 + 0.1345i 0.2143 - 1.6187i -0.5697 - 0.1176i -0.5023 + 0.0290i -0.4719 - 0.1788i -0.5160 + 0.0430i -0.1601 + 0.3006i 0.0933 + 0.0916i -0.1956 + 0.1846i -0.7991 + 0.1345i Columns 298 through 306 0.2050 + 0.5125i -0.2617 - 0.5269i -0.8753 - 0.9326i 0.3037 - 0.7557i -0.0139 - 1.1499i -0.1394 - 0.7264i 0.4830 - 0.5057i -0.3165 - 0.6060i 0.8278 - 0.5580i 0.2050 + 0.5125i -0.2617 - 0.5269i -0.8753 - 0.9326i 0.3037 - 0.7557i -0.0139 - 1.1499i -0.1394 - 0.7264i 0.4830 - 0.5057i -0.3165 - 0.6060i 0.8278 - 0.5580i Columns 307 through 315 -0.2177 + 1.3837i -1.1520 + 0.5462i 0.1069 + 0.1821i 0.4125 - 0.3048i -0.7267 + 0.8697i -0.3894 - 0.0854i 0.1164 + 0.2944i -0.1174 - 0.2127i 0.4994 - 0.1109i -0.2177 + 1.3837i -1.1520 + 0.5462i 0.1069 + 0.1821i 0.4125 - 0.3048i -0.7267 + 0.8697i -0.3894 - 0.0854i 0.1164 + 0.2944i -0.1174 - 0.2127i 0.4994 - 0.1109i Columns 316 through 324 -0.2870 + 0.8028i 1.1452 - 0.8547i -0.1281 - 0.1141i 0.6692 + 0.0766i -0.2746 - 0.5635i 0.4357 + 0.9363i 0.3905 - 0.0699i -0.4758 - 0.8751i -0.6203 - 0.7937i -0.2870 + 0.8028i 1.1452 - 0.8547i -0.1281 - 0.1141i 0.6692 + 0.0766i -0.2746 - 0.5635i 0.4357 + 0.9363i 0.3905 - 0.0699i -0.4758 - 0.8751i -0.6203 - 0.7937i Columns 325 through 333 0.0890 - 0.7304i 0.7655 + 1.0532i 0.0016 - 0.6222i -1.2261 - 0.8937i -0.3592 - 0.1244i -0.9930 + 1.0189i 0.4719 - 0.2816i 0.5100 + 0.3542i -0.1881 - 0.3456i 0.0890 - 0.7304i 0.7655 + 1.0532i 0.0016 - 0.6222i -1.2261 - 0.8937i -0.3592 - 0.1244i -0.9930 + 1.0189i 0.4719 - 0.2816i 0.5100 + 0.3542i -0.1881 - 0.3456i Columns 334 through 342 0.0823 - 0.6173i 0.4074 + 0.0847i 0.0203 + 0.1877i 0.4931 - 0.1128i -0.3138 - 0.4542i 0.8078 - 0.3388i -1.0445 - 0.3479i 0.1200 - 0.5006i 0.9462 - 0.3743i 0.0823 - 0.6173i 0.4074 + 0.0847i 0.0203 + 0.1877i 0.4931 - 0.1128i -0.3138 - 0.4542i 0.8078 - 0.3388i -1.0445 - 0.3479i 0.1200 - 0.5006i 0.9462 - 0.3743i Columns 343 through 351 0.7213 - 0.2714i -0.0128 + 0.2321i 0.2718 - 1.2150i -0.1946 + 0.1702i -0.0364 - 0.2613i 0.4784 + 0.7063i 0.1367 + 0.7856i -0.6493 + 1.2302i 0.0287 + 0.5391i 0.7213 - 0.2714i -0.0128 + 0.2321i 0.2718 - 1.2150i -0.1946 + 0.1702i -0.0364 - 0.2613i 0.4784 + 0.7063i 0.1367 + 0.7856i -0.6493 + 1.2302i 0.0287 + 0.5391i Columns 352 through 360 0.4551 + 0.8099i -0.5271 + 0.3819i -0.0473 - 0.5159i 1.4531 - 0.6376i 0.1152 - 0.0719i -0.6970 + 0.4924i -0.6528 + 0.0574i -0.6857 - 0.6095i -0.9102 - 1.0721i 0.4551 + 0.8099i -0.5271 + 0.3819i -0.0473 - 0.5159i 1.4531 - 0.6376i 0.1152 - 0.0719i -0.6970 + 0.4924i -0.6528 + 0.0574i -0.6857 - 0.6095i -0.9102 - 1.0721i Columns 361 through 369 -0.2145 + 0.9039i 0.5456 + 0.4047i -0.4826 + 0.2876i 0.2839 + 0.5934i 0.0100 + 0.9151i 0.6555 + 0.3976i 0.4706 - 0.4107i -0.7025 + 0.1871i 0.0274 + 0.0711i -0.2145 + 0.9039i 0.5456 + 0.4047i -0.4826 + 0.2876i 0.2839 + 0.5934i 0.0100 + 0.9151i 0.6555 + 0.3976i 0.4706 - 0.4107i -0.7025 + 0.1871i 0.0274 + 0.0711i Columns 370 through 378 -0.2054 - 0.7041i -0.8437 - 1.2069i -0.7244 - 0.6242i 0.3895 + 1.0220i 0.8706 - 0.1424i 0.0955 + 1.5444i -0.8000 - 0.1511i 1.4013 + 0.5624i -0.4943 + 0.2324i -0.2054 - 0.7041i -0.8437 - 1.2069i -0.7244 - 0.6242i 0.3895 + 1.0220i 0.8706 - 0.1424i 0.0955 + 1.5444i -0.8000 - 0.1511i 1.4013 + 0.5624i -0.4943 + 0.2324i Columns 379 through 387 0.6477 + 0.7168i 0.1663 - 0.8324i 0.0757 + 0.3563i 0.8585 - 0.3655i -0.4474 + 1.0009i 0.0021 - 0.3283i -0.7639 + 0.2843i -0.4141 + 1.0446i -0.6161 + 0.3904i 0.6477 + 0.7168i 0.1663 - 0.8324i 0.0757 + 0.3563i 0.8585 - 0.3655i -0.4474 + 1.0009i 0.0021 - 0.3283i -0.7639 + 0.2843i -0.4141 + 1.0446i -0.6161 + 0.3904i Columns 388 through 396 -0.7583 - 0.2662i -0.4335 + 0.1334i -0.8608 + 0.0569i 0.1922 + 0.2801i -0.6481 - 0.4986i 0.0975 + 0.7843i -0.3691 - 0.6722i -0.3558 - 0.0524i -0.3317 + 0.7125i -0.7583 - 0.2662i -0.4335 + 0.1334i -0.8608 + 0.0569i 0.1922 + 0.2801i -0.6481 - 0.4986i 0.0975 + 0.7843i -0.3691 - 0.6722i -0.3558 - 0.0524i -0.3317 + 0.7125i Columns 397 through 405 -0.7112 + 0.0208i -0.6825 - 0.4276i 0.5705 - 0.3847i -1.0901 + 0.4084i 0.0617 - 0.0823i 0.5150 + 0.0676i -0.0856 + 0.3413i 0.0598 + 0.0649i 0.4016 + 0.8181i -0.7112 + 0.0208i -0.6825 - 0.4276i 0.5705 - 0.3847i -1.0901 + 0.4084i 0.0617 - 0.0823i 0.5150 + 0.0676i -0.0856 + 0.3413i 0.0598 + 0.0649i 0.4016 + 0.8181i Columns 406 through 414 0.2285 - 0.2960i -0.0088 - 0.0231i 0.3331 + 0.3999i 0.5639 + 0.2141i -0.5222 - 0.8312i 0.2411 - 0.6897i -0.6778 + 0.3489i -0.2587 - 0.4401i -0.5925 - 0.0179i 0.2285 - 0.2960i -0.0088 - 0.0231i 0.3331 + 0.3999i 0.5639 + 0.2141i -0.5222 - 0.8312i 0.2411 - 0.6897i -0.6778 + 0.3489i -0.2587 - 0.4401i -0.5925 - 0.0179i Columns 415 through 423 0.2771 - 0.0480i -0.5299 - 0.6169i 0.0307 + 1.0997i -0.0076 - 0.0603i 0.4128 - 0.4872i 0.0642 + 0.3405i -0.4448 - 0.3499i 0.1105 - 0.1470i 0.6612 + 0.1526i 0.2771 - 0.0480i -0.5299 - 0.6169i 0.0307 + 1.0997i -0.0076 - 0.0603i 0.4128 - 0.4872i 0.0642 + 0.3405i -0.4448 - 0.3499i 0.1105 - 0.1470i 0.6612 + 0.1526i Columns 424 through 432 -0.0013 - 0.4604i -0.0165 - 0.6918i 0.0707 + 0.3200i -0.8616 - 0.7055i 0.1976 + 0.9382i 0.4366 - 0.0211i -0.3412 - 0.4200i -0.0302 + 0.8121i 0.7987 - 0.1253i -0.0013 - 0.4604i -0.0165 - 0.6918i 0.0707 + 0.3200i -0.8616 - 0.7055i 0.1976 + 0.9382i 0.4366 - 0.0211i -0.3412 - 0.4200i -0.0302 + 0.8121i 0.7987 - 0.1253i Columns 433 through 441 0.4176 - 1.0580i -0.2133 + 0.5202i -0.6301 + 0.1971i -0.2746 + 0.0092i -0.8225 - 1.6132i 0.4731 + 0.3101i 0.0557 - 0.6379i 0.0729 + 0.2483i 0.4007 + 0.5085i 0.4176 - 1.0580i -0.2133 + 0.5202i -0.6301 + 0.1971i -0.2746 + 0.0092i -0.8225 - 1.6132i 0.4731 + 0.3101i 0.0557 - 0.6379i 0.0729 + 0.2483i 0.4007 + 0.5085i Columns 442 through 450 0.5227 - 0.3880i -0.5089 - 0.0918i -0.8964 - 0.1580i -0.5730 + 0.4880i -0.0779 + 1.2162i -0.0601 + 0.0114i 0.3803 - 0.0237i -0.1786 - 0.8621i -0.0872 - 0.2780i 0.5227 - 0.3880i -0.5089 - 0.0918i -0.8964 - 0.1580i -0.5730 + 0.4880i -0.0779 + 1.2162i -0.0601 + 0.0114i 0.3803 - 0.0237i -0.1786 - 0.8621i -0.0872 - 0.2780i Columns 451 through 459 -0.7148 - 0.4674i 0.5964 + 0.9704i -0.1966 - 0.0301i -1.0269 - 0.7433i 0.7618 + 0.5374i -0.5781 + 0.8205i -0.2592 + 0.7290i -0.5622 + 1.1248i -0.2680 + 0.6503i -0.7148 - 0.4674i 0.5964 + 0.9704i -0.1966 - 0.0301i -1.0269 - 0.7433i 0.7618 + 0.5374i -0.5781 + 0.8205i -0.2592 + 0.7290i -0.5622 + 1.1248i -0.2680 + 0.6503i Columns 460 through 468 -0.2889 + 0.3183i -0.4255 + 0.2400i 0.2154 + 0.1555i -0.3777 - 0.2515i -0.0441 + 0.0392i -0.7223 - 0.1890i 0.6926 + 0.0783i -0.2478 + 0.0857i 0.1422 - 0.1833i -0.2889 + 0.3183i -0.4255 + 0.2400i 0.2154 + 0.1555i -0.3777 - 0.2515i -0.0441 + 0.0392i -0.7223 - 0.1890i 0.6926 + 0.0783i -0.2478 + 0.0857i 0.1422 - 0.1833i Columns 469 through 477 0.2416 + 0.0515i 1.0169 + 0.1295i 1.0489 + 0.4841i -0.8365 - 0.1325i 0.2840 - 0.5513i 1.0755 - 0.4618i -0.3808 + 0.0098i -0.5076 + 0.5333i 0.5255 + 0.2411i 0.2416 + 0.0515i 1.0169 + 0.1295i 1.0489 + 0.4841i -0.8365 - 0.1325i 0.2840 - 0.5513i 1.0755 - 0.4618i -0.3808 + 0.0098i -0.5076 + 0.5333i 0.5255 + 0.2411i Columns 478 through 486 0.1897 + 0.1130i 0.3421 - 0.9451i -0.2041 + 1.2036i -0.5729 - 1.1277i -0.7104 + 0.4253i 0.2654 - 0.5241i -0.1888 + 0.4362i -0.3428 + 0.2137i -0.2981 + 0.3275i 0.1897 + 0.1130i 0.3421 - 0.9451i -0.2041 + 1.2036i -0.5729 - 1.1277i -0.7104 + 0.4253i 0.2654 - 0.5241i -0.1888 + 0.4362i -0.3428 + 0.2137i -0.2981 + 0.3275i Columns 487 through 495 -0.0776 + 0.5729i 0.6057 + 0.1150i -0.4422 + 0.6297i -0.0702 + 0.7242i -0.5470 + 0.2848i 0.3538 - 1.2591i -0.1315 + 0.1749i -0.4450 + 0.5447i -0.5752 - 0.1459i -0.0776 + 0.5729i 0.6057 + 0.1150i -0.4422 + 0.6297i -0.0702 + 0.7242i -0.5470 + 0.2848i 0.3538 - 1.2591i -0.1315 + 0.1749i -0.4450 + 0.5447i -0.5752 - 0.1459i Columns 496 through 504 -0.3839 + 0.1689i -0.1236 + 0.8678i -0.7394 - 0.5310i -0.1639 + 0.7962i 0.6987 + 0.9008i -0.2557 - 0.2128i -0.4320 - 0.1214i 0.1380 - 1.2931i -1.3212 + 0.2792i -0.3839 + 0.1689i -0.1236 + 0.8678i -0.7394 - 0.5310i -0.1639 + 0.7962i 0.6987 + 0.9008i -0.2557 - 0.2128i -0.4320 - 0.1214i 0.1380 - 1.2931i -1.3212 + 0.2792i Columns 505 through 513 -0.9441 - 0.8719i 0.7073 + 0.4958i 0.2045 + 0.4061i 0.2172 + 0.6263i 1.3645 - 0.3251i -0.2766 - 0.2684i 0.6541 + 0.0132i -0.6244 - 0.1776i -0.7134 - 0.4718i -0.9441 - 0.8719i 0.7073 + 0.4958i 0.2045 + 0.4061i 0.2172 + 0.6263i 1.3645 - 0.3251i -0.2766 - 0.2684i 0.6541 + 0.0132i -0.6244 - 0.1776i -0.7134 - 0.4718i Columns 514 through 522 -1.2216 - 0.0867i 0.7818 - 0.4755i 0.8731 - 0.4057i 0.0396 + 0.2448i -0.2509 - 0.0582i -0.5394 + 0.6446i 0.0812 - 0.5601i -0.3014 + 0.7792i -0.4852 + 0.1125i -1.2216 - 0.0867i 0.7818 - 0.4755i 0.8731 - 0.4057i 0.0396 + 0.2448i -0.2509 - 0.0582i -0.5394 + 0.6446i 0.0812 - 0.5601i -0.3014 + 0.7792i -0.4852 + 0.1125i Columns 523 through 531 0.3994 + 0.4863i 0.2277 - 0.1744i -0.2075 + 0.4682i 0.2077 - 0.5861i 0.9681 + 0.1704i -0.6681 + 0.4179i -0.2725 - 0.2447i 0.0493 - 0.6032i -0.1050 + 0.3789i 0.3994 + 0.4863i 0.2277 - 0.1744i -0.2075 + 0.4682i 0.2077 - 0.5861i 0.9681 + 0.1704i -0.6681 + 0.4179i -0.2725 - 0.2447i 0.0493 - 0.6032i -0.1050 + 0.3789i Columns 532 through 540 0.8510 + 0.7325i 0.2742 - 0.2518i 0.7622 + 0.5359i -0.3582 - 0.2574i 0.3839 + 0.5285i 0.0752 + 0.2587i -0.2249 - 0.0490i -0.6632 + 0.0249i -0.9090 - 0.4559i 0.8510 + 0.7325i 0.2742 - 0.2518i 0.7622 + 0.5359i -0.3582 - 0.2574i 0.3839 + 0.5285i 0.0752 + 0.2587i -0.2249 - 0.0490i -0.6632 + 0.0249i -0.9090 - 0.4559i Columns 541 through 549 0.4131 - 0.2654i 0.0985 - 0.0517i 0.4646 + 0.0445i -0.7463 + 0.2641i 0.3029 + 0.0315i 0.5670 - 0.4886i 1.1811 + 0.4084i -0.7148 + 0.2514i 0.6176 - 0.0703i 0.4131 - 0.2654i 0.0985 - 0.0517i 0.4646 + 0.0445i -0.7463 + 0.2641i 0.3029 + 0.0315i 0.5670 - 0.4886i 1.1811 + 0.4084i -0.7148 + 0.2514i 0.6176 - 0.0703i Columns 550 through 558 -0.6437 + 0.0020i 0.7578 + 0.7182i 0.1065 - 0.4782i 1.3646 + 0.5360i -1.3359 + 0.0752i 0.3529 + 0.1989i -0.0311 + 0.3017i -0.2076 - 0.4541i -1.0340 - 0.2398i -0.6437 + 0.0020i 0.7578 + 0.7182i 0.1065 - 0.4782i 1.3646 + 0.5360i -1.3359 + 0.0752i 0.3529 + 0.1989i -0.0311 + 0.3017i -0.2076 - 0.4541i -1.0340 - 0.2398i Columns 559 through 567 0.9310 - 0.9083i 0.4460 + 1.1631i -0.9760 + 0.0478i 0.3835 + 0.0372i 0.5133 + 0.3989i 0.1211 + 0.1843i -0.1470 + 0.2627i -0.5163 + 0.1541i -0.4452 + 1.1909i 0.9310 - 0.9083i 0.4460 + 1.1631i -0.9760 + 0.0478i 0.3835 + 0.0372i 0.5133 + 0.3989i 0.1211 + 0.1843i -0.1470 + 0.2627i -0.5163 + 0.1541i -0.4452 + 1.1909i Columns 568 through 576 -0.1434 - 0.1157i -0.1022 + 0.0849i -0.1973 - 0.0075i 0.1869 - 0.7624i -0.9901 - 0.5272i -0.3333 + 0.3636i -0.4850 - 0.5383i -0.3475 + 0.1143i 0.1195 + 0.0018i -0.1434 - 0.1157i -0.1022 + 0.0849i -0.1973 - 0.0075i 0.1869 - 0.7624i -0.9901 - 0.5272i -0.3333 + 0.3636i -0.4850 - 0.5383i -0.3475 + 0.1143i 0.1195 + 0.0018i Columns 577 through 585 0.3408 + 0.8416i -0.0052 + 0.0728i -0.4226 - 0.5092i -0.5876 + 0.0852i -0.2151 + 0.3932i 0.5252 + 0.0374i -0.7678 - 0.5736i 0.1698 - 0.2305i 0.5118 + 0.4603i 0.3408 + 0.8416i -0.0052 + 0.0728i -0.4226 - 0.5092i -0.5876 + 0.0852i -0.2151 + 0.3932i 0.5252 + 0.0374i -0.7678 - 0.5736i 0.1698 - 0.2305i 0.5118 + 0.4603i Columns 586 through 594 -1.0156 + 0.3259i 0.2416 + 0.6309i -0.3840 + 0.1449i 0.1201 + 0.5313i 0.4705 + 0.2951i 1.1308 + 0.7273i -0.6428 + 0.6129i -0.4879 + 0.7851i 0.4136 + 1.3827i -1.0156 + 0.3259i 0.2416 + 0.6309i -0.3840 + 0.1449i 0.1201 + 0.5313i 0.4705 + 0.2951i 1.1308 + 0.7273i -0.6428 + 0.6129i -0.4879 + 0.7851i 0.4136 + 1.3827i Columns 595 through 603 -0.3257 + 0.7250i -1.1771 + 1.2981i 0.5781 - 0.0284i 0.2163 - 0.0047i -0.6012 + 0.3381i -0.0290 - 0.5784i 1.1290 - 0.3916i -0.6103 + 0.6014i -0.4788 - 0.6067i -0.3257 + 0.7250i -1.1771 + 1.2981i 0.5781 - 0.0284i 0.2163 - 0.0047i -0.6012 + 0.3381i -0.0290 - 0.5784i 1.1290 - 0.3916i -0.6103 + 0.6014i -0.4788 - 0.6067i Columns 604 through 612 -0.7996 + 0.2364i 0.0616 - 0.1493i 0.1629 - 0.8930i -0.0638 - 0.3131i -0.2269 + 0.6467i 0.0715 + 0.4574i 0.3813 - 0.4610i -0.5028 + 0.3882i 0.2569 - 1.0884i -0.7996 + 0.2364i 0.0616 - 0.1493i 0.1629 - 0.8930i -0.0638 - 0.3131i -0.2269 + 0.6467i 0.0715 + 0.4574i 0.3813 - 0.4610i -0.5028 + 0.3882i 0.2569 - 1.0884i Columns 613 through 621 -0.8094 - 0.0812i -0.0766 + 0.3634i 0.2887 - 0.1332i 0.0113 - 0.8347i -0.1410 - 0.2325i 0.2518 + 0.1975i -0.0374 + 0.8958i -0.1060 - 0.3986i -0.0762 - 0.0070i -0.8094 - 0.0812i -0.0766 + 0.3634i 0.2887 - 0.1332i 0.0113 - 0.8347i -0.1410 - 0.2325i 0.2518 + 0.1975i -0.0374 + 0.8958i -0.1060 - 0.3986i -0.0762 - 0.0070i Columns 622 through 630 0.2682 + 0.2111i -0.0261 - 0.0870i -0.2827 + 0.2015i -0.3505 + 0.1844i 0.6152 - 0.4094i -0.3261 + 0.3803i 0.2878 + 0.3780i 0.1170 - 0.9819i -0.3535 - 0.3508i 0.2682 + 0.2111i -0.0261 - 0.0870i -0.2827 + 0.2015i -0.3505 + 0.1844i 0.6152 - 0.4094i -0.3261 + 0.3803i 0.2878 + 0.3780i 0.1170 - 0.9819i -0.3535 - 0.3508i Columns 631 through 639 -0.6871 + 0.0263i -0.3915 + 0.0132i -0.4781 - 0.2143i 1.1930 + 0.0350i -0.2278 - 0.7677i 1.0079 + 0.3886i 0.9612 - 0.4148i 0.7225 - 0.4291i 0.3258 + 0.4405i -0.6871 + 0.0263i -0.3915 + 0.0132i -0.4781 - 0.2143i 1.1930 + 0.0350i -0.2278 - 0.7677i 1.0079 + 0.3886i 0.9612 - 0.4148i 0.7225 - 0.4291i 0.3258 + 0.4405i Columns 640 through 648 -0.0519 + 0.1161i -0.3458 - 0.3229i 0.9204 - 0.4523i -0.5303 - 0.4960i 0.3571 + 0.2991i 0.0138 + 0.2965i 0.2157 - 0.1288i -0.1750 + 0.2661i -0.0066 - 0.7339i -0.0519 + 0.1161i -0.3458 - 0.3229i 0.9204 - 0.4523i -0.5303 - 0.4960i 0.3571 + 0.2991i 0.0138 + 0.2965i 0.2157 - 0.1288i -0.1750 + 0.2661i -0.0066 - 0.7339i Columns 649 through 657 -0.9478 + 0.1748i 0.3661 + 0.6526i 0.6735 - 0.3289i -0.1854 + 0.4893i 0.0396 + 0.5575i 0.3868 + 0.1813i 0.1555 - 0.1588i -0.3026 - 0.2503i -0.2363 - 0.7013i -0.9478 + 0.1748i 0.3661 + 0.6526i 0.6735 - 0.3289i -0.1854 + 0.4893i 0.0396 + 0.5575i 0.3868 + 0.1813i 0.1555 - 0.1588i -0.3026 - 0.2503i -0.2363 - 0.7013i Columns 658 through 666 -0.2125 + 0.8274i -0.4049 - 0.3555i -0.1906 - 0.2455i 1.0955 - 0.2512i -0.5690 + 1.0977i -0.3225 - 0.0127i -0.0705 - 0.6749i 0.6261 + 0.7277i -0.0258 - 0.3741i -0.2125 + 0.8274i -0.4049 - 0.3555i -0.1906 - 0.2455i 1.0955 - 0.2512i -0.5690 + 1.0977i -0.3225 - 0.0127i -0.0705 - 0.6749i 0.6261 + 0.7277i -0.0258 - 0.3741i Columns 667 through 675 0.9873 + 0.3845i -0.6813 + 0.4497i 0.6341 - 0.3903i -0.0907 + 0.9534i -0.0188 + 0.1282i -0.0193 + 0.3880i 0.4606 - 0.1359i -0.6095 - 0.1133i 0.3443 - 0.1307i 0.9873 + 0.3845i -0.6813 + 0.4497i 0.6341 - 0.3903i -0.0907 + 0.9534i -0.0188 + 0.1282i -0.0193 + 0.3880i 0.4606 - 0.1359i -0.6095 - 0.1133i 0.3443 - 0.1307i Columns 676 through 684 -0.6061 - 0.3057i -0.2309 + 0.2671i 0.8449 - 0.6444i 0.3921 + 0.5547i -0.2146 + 0.3709i -0.1390 + 0.0209i 0.1362 - 0.6283i 1.1096 + 0.2243i 0.9461 - 0.1015i -0.6061 - 0.3057i -0.2309 + 0.2671i 0.8449 - 0.6444i 0.3921 + 0.5547i -0.2146 + 0.3709i -0.1390 + 0.0209i 0.1362 - 0.6283i 1.1096 + 0.2243i 0.9461 - 0.1015i Columns 685 through 693 0.4437 - 0.0731i -0.1663 + 0.5364i -0.0585 - 0.3314i -0.0119 + 0.1571i 0.4475 + 0.2323i -0.7235 + 0.0250i -0.8225 + 0.2728i 0.0152 - 0.1767i -0.2026 + 0.3105i 0.4437 - 0.0731i -0.1663 + 0.5364i -0.0585 - 0.3314i -0.0119 + 0.1571i 0.4475 + 0.2323i -0.7235 + 0.0250i -0.8225 + 0.2728i 0.0152 - 0.1767i -0.2026 + 0.3105i Columns 694 through 702 -0.0727 + 0.3042i 0.1733 + 1.5575i -0.5739 + 0.0102i 0.3752 + 0.3105i 0.0582 + 0.2751i -0.6487 + 0.7132i 0.0009 + 0.4866i -0.3539 + 1.1929i -0.1833 - 0.3285i -0.0727 + 0.3042i 0.1733 + 1.5575i -0.5739 + 0.0102i 0.3752 + 0.3105i 0.0582 + 0.2751i -0.6487 + 0.7132i 0.0009 + 0.4866i -0.3539 + 1.1929i -0.1833 - 0.3285i Columns 703 through 711 0.1246 + 0.3025i 0.0159 + 0.3053i 0.4986 + 0.0490i -0.3639 + 0.2519i 0.3625 - 0.2395i -0.2585 - 0.0855i -0.1706 - 0.9260i -0.2386 + 0.5208i 0.3168 + 0.6737i 0.1246 + 0.3025i 0.0159 + 0.3053i 0.4986 + 0.0490i -0.3639 + 0.2519i 0.3625 - 0.2395i -0.2585 - 0.0855i -0.1706 - 0.9260i -0.2386 + 0.5208i 0.3168 + 0.6737i Columns 712 through 720 -0.3415 - 0.4072i 0.8381 - 0.2218i -0.4221 - 0.1926i -0.9692 + 0.2394i -0.4600 + 0.3065i -0.4178 - 0.7374i -0.4515 - 0.5961i -0.0914 - 0.1125i -0.0696 - 0.1560i -0.3415 - 0.4072i 0.8381 - 0.2218i -0.4221 - 0.1926i -0.9692 + 0.2394i -0.4600 + 0.3065i -0.4178 - 0.7374i -0.4515 - 0.5961i -0.0914 - 0.1125i -0.0696 - 0.1560i Columns 721 through 729 0.6475 - 0.2786i 0.8505 - 0.4124i -0.1093 + 0.0757i 0.2064 - 0.6775i 0.9567 + 0.4614i 0.0685 - 0.9741i -0.6918 - 0.1960i -0.2320 - 0.0896i -0.7812 + 0.1795i 0.6475 - 0.2786i 0.8505 - 0.4124i -0.1093 + 0.0757i 0.2064 - 0.6775i 0.9567 + 0.4614i 0.0685 - 0.9741i -0.6918 - 0.1960i -0.2320 - 0.0896i -0.7812 + 0.1795i Columns 730 through 738 -0.3002 - 0.3401i -0.5738 - 0.2829i 0.4088 + 0.4271i 0.0610 - 0.1932i 0.8609 - 0.0074i -0.1218 + 0.4971i 0.3840 - 0.1665i 0.8714 - 0.6298i -0.0368 - 0.5126i -0.3002 - 0.3401i -0.5738 - 0.2829i 0.4088 + 0.4271i 0.0610 - 0.1932i 0.8609 - 0.0074i -0.1218 + 0.4971i 0.3840 - 0.1665i 0.8714 - 0.6298i -0.0368 - 0.5126i Columns 739 through 747 0.3821 + 0.4142i -0.3952 - 0.5210i -0.3742 - 0.0331i -0.2592 + 0.0979i 0.0959 + 0.1132i -0.0513 - 1.1606i 0.2363 - 0.3889i 0.5234 - 0.1233i -1.4727 + 0.0477i 0.3821 + 0.4142i -0.3952 - 0.5210i -0.3742 - 0.0331i -0.2592 + 0.0979i 0.0959 + 0.1132i -0.0513 - 1.1606i 0.2363 - 0.3889i 0.5234 - 0.1233i -1.4727 + 0.0477i Columns 748 through 756 -1.6480 - 0.3583i 0.0043 + 0.1578i 0.0406 - 0.6323i -1.0869 + 0.0000i 0.0406 + 0.6323i 0.0043 - 0.1578i -1.6480 + 0.3583i -1.4727 - 0.0477i 0.5234 + 0.1233i -1.6480 - 0.3583i 0.0043 + 0.1578i 0.0406 - 0.6323i -1.0869 + 0.0000i 0.0406 + 0.6323i 0.0043 - 0.1578i -1.6480 + 0.3583i -1.4727 - 0.0477i 0.5234 + 0.1233i Columns 757 through 765 0.2363 + 0.3889i -0.0513 + 1.1606i 0.0959 - 0.1132i -0.2592 - 0.0979i -0.3742 + 0.0331i -0.3952 + 0.5210i 0.3821 - 0.4142i -0.0368 + 0.5126i 0.8714 + 0.6298i 0.2363 + 0.3889i -0.0513 + 1.1606i 0.0959 - 0.1132i -0.2592 - 0.0979i -0.3742 + 0.0331i -0.3952 + 0.5210i 0.3821 - 0.4142i -0.0368 + 0.5126i 0.8714 + 0.6298i Columns 766 through 774 0.3840 + 0.1665i -0.1218 - 0.4971i 0.8609 + 0.0074i 0.0610 + 0.1932i 0.4088 - 0.4271i -0.5738 + 0.2829i -0.3002 + 0.3401i -0.7812 - 0.1795i -0.2320 + 0.0896i 0.3840 + 0.1665i -0.1218 - 0.4971i 0.8609 + 0.0074i 0.0610 + 0.1932i 0.4088 - 0.4271i -0.5738 + 0.2829i -0.3002 + 0.3401i -0.7812 - 0.1795i -0.2320 + 0.0896i Columns 775 through 783 -0.6918 + 0.1960i 0.0685 + 0.9741i 0.9567 - 0.4614i 0.2064 + 0.6775i -0.1093 - 0.0757i 0.8505 + 0.4124i 0.6475 + 0.2786i -0.0696 + 0.1560i -0.0914 + 0.1125i -0.6918 + 0.1960i 0.0685 + 0.9741i 0.9567 - 0.4614i 0.2064 + 0.6775i -0.1093 - 0.0757i 0.8505 + 0.4124i 0.6475 + 0.2786i -0.0696 + 0.1560i -0.0914 + 0.1125i Columns 784 through 792 -0.4515 + 0.5961i -0.4178 + 0.7374i -0.4600 - 0.3065i -0.9692 - 0.2394i -0.4221 + 0.1926i 0.8381 + 0.2218i -0.3415 + 0.4072i 0.3168 - 0.6737i -0.2386 - 0.5208i -0.4515 + 0.5961i -0.4178 + 0.7374i -0.4600 - 0.3065i -0.9692 - 0.2394i -0.4221 + 0.1926i 0.8381 + 0.2218i -0.3415 + 0.4072i 0.3168 - 0.6737i -0.2386 - 0.5208i Columns 793 through 801 -0.1706 + 0.9260i -0.2585 + 0.0855i 0.3625 + 0.2395i -0.3639 - 0.2519i 0.4986 - 0.0490i 0.0159 - 0.3053i 0.1246 - 0.3025i -0.1833 + 0.3285i -0.3539 - 1.1929i -0.1706 + 0.9260i -0.2585 + 0.0855i 0.3625 + 0.2395i -0.3639 - 0.2519i 0.4986 - 0.0490i 0.0159 - 0.3053i 0.1246 - 0.3025i -0.1833 + 0.3285i -0.3539 - 1.1929i Columns 802 through 810 0.0009 - 0.4866i -0.6487 - 0.7132i 0.0582 - 0.2751i 0.3752 - 0.3105i -0.5739 - 0.0102i 0.1733 - 1.5575i -0.0727 - 0.3042i -0.2026 - 0.3105i 0.0152 + 0.1767i 0.0009 - 0.4866i -0.6487 - 0.7132i 0.0582 - 0.2751i 0.3752 - 0.3105i -0.5739 - 0.0102i 0.1733 - 1.5575i -0.0727 - 0.3042i -0.2026 - 0.3105i 0.0152 + 0.1767i Columns 811 through 819 -0.8225 - 0.2728i -0.7235 - 0.0250i 0.4475 - 0.2323i -0.0119 - 0.1571i -0.0585 + 0.3314i -0.1663 - 0.5364i 0.4437 + 0.0731i 0.9461 + 0.1015i 1.1096 - 0.2243i -0.8225 - 0.2728i -0.7235 - 0.0250i 0.4475 - 0.2323i -0.0119 - 0.1571i -0.0585 + 0.3314i -0.1663 - 0.5364i 0.4437 + 0.0731i 0.9461 + 0.1015i 1.1096 - 0.2243i Columns 820 through 828 0.1362 + 0.6283i -0.1390 - 0.0209i -0.2146 - 0.3709i 0.3921 - 0.5547i 0.8449 + 0.6444i -0.2309 - 0.2671i -0.6061 + 0.3057i 0.3443 + 0.1307i -0.6095 + 0.1133i 0.1362 + 0.6283i -0.1390 - 0.0209i -0.2146 - 0.3709i 0.3921 - 0.5547i 0.8449 + 0.6444i -0.2309 - 0.2671i -0.6061 + 0.3057i 0.3443 + 0.1307i -0.6095 + 0.1133i Columns 829 through 837 0.4606 + 0.1359i -0.0193 - 0.3880i -0.0188 - 0.1282i -0.0907 - 0.9534i 0.6341 + 0.3903i -0.6813 - 0.4497i 0.9873 - 0.3845i -0.0258 + 0.3741i 0.6261 - 0.7277i 0.4606 + 0.1359i -0.0193 - 0.3880i -0.0188 - 0.1282i -0.0907 - 0.9534i 0.6341 + 0.3903i -0.6813 - 0.4497i 0.9873 - 0.3845i -0.0258 + 0.3741i 0.6261 - 0.7277i Columns 838 through 846 -0.0705 + 0.6749i -0.3225 + 0.0127i -0.5690 - 1.0977i 1.0955 + 0.2512i -0.1906 + 0.2455i -0.4049 + 0.3555i -0.2125 - 0.8274i -0.2363 + 0.7013i -0.3026 + 0.2503i -0.0705 + 0.6749i -0.3225 + 0.0127i -0.5690 - 1.0977i 1.0955 + 0.2512i -0.1906 + 0.2455i -0.4049 + 0.3555i -0.2125 - 0.8274i -0.2363 + 0.7013i -0.3026 + 0.2503i Columns 847 through 855 0.1555 + 0.1588i 0.3868 - 0.1813i 0.0396 - 0.5575i -0.1854 - 0.4893i 0.6735 + 0.3289i 0.3661 - 0.6526i -0.9478 - 0.1748i -0.0066 + 0.7339i -0.1750 - 0.2661i 0.1555 + 0.1588i 0.3868 - 0.1813i 0.0396 - 0.5575i -0.1854 - 0.4893i 0.6735 + 0.3289i 0.3661 - 0.6526i -0.9478 - 0.1748i -0.0066 + 0.7339i -0.1750 - 0.2661i Columns 856 through 864 0.2157 + 0.1288i 0.0138 - 0.2965i 0.3571 - 0.2991i -0.5303 + 0.4960i 0.9204 + 0.4523i -0.3458 + 0.3229i -0.0519 - 0.1161i 0.3258 - 0.4405i 0.7225 + 0.4291i 0.2157 + 0.1288i 0.0138 - 0.2965i 0.3571 - 0.2991i -0.5303 + 0.4960i 0.9204 + 0.4523i -0.3458 + 0.3229i -0.0519 - 0.1161i 0.3258 - 0.4405i 0.7225 + 0.4291i Columns 865 through 873 0.9612 + 0.4148i 1.0079 - 0.3886i -0.2278 + 0.7677i 1.1930 - 0.0350i -0.4781 + 0.2143i -0.3915 - 0.0132i -0.6871 - 0.0263i -0.3535 + 0.3508i 0.1170 + 0.9819i 0.9612 + 0.4148i 1.0079 - 0.3886i -0.2278 + 0.7677i 1.1930 - 0.0350i -0.4781 + 0.2143i -0.3915 - 0.0132i -0.6871 - 0.0263i -0.3535 + 0.3508i 0.1170 + 0.9819i Columns 874 through 882 0.2878 - 0.3780i -0.3261 - 0.3803i 0.6152 + 0.4094i -0.3505 - 0.1844i -0.2827 - 0.2015i -0.0261 + 0.0870i 0.2682 - 0.2111i -0.0762 + 0.0070i -0.1060 + 0.3986i 0.2878 - 0.3780i -0.3261 - 0.3803i 0.6152 + 0.4094i -0.3505 - 0.1844i -0.2827 - 0.2015i -0.0261 + 0.0870i 0.2682 - 0.2111i -0.0762 + 0.0070i -0.1060 + 0.3986i Columns 883 through 891 -0.0374 - 0.8958i 0.2518 - 0.1975i -0.1410 + 0.2325i 0.0113 + 0.8347i 0.2887 + 0.1332i -0.0766 - 0.3634i -0.8094 + 0.0812i 0.2569 + 1.0884i -0.5028 - 0.3882i -0.0374 - 0.8958i 0.2518 - 0.1975i -0.1410 + 