How to pass this signal in time to frequency?

I need to pass this signal in time to frequency. A frequency range of interest is from 100Hz to 2MHz. I did the following code, but the answer doesn't come out as expected. Could someone tell me the error?

C=corrente_at_500;

V=tensao_at_500;

n = length(t);%NUMERO DE AMSTRAS

tmax = t(end);%TEMPO TOTAL DA SIMULAÇÃO

T = tmax*1.0;%TEMPO MÁXIMO DA SIMULAÇÃO = TMAX

c = -log(0.001)/T; %VARIAVEL AUXILIAR

dt = T/n;%INTERVALO NO TEMPO

dw = 2*pi/(n*dt);%INTERVALO NA FREQ.

kk = 0:n/2;

s= (-1i*c + dw*kk)./1000;

%Sinal

C= Z_5T_150;% Sinal no tempo para análise

xlen = length(C);

% Janelamento

xwin = flattopwin(xlen, 'periodic');

% Calculo do tamanho da janela coerente

Cx = sum(xwin)/xlen;

% FFT do sinal

L = length(V);

px = nextpow2(10*xlen);

nfftx = 2^px;

X = fft(C, nfftx);% X = fft(x.*hamming(xlen), nfftx);

Y = fft(V, nfftx);% X = fft(x.*hamming(xlen), nfftx);

Z=Y./X;

[Tyler F]

You didnt provide the V signal. Can you provide more details on what you were expecting? The signal you are taking the FFT of does not have much frequency content.

[Amanda Botelho Amaral]

I have put in the original data now. I think it will be easier to understand.

Answer 1

[Tyler F]

Assuming t is a vector of time stamps, dt is your sampling time, to get a "proper" fft plot I would add this to the end of your script;

fs = 1/dt;
f = fs*(0:(nfftx/2))/nfftx;
XdB = 10*log10(abs([X(1) 2*X(2:nfftx/2+1)']./nfftx));
figure
plot(f,XdB)
xlabel('Frequency (Hz)')
ylabel('Magnitude (dB)')

fs is your sampling frequency

f is the vector of frequency points in your fft

XdB is the real magnitude of your signal. The matlab fft() function returns the complex DFT which is mirrored for a real input signal, so we are only taking the first half of it. Because the signal is mirrored, we need to multiple all of the sample points that are mirrorer (everything