0.2325i 0.0113 + 0.8347i 0.2887 + 0.1332i -0.0766 - 0.3634i -0.8094 + 0.0812i 0.2569 + 1.0884i -0.5028 - 0.3882i Columns 892 through 900 0.3813 + 0.4610i 0.0715 - 0.4574i -0.2269 - 0.6467i -0.0638 + 0.3131i 0.1629 + 0.8930i 0.0616 + 0.1493i -0.7996 - 0.2364i -0.4788 + 0.6067i -0.6103 - 0.6014i 0.3813 + 0.4610i 0.0715 - 0.4574i -0.2269 - 0.6467i -0.0638 + 0.3131i 0.1629 + 0.8930i 0.0616 + 0.1493i -0.7996 - 0.2364i -0.4788 + 0.6067i -0.6103 - 0.6014i Columns 901 through 909 1.1290 + 0.3916i -0.0290 + 0.5784i -0.6012 - 0.3381i 0.2163 + 0.0047i 0.5781 + 0.0284i -1.1771 - 1.2981i -0.3257 - 0.7250i 0.4136 - 1.3827i -0.4879 - 0.7851i 1.1290 + 0.3916i -0.0290 + 0.5784i -0.6012 - 0.3381i 0.2163 + 0.0047i 0.5781 + 0.0284i -1.1771 - 1.2981i -0.3257 - 0.7250i 0.4136 - 1.3827i -0.4879 - 0.7851i Columns 910 through 918 -0.6428 - 0.6129i 1.1308 - 0.7273i 0.4705 - 0.2951i 0.1201 - 0.5313i -0.3840 - 0.1449i 0.2416 - 0.6309i -1.0156 - 0.3259i 0.5118 - 0.4603i 0.1698 + 0.2305i -0.6428 - 0.6129i 1.1308 - 0.7273i 0.4705 - 0.2951i 0.1201 - 0.5313i -0.3840 - 0.1449i 0.2416 - 0.6309i -1.0156 - 0.3259i 0.5118 - 0.4603i 0.1698 + 0.2305i Columns 919 through 927 -0.7678 + 0.5736i 0.5252 - 0.0374i -0.2151 - 0.3932i -0.5876 - 0.0852i -0.4226 + 0.5092i -0.0052 - 0.0728i 0.3408 - 0.8416i 0.1195 - 0.0018i -0.3475 - 0.1143i -0.7678 + 0.5736i 0.5252 - 0.0374i -0.2151 - 0.3932i -0.5876 - 0.0852i -0.4226 + 0.5092i -0.0052 - 0.0728i 0.3408 - 0.8416i 0.1195 - 0.0018i -0.3475 - 0.1143i Columns 928 through 936 -0.4850 + 0.5383i -0.3333 - 0.3636i -0.9901 + 0.5272i 0.1869 + 0.7624i -0.1973 + 0.0075i -0.1022 - 0.0849i -0.1434 + 0.1157i -0.4452 - 1.1909i -0.5163 - 0.1541i -0.4850 + 0.5383i -0.3333 - 0.3636i -0.9901 + 0.5272i 0.1869 + 0.7624i -0.1973 + 0.0075i -0.1022 - 0.0849i -0.1434 + 0.1157i -0.4452 - 1.1909i -0.5163 - 0.1541i Columns 937 through 945 -0.1470 - 0.2627i 0.1211 - 0.1843i 0.5133 - 0.3989i 0.3835 - 0.0372i -0.9760 - 0.0478i 0.4460 - 1.1631i 0.9310 + 0.9083i -1.0340 + 0.2398i -0.2076 + 0.4541i -0.1470 - 0.2627i 0.1211 - 0.1843i 0.5133 - 0.3989i 0.3835 - 0.0372i -0.9760 - 0.0478i 0.4460 - 1.1631i 0.9310 + 0.9083i -1.0340 + 0.2398i -0.2076 + 0.4541i Columns 946 through 954 -0.0311 - 0.3017i 0.3529 - 0.1989i -1.3359 - 0.0752i 1.3646 - 0.5360i 0.1065 + 0.4782i 0.7578 - 0.7182i -0.6437 - 0.0020i 0.6176 + 0.0703i -0.7148 - 0.2514i -0.0311 - 0.3017i 0.3529 - 0.1989i -1.3359 - 0.0752i 1.3646 - 0.5360i 0.1065 + 0.4782i 0.7578 - 0.7182i -0.6437 - 0.0020i 0.6176 + 0.0703i -0.7148 - 0.2514i Columns 955 through 963 1.1811 - 0.4084i 0.5670 + 0.4886i 0.3029 - 0.0315i -0.7463 - 0.2641i 0.4646 - 0.0445i 0.0985 + 0.0517i 0.4131 + 0.2654i -0.9090 + 0.4559i -0.6632 - 0.0249i 1.1811 - 0.4084i 0.5670 + 0.4886i 0.3029 - 0.0315i -0.7463 - 0.2641i 0.4646 - 0.0445i 0.0985 + 0.0517i 0.4131 + 0.2654i -0.9090 + 0.4559i -0.6632 - 0.0249i Columns 964 through 972 -0.2249 + 0.0490i 0.0752 - 0.2587i 0.3839 - 0.5285i -0.3582 + 0.2574i 0.7622 - 0.5359i 0.2742 + 0.2518i 0.8510 - 0.7325i -0.1050 - 0.3789i 0.0493 + 0.6032i -0.2249 + 0.0490i 0.0752 - 0.2587i 0.3839 - 0.5285i -0.3582 + 0.2574i 0.7622 - 0.5359i 0.2742 + 0.2518i 0.8510 - 0.7325i -0.1050 - 0.3789i 0.0493 + 0.6032i Columns 973 through 981 -0.2725 + 0.2447i -0.6681 - 0.4179i 0.9681 - 0.1704i 0.2077 + 0.5861i -0.2075 - 0.4682i 0.2277 + 0.1744i 0.3994 - 0.4863i -0.4852 - 0.1125i -0.3014 - 0.7792i -0.2725 + 0.2447i -0.6681 - 0.4179i 0.9681 - 0.1704i 0.2077 + 0.5861i -0.2075 - 0.4682i 0.2277 + 0.1744i 0.3994 - 0.4863i -0.4852 - 0.1125i -0.3014 - 0.7792i Columns 982 through 990 0.0812 + 0.5601i -0.5394 - 0.6446i -0.2509 + 0.0582i 0.0396 - 0.2448i 0.8731 + 0.4057i 0.7818 + 0.4755i -1.2216 + 0.0867i -0.7134 + 0.4718i -0.6244 + 0.1776i 0.0812 + 0.5601i -0.5394 - 0.6446i -0.2509 + 0.0582i 0.0396 - 0.2448i 0.8731 + 0.4057i 0.7818 + 0.4755i -1.2216 + 0.0867i -0.7134 + 0.4718i -0.6244 + 0.1776i Columns 991 through 999 0.6541 - 0.0132i -0.2766 + 0.2684i 1.3645 + 0.3251i 0.2172 - 0.6263i 0.2045 - 0.4061i 0.7073 - 0.4958i -0.9441 + 0.8719i -1.3212 - 0.2792i 0.1380 + 1.2931i 0.6541 - 0.0132i -0.2766 + 0.2684i 1.3645 + 0.3251i 0.2172 - 0.6263i 0.2045 - 0.4061i 0.7073 - 0.4958i -0.9441 + 0.8719i -1.3212 - 0.2792i 0.1380 + 1.2931i Columns 1,000 through 1,008 -0.4320 + 0.1214i -0.2557 + 0.2128i 0.6987 - 0.9008i -0.1639 - 0.7962i -0.7394 + 0.5310i -0.1236 - 0.8678i -0.3839 - 0.1689i -0.5752 + 0.1459i -0.4450 - 0.5447i -0.4320 + 0.1214i -0.2557 + 0.2128i 0.6987 - 0.9008i -0.1639 - 0.7962i -0.7394 + 0.5310i -0.1236 - 0.8678i -0.3839 - 0.1689i -0.5752 + 0.1459i -0.4450 - 0.5447i Columns 1,009 through 1,017 -0.1315 - 0.1749i 0.3538 + 1.2591i -0.5470 - 0.2848i -0.0702 - 0.7242i -0.4422 - 0.6297i 0.6057 - 0.1150i -0.0776 - 0.5729i -0.2981 - 0.3275i -0.3428 - 0.2137i -0.1315 - 0.1749i 0.3538 + 1.2591i -0.5470 - 0.2848i -0.0702 - 0.7242i -0.4422 - 0.6297i 0.6057 - 0.1150i -0.0776 - 0.5729i -0.2981 - 0.3275i -0.3428 - 0.2137i Columns 1,018 through 1,026 -0.1888 - 0.4362i 0.2654 + 0.5241i -0.7104 - 0.4253i -0.5729 + 1.1277i -0.2041 - 1.2036i 0.3421 + 0.9451i 0.1897 - 0.1130i 0.5255 - 0.2411i -0.5076 - 0.5333i -0.1888 - 0.4362i 0.2654 + 0.5241i -0.7104 - 0.4253i -0.5729 + 1.1277i -0.2041 - 1.2036i 0.3421 + 0.9451i 0.1897 - 0.1130i 0.5255 - 0.2411i -0.5076 - 0.5333i Columns 1,027 through 1,035 -0.3808 - 0.0098i 1.0755 + 0.4618i 0.2840 + 0.5513i -0.8365 + 0.1325i 1.0489 - 0.4841i 1.0169 - 0.1295i 0.2416 - 0.0515i 0.1422 + 0.1833i -0.2478 - 0.0857i -0.3808 - 0.0098i 1.0755 + 0.4618i 0.2840 + 0.5513i -0.8365 + 0.1325i 1.0489 - 0.4841i 1.0169 - 0.1295i 0.2416 - 0.0515i 0.1422 + 0.1833i -0.2478 - 0.0857i Columns 1,036 through 1,044 0.6926 - 0.0783i -0.7223 + 0.1890i -0.0441 - 0.0392i -0.3777 + 0.2515i 0.2154 - 0.1555i -0.4255 - 0.2400i -0.2889 - 0.3183i -0.2680 - 0.6503i -0.5622 - 1.1248i 0.6926 - 0.0783i -0.7223 + 0.1890i -0.0441 - 0.0392i -0.3777 + 0.2515i 0.2154 - 0.1555i -0.4255 - 0.2400i -0.2889 - 0.3183i -0.2680 - 0.6503i -0.5622 - 1.1248i Columns 1,045 through 1,053 -0.2592 - 0.7290i -0.5781 - 0.8205i 0.7618 - 0.5374i -1.0269 + 0.7433i -0.1966 + 0.0301i 0.5964 - 0.9704i -0.7148 + 0.4674i -0.0872 + 0.2780i -0.1786 + 0.8621i -0.2592 - 0.7290i -0.5781 - 0.8205i 0.7618 - 0.5374i -1.0269 + 0.7433i -0.1966 + 0.0301i 0.5964 - 0.9704i -0.7148 + 0.4674i -0.0872 + 0.2780i -0.1786 + 0.8621i Columns 1,054 through 1,062 0.3803 + 0.0237i -0.0601 - 0.0114i -0.0779 - 1.2162i -0.5730 - 0.4880i -0.8964 + 0.1580i -0.5089 + 0.0918i 0.5227 + 0.3880i 0.4007 - 0.5085i 0.0729 - 0.2483i 0.3803 + 0.0237i -0.0601 - 0.0114i -0.0779 - 1.2162i -0.5730 - 0.4880i -0.8964 + 0.1580i -0.5089 + 0.0918i 0.5227 + 0.3880i 0.4007 - 0.5085i 0.0729 - 0.2483i Columns 1,063 through 1,071 0.0557 + 0.6379i 0.4731 - 0.3101i -0.8225 + 1.6132i -0.2746 - 0.0092i -0.6301 - 0.1971i -0.2133 - 0.5202i 0.4176 + 1.0580i 0.7987 + 0.1253i -0.0302 - 0.8121i 0.0557 + 0.6379i 0.4731 - 0.3101i -0.8225 + 1.6132i -0.2746 - 0.0092i -0.6301 - 0.1971i -0.2133 - 0.5202i 0.4176 + 1.0580i 0.7987 + 0.1253i -0.0302 - 0.8121i Columns 1,072 through 1,080 -0.3412 + 0.4200i 0.4366 + 0.0211i 0.1976 - 0.9382i -0.8616 + 0.7055i 0.0707 - 0.3200i -0.0165 + 0.6918i -0.0013 + 0.4604i 0.6612 - 0.1526i 0.1105 + 0.1470i -0.3412 + 0.4200i 0.4366 + 0.0211i 0.1976 - 0.9382i -0.8616 + 0.7055i 0.0707 - 0.3200i -0.0165 + 0.6918i -0.0013 + 0.4604i 0.6612 - 0.1526i 0.1105 + 0.1470i Columns 1,081 through 1,089 -0.4448 + 0.3499i 0.0642 - 0.3405i 0.4128 + 0.4872i -0.0076 + 0.0603i 0.0307 - 1.0997i -0.5299 + 0.6169i 0.2771 + 0.0480i -0.5925 + 0.0179i -0.2587 + 0.4401i -0.4448 + 0.3499i 0.0642 - 0.3405i 0.4128 + 0.4872i -0.0076 + 0.0603i 0.0307 - 1.0997i -0.5299 + 0.6169i 0.2771 + 0.0480i -0.5925 + 0.0179i -0.2587 + 0.4401i Columns 1,090 through 1,098 -0.6778 - 0.3489i 0.2411 + 0.6897i -0.5222 + 0.8312i 0.5639 - 0.2141i 0.3331 - 0.3999i -0.0088 + 0.0231i 0.2285 + 0.2960i 0.4016 - 0.8181i 0.0598 - 0.0649i -0.6778 - 0.3489i 0.2411 + 0.6897i -0.5222 + 0.8312i 0.5639 - 0.2141i 0.3331 - 0.3999i -0.0088 + 0.0231i 0.2285 + 0.2960i 0.4016 - 0.8181i 0.0598 - 0.0649i Columns 1,099 through 1,107 -0.0856 - 0.3413i 0.5150 - 0.0676i 0.0617 + 0.0823i -1.0901 - 0.4084i 0.5705 + 0.3847i -0.6825 + 0.4276i -0.7112 - 0.0208i -0.3317 - 0.7125i -0.3558 + 0.0524i -0.0856 - 0.3413i 0.5150 - 0.0676i 0.0617 + 0.0823i -1.0901 - 0.4084i 0.5705 + 0.3847i -0.6825 + 0.4276i -0.7112 - 0.0208i -0.3317 - 0.7125i -0.3558 + 0.0524i Columns 1,108 through 1,116 -0.3691 + 0.6722i 0.0975 - 0.7843i -0.6481 + 0.4986i 0.1922 - 0.2801i -0.8608 - 0.0569i -0.4335 - 0.1334i -0.7583 + 0.2662i -0.6161 - 0.3904i -0.4141 - 1.0446i -0.3691 + 0.6722i 0.0975 - 0.7843i -0.6481 + 0.4986i 0.1922 - 0.2801i -0.8608 - 0.0569i -0.4335 - 0.1334i -0.7583 + 0.2662i -0.6161 - 0.3904i -0.4141 - 1.0446i Columns 1,117 through 1,125 -0.7639 - 0.2843i 0.0021 + 0.3283i -0.4474 - 1.0009i 0.8585 + 0.3655i 0.0757 - 0.3563i 0.1663 + 0.8324i 0.6477 - 0.7168i -0.4943 - 0.2324i 1.4013 - 0.5624i -0.7639 - 0.2843i 0.0021 + 0.3283i -0.4474 - 1.0009i 0.8585 + 0.3655i 0.0757 - 0.3563i 0.1663 + 0.8324i 0.6477 - 0.7168i -0.4943 - 0.2324i 1.4013 - 0.5624i Columns 1,126 through 1,134 -0.8000 + 0.1511i 0.0955 - 1.5444i 0.8706 + 0.1424i 0.3895 - 1.0220i -0.7244 + 0.6242i -0.8437 + 1.2069i -0.2054 + 0.7041i 0.0274 - 0.0711i -0.7025 - 0.1871i -0.8000 + 0.1511i 0.0955 - 1.5444i 0.8706 + 0.1424i 0.3895 - 1.0220i -0.7244 + 0.6242i -0.8437 + 1.2069i -0.2054 + 0.7041i 0.0274 - 0.0711i -0.7025 - 0.1871i Columns 1,135 through 1,143 0.4706 + 0.4107i 0.6555 - 0.3976i 0.0100 - 0.9151i 0.2839 - 0.5934i -0.4826 - 0.2876i 0.5456 - 0.4047i -0.2145 - 0.9039i -0.9102 + 1.0721i -0.6857 + 0.6095i 0.4706 + 0.4107i 0.6555 - 0.3976i 0.0100 - 0.9151i 0.2839 - 0.5934i -0.4826 - 0.2876i 0.5456 - 0.4047i -0.2145 - 0.9039i -0.9102 + 1.0721i -0.6857 + 0.6095i Columns 1,144 through 1,152 -0.6528 - 0.0574i -0.6970 - 0.4924i 0.1152 + 0.0719i 1.4531 + 0.6376i -0.0473 + 0.5159i -0.5271 - 0.3819i 0.4551 - 0.8099i 0.0287 - 0.5391i -0.6493 - 1.2302i -0.6528 - 0.0574i -0.6970 - 0.4924i 0.1152 + 0.0719i 1.4531 + 0.6376i -0.0473 + 0.5159i -0.5271 - 0.3819i 0.4551 - 0.8099i 0.0287 - 0.5391i -0.6493 - 1.2302i Columns 1,153 through 1,161 0.1367 - 0.7856i 0.4784 - 0.7063i -0.0364 + 0.2613i -0.1946 - 0.1702i 0.2718 + 1.2150i -0.0128 - 0.2321i 0.7213 + 0.2714i 0.9462 + 0.3743i 0.1200 + 0.5006i 0.1367 - 0.7856i 0.4784 - 0.7063i -0.0364 + 0.2613i -0.1946 - 0.1702i 0.2718 + 1.2150i -0.0128 - 0.2321i 0.7213 + 0.2714i 0.9462 + 0.3743i 0.1200 + 0.5006i Columns 1,162 through 1,170 -1.0445 + 0.3479i 0.8078 + 0.3388i -0.3138 + 0.4542i 0.4931 + 0.1128i 0.0203 - 0.1877i 0.4074 - 0.0847i 0.0823 + 0.6173i -0.1881 + 0.3456i 0.5100 - 0.3542i -1.0445 + 0.3479i 0.8078 + 0.3388i -0.3138 + 0.4542i 0.4931 + 0.1128i 0.0203 - 0.1877i 0.4074 - 0.0847i 0.0823 + 0.6173i -0.1881 + 0.3456i 0.5100 - 0.3542i Columns 1,171 through 1,179 0.4719 + 0.2816i -0.9930 - 1.0189i -0.3592 + 0.1244i -1.2261 + 0.8937i 0.0016 + 0.6222i 0.7655 - 1.0532i 0.0890 + 0.7304i -0.6203 + 0.7937i -0.4758 + 0.8751i 0.4719 + 0.2816i -0.9930 - 1.0189i -0.3592 + 0.1244i -1.2261 + 0.8937i 0.0016 + 0.6222i 0.7655 - 1.0532i 0.0890 + 0.7304i -0.6203 + 0.7937i -0.4758 + 0.8751i Columns 1,180 through 1,188 0.3905 + 0.0699i 0.4357 - 0.9363i -0.2746 + 0.5635i 0.6692 - 0.0766i -0.1281 + 0.1141i 1.1452 + 0.8547i -0.2870 - 0.8028i 0.4994 + 0.1109i -0.1174 + 0.2127i 0.3905 + 0.0699i 0.4357 - 0.9363i -0.2746 + 0.5635i 0.6692 - 0.0766i -0.1281 + 0.1141i 1.1452 + 0.8547i -0.2870 - 0.8028i 0.4994 + 0.1109i -0.1174 + 0.2127i Columns 1,189 through 1,197 0.1164 - 0.2944i -0.3894 + 0.0854i -0.7267 - 0.8697i 0.4125 + 0.3048i 0.1069 - 0.1821i -1.1520 - 0.5462i -0.2177 - 1.3837i 0.8278 + 0.5580i -0.3165 + 0.6060i 0.1164 - 0.2944i -0.3894 + 0.0854i -0.7267 - 0.8697i 0.4125 + 0.3048i 0.1069 - 0.1821i -1.1520 - 0.5462i -0.2177 - 1.3837i 0.8278 + 0.5580i -0.3165 + 0.6060i Columns 1,198 through 1,206 0.4830 + 0.5057i -0.1394 + 0.7264i -0.0139 + 1.1499i 0.3037 + 0.7557i -0.8753 + 0.9326i -0.2617 + 0.5269i 0.2050 - 0.5125i -0.7991 - 0.1345i -0.1956 - 0.1846i 0.4830 + 0.5057i -0.1394 + 0.7264i -0.0139 + 1.1499i 0.3037 + 0.7557i -0.8753 + 0.9326i -0.2617 + 0.5269i 0.2050 - 0.5125i -0.7991 - 0.1345i -0.1956 - 0.1846i Columns 1,207 through 1,215 0.0933 - 0.0916i -0.1601 - 0.3006i -0.5160 - 0.0430i -0.4719 + 0.1788i -0.5023 - 0.0290i -0.5697 + 0.1176i 0.2143 + 1.6187i -0.3541 - 0.3956i -0.4111 - 0.1534i 0.0933 - 0.0916i -0.1601 - 0.3006i -0.5160 - 0.0430i -0.4719 + 0.1788i -0.5023 - 0.0290i -0.5697 + 0.1176i 0.2143 + 1.6187i -0.3541 - 0.3956i -0.4111 - 0.1534i Columns 1,216 through 1,224 0.9427 + 0.2290i 0.0339 + 0.4610i -0.1434 + 0.0745i -0.1529 + 0.1524i 0.4566 - 0.1158i -0.3265 + 0.0701i -0.4719 - 0.3285i -0.7359 + 0.6149i -0.3115 + 0.3772i 0.9427 + 0.2290i 0.0339 + 0.4610i -0.1434 + 0.0745i -0.1529 + 0.1524i 0.4566 - 0.1158i -0.3265 + 0.0701i -0.4719 - 0.3285i -0.7359 + 0.6149i -0.3115 + 0.3772i Columns 1,225 through 1,233 -0.7034 + 1.1767i 0.4790 - 0.1400i -0.4273 - 0.0288i -0.0749 + 0.3175i -0.4918 + 0.1792i 0.2075 + 0.4511i 0.3983 - 0.5766i -0.2127 + 0.2738i -0.2415 - 0.2783i -0.7034 + 1.1767i 0.4790 - 0.1400i -0.4273 - 0.0288i -0.0749 + 0.3175i -0.4918 + 0.1792i 0.2075 + 0.4511i 0.3983 - 0.5766i -0.2127 + 0.2738i -0.2415 - 0.2783i Columns 1,234 through 1,242 -0.4071 + 0.1296i 0.5572 - 0.7762i -0.0205 - 0.4709i -0.0402 - 0.1522i 0.3961 + 0.4284i -0.1560 + 0.7638i -0.8649 + 0.2182i -0.5288 - 0.6553i -0.2978 - 0.2519i -0.4071 + 0.1296i 0.5572 - 0.7762i -0.0205 - 0.4709i -0.0402 - 0.1522i 0.3961 + 0.4284i -0.1560 + 0.7638i -0.8649 + 0.2182i -0.5288 - 0.6553i -0.2978 - 0.2519i Columns 1,243 through 1,251 0.9741 + 0.4876i 0.7301 + 0.9061i 1.1799 + 0.3571i 1.7876 + 0.3532i -0.3612 - 0.2098i 0.5628 - 0.6835i -0.9435 + 0.3907i -0.1532 - 0.7543i 0.8619 - 0.1361i 0.9741 + 0.4876i 0.7301 + 0.9061i 1.1799 + 0.3571i 1.7876 + 0.3532i -0.3612 - 0.2098i 0.5628 - 0.6835i -0.9435 + 0.3907i -0.1532 - 0.7543i 0.8619 - 0.1361i Columns 1,252 through 1,260 0.0363 + 0.4289i -0.5772 - 1.0660i 0.8757 + 0.0262i 0.7918 - 0.2849i -0.5080 + 0.4167i 0.0789 - 1.1149i 0.7069 - 0.4829i 0.0880 + 0.1137i 0.2546 + 0.1646i 0.0363 + 0.4289i -0.5772 - 1.0660i 0.8757 + 0.0262i 0.7918 - 0.2849i -0.5080 + 0.4167i 0.0789 - 1.1149i 0.7069 - 0.4829i 0.0880 + 0.1137i 0.2546 + 0.1646i Columns 1,261 through 1,269 -0.8260 - 0.9899i -0.1696 - 0.9134i -0.0431 - 0.1637i -1.2736 - 0.6638i 0.3503 + 0.3557i -0.5685 - 0.8472i 0.4747 + 0.2068i -0.1148 - 0.5457i -1.0055 + 0.8167i -0.8260 - 0.9899i -0.1696 - 0.9134i -0.0431 - 0.1637i -1.2736 - 0.6638i 0.3503 + 0.3557i -0.5685 - 0.8472i 0.4747 + 0.2068i -0.1148 - 0.5457i -1.0055 + 0.8167i Columns 1,270 through 1,278 -0.7018 + 0.3729i 0.7631 - 0.1957i -0.7207 + 0.0128i -0.7173 - 0.3920i -1.1941 - 0.5176i -0.1238 + 0.2206i 0.2852 - 0.0469i 0.5139 + 0.9623i 0.5703 - 0.0951i -0.7018 + 0.3729i 0.7631 - 0.1957i -0.7207 + 0.0128i -0.7173 - 0.3920i -1.1941 - 0.5176i -0.1238 + 0.2206i 0.2852 - 0.0469i 0.5139 + 0.9623i 0.5703 - 0.0951i Columns 1,279 through 1,287 -0.2240 - 1.1389i 0.5035 + 0.3027i -0.5514 - 0.6977i 0.7437 + 0.1794i 0.7289 - 0.5857i -0.7604 + 0.5047i -1.0355 + 0.3260i -0.0542 + 0.7347i 0.7659 - 0.0776i -0.2240 - 1.1389i 0.5035 + 0.3027i -0.5514 - 0.6977i 0.7437 + 0.1794i 0.7289 - 0.5857i -0.7604 + 0.5047i -1.0355 + 0.3260i -0.0542 + 0.7347i 0.7659 - 0.0776i Columns 1,288 through 1,296 0.2642 + 0.3165i -0.2450 + 0.2149i 0.0267 + 0.6131i 0.5738 - 0.1032i -0.2614 + 0.7167i -0.3692 + 0.2421i 0.3383 - 0.7181i -0.1162 + 0.2140i -0.2020 - 0.0353i 0.2642 + 0.3165i -0.2450 + 0.2149i 0.0267 + 0.6131i 0.5738 - 0.1032i -0.2614 + 0.7167i -0.3692 + 0.2421i 0.3383 - 0.7181i -0.1162 + 0.2140i -0.2020 - 0.0353i Columns 1,297 through 1,305 -0.7946 + 0.7938i 0.2673 - 0.2757i 0.4999 + 0.2880i 0.1149 - 0.6497i 0.5528 - 0.2621i -0.6070 + 0.5261i 0.0325 + 0.3917i -0.2886 + 0.6429i -0.3304 - 0.2679i -0.7946 + 0.7938i 0.2673 - 0.2757i 0.4999 + 0.2880i 0.1149 - 0.6497i 0.5528 - 0.2621i -0.6070 + 0.5261i 0.0325 + 0.3917i -0.2886 + 0.6429i -0.3304 - 0.2679i Columns 1,306 through 1,314 0.5936 - 0.0054i 0.3551 + 0.2029i -1.0817 - 0.6393i 0.0817 - 0.3077i -0.3947 - 0.5681i 0.2267 + 0.2742i 0.3339 + 0.1278i 0.5812 - 0.0800i -0.2858 + 1.1116i 0.5936 - 0.0054i 0.3551 + 0.2029i -1.0817 - 0.6393i 0.0817 - 0.3077i -0.3947 - 0.5681i 0.2267 + 0.2742i 0.3339 + 0.1278i 0.5812 - 0.0800i -0.2858 + 1.1116i Columns 1,315 through 1,323 1.1586 + 0.6749i 0.4215 - 0.4795i 0.3415 + 0.2017i -0.4279 - 0.4167i 0.2372 + 0.2108i -0.7628 - 1.0036i -0.6500 + 8.2004i -0.1661 + 0.4108i 0.4336 - 0.5456i 1.1586 + 0.6749i 0.4215 - 0.4795i 0.3415 + 0.2017i -0.4279 - 0.4167i 0.2372 + 0.2108i -0.7628 - 1.0036i -0.6500 + 8.2004i -0.1661 + 0.4108i 0.4336 - 0.5456i Columns 1,324 through 1,332 -0.0044 - 0.0164i 0.4452 + 0.1542i 0.2559 - 0.1707i -0.2408 - 1.0441i -0.3975 + 0.1010i -0.2666 + 0.0575i 0.3008 - 0.1699i 0.4746 - 0.7109i -0.2644 + 0.8495i -0.0044 - 0.0164i 0.4452 + 0.1542i 0.2559 - 0.1707i -0.2408 - 1.0441i -0.3975 + 0.1010i -0.2666 + 0.0575i 0.3008 - 0.1699i 0.4746 - 0.7109i -0.2644 + 0.8495i Columns 1,333 through 1,341 0.9579 - 0.1152i 0.7301 - 0.0446i -0.2399 + 0.7713i 0.5456 - 0.1951i -0.0470 + 1.1353i -0.3491 - 1.0137i -0.4921 + 0.3886i 0.9948 - 0.6923i 0.0010 - 0.7462i 0.9579 - 0.1152i 0.7301 - 0.0446i -0.2399 + 0.7713i 0.5456 - 0.1951i -0.0470 + 1.1353i -0.3491 - 1.0137i -0.4921 + 0.3886i 0.9948 - 0.6923i 0.0010 - 0.7462i Columns 1,342 through 1,350 0.0690 - 0.1772i 0.1260 - 0.1731i -0.6455 + 0.1014i -0.1597 - 0.6976i 0.6739 + 0.0151i 0.3461 - 0.5462i 0.0152 - 0.9018i 0.7568 - 0.3328i 0.4825 - 0.7799i 0.0690 - 0.1772i 0.1260 - 0.1731i -0.6455 + 0.1014i -0.1597 - 0.6976i 0.6739 + 0.0151i 0.3461 - 0.5462i 0.0152 - 0.9018i 0.7568 - 0.3328i 0.4825 - 0.7799i Columns 1,351 through 1,359 0.3015 - 0.0115i 0.5837 + 0.1399i -0.4114 + 0.5704i -0.2124 + 0.0304i 0.5552 + 0.0869i -0.3131 - 0.7414i -0.5292 + 0.3840i 0.3762 + 0.8680i -0.8393 + 0.3414i 0.3015 - 0.0115i 0.5837 + 0.1399i -0.4114 + 0.5704i -0.2124 + 0.0304i 0.5552 + 0.0869i -0.3131 - 0.7414i -0.5292 + 0.3840i 0.3762 + 0.8680i -0.8393 + 0.3414i Columns 1,360 through 1,368 -0.2675 - 0.0827i -0.0523 + 0.9016i 0.3437 + 0.5529i 0.2982 - 0.5171i -0.4262 + 0.4046i 0.1225 - 0.3840i -0.1150 - 0.4904i 0.7401 + 0.8717i 0.5028 + 0.2895i -0.2675 - 0.0827i -0.0523 + 0.9016i 0.3437 + 0.5529i 0.2982 - 0.5171i -0.4262 + 0.4046i 0.1225 - 0.3840i -0.1150 - 0.4904i 0.7401 + 0.8717i 0.5028 + 0.2895i Columns 1,369 through 1,377 0.6192 + 0.4147i 0.2802 + 0.0788i 0.1394 + 1.0061i 0.3709 + 0.1030i -1.0955 + 0.5859i 0.0176 - 0.8373i -0.6007 + 0.4403i 0.8721 + 0.0891i -0.0903 + 0.1492i 0.6192 + 0.4147i 0.2802 + 0.0788i 0.1394 + 1.0061i 0.3709 + 0.1030i -1.0955 + 0.5859i 0.0176 - 0.8373i -0.6007 + 0.4403i 0.8721 + 0.0891i -0.0903 + 0.1492i Columns 1,378 through 1,386 -0.3881 + 0.3684i 1.2645 - 0.0069i -0.0694 - 0.4570i -0.4247 - 0.1653i -0.1133 - 0.5948i 0.3573 - 0.1634i -0.4048 + 0.2312i -0.5216 - 0.0401i -0.3413 + 0.0441i -0.3881 + 0.3684i 1.2645 - 0.0069i -0.0694 - 0.4570i -0.4247 - 0.1653i -0.1133 - 0.5948i 0.3573 - 0.1634i -0.4048 + 0.2312i -0.5216 - 0.0401i -0.3413 + 0.0441i Columns 1,387 through 1,395 0.1189 + 0.0140i -0.2460 + 0.0912i 0.4782 + 0.5115i -0.5240 + 0.1372i 0.1724 + 0.1895i -1.1329 + 0.6168i 0.2321 - 0.1331i 0.3785 + 0.0404i -1.4226 + 0.5561i 0.1189 + 0.0140i -0.2460 + 0.0912i 0.4782 + 0.5115i -0.5240 + 0.1372i 0.1724 + 0.1895i -1.1329 + 0.6168i 0.2321 - 0.1331i 0.3785 + 0.0404i -1.4226 + 0.5561i Columns 1,396 through 1,404 -0.7267 + 0.0082i -0.2563 - 1.0383i -0.6191 - 0.5376i -0.2407 - 0.7200i -0.0717 - 0.2884i 0.0056 + 0.3621i 1.0403 + 0.3113i -0.2526 + 0.3082i 0.4884 + 0.7478i -0.7267 + 0.0082i -0.2563 - 1.0383i -0.6191 - 0.5376i -0.2407 - 0.7200i -0.0717 - 0.2884i 0.0056 + 0.3621i 1.0403 + 0.3113i -0.2526 + 0.3082i 0.4884 + 0.7478i Columns 1,405 through 1,413 -0.0937 - 0.7034i 0.0930 - 0.0471i 0.1413 + 0.0593i -0.2965 + 0.2791i -1.0381 - 0.3321i -0.8230 - 0.5935i 0.3908 + 0.0085i -0.2350 + 0.6952i -0.4365 - 1.3117i -0.0937 - 0.7034i 0.0930 - 0.0471i 0.1413 + 0.0593i -0.2965 + 0.2791i -1.0381 - 0.3321i -0.8230 - 0.5935i 0.3908 + 0.0085i -0.2350 + 0.6952i -0.4365 - 1.3117i Columns 1,414 through 1,422 0.2828 - 0.5478i 0.0616 - 1.0753i 0.8034 - 1.2062i -1.4325 + 0.2173i -0.3844 + 0.0006i 0.5448 - 0.2742i -0.3172 + 1.0701i 0.7014 + 0.1698i -0.3245 - 0.8793i 0.2828 - 0.5478i 0.0616 - 1.0753i 0.8034 - 1.2062i -1.4325 + 0.2173i -0.3844 + 0.0006i 0.5448 - 0.2742i -0.3172 + 1.0701i 0.7014 + 0.1698i -0.3245 - 0.8793i Columns 1,423 through 1,431 0.0720 + 0.2640i -0.1614 - 0.5115i 0.6240 + 0.3417i 0.0116 + 4.8502i -0.0380 + 0.0127i 0.0521 + 0.5187i -0.6484 + 0.6162i -0.0356 + 0.7771i 0.4557 - 1.0042i 0.0720 + 0.2640i -0.1614 - 0.5115i 0.6240 + 0.3417i 0.0116 + 4.8502i -0.0380 + 0.0127i 0.0521 + 0.5187i -0.6484 + 0.6162i -0.0356 + 0.7771i 0.4557 - 1.0042i Columns 1,432 through 1,440 -0.4228 + 0.7471i 0.5036 + 0.1983i 0.4145 + 0.6600i -0.0179 + 0.1750i 1.1594 - 0.4242i -0.0349 - 0.0508i -1.0494 - 0.0730i -1.0926 - 0.3091i 0.0081 - 0.4450i -0.4228 + 0.7471i 0.5036 + 0.1983i 0.4145 + 0.6600i -0.0179 + 0.1750i 1.1594 - 0.4242i -0.0349 - 0.0508i -1.0494 - 0.0730i -1.0926 - 0.3091i 0.0081 - 0.4450i Columns 1,441 through 1,449 -0.7902 + 0.1437i 0.7329 - 0.0296i 1.2963 + 1.0287i 0.0947 + 0.4745i -0.3772 + 0.5141i -0.4229 + 0.1297i -0.7116 + 0.3801i 0.5920 - 0.7406i -0.2531 + 0.3224i
Check = mean(Y - Y2) % Equal Within Floating-Point Approximation Error
Check = 1.3940e-15 - 2.2341e-17i
.
  2 件のコメント
Hans
Hans 2024 年 4 月 23 日
Thank you for looking into this but I actually want to recover the original signal exclusively from the single-sided spectrum, without knowing the original signal of course
Star Strider
Star Strider 2024 年 4 月 23 日
My pleasure!
It will always be necessary to calculate the phase so that you can fully reconstitute the original signal. Add that and your code should work. Treat the phase values the same way you treat the magnitude values, with the appropriate sign change for the ‘second half’ of the reconstituted Fourier transform vector —
v = randn + 1i*randn;
vs = [v; conj(v)]
vs =
0.1080 + 1.0408i 0.1080 - 1.0408i
M = abs(vs)
M = 2x1
1.0464 1.0464
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
phi = angle(vs)
phi = 2x1
1.4674 -1.4674
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
Also note that you need to add the ‘symmetry flag’ to your ifft call. In this instance, use 'symmetric' because your signal has an even number of elements originally, so the fft result will also. (If you use the default 'asymmetric' your ifft result will have complex values.)
.

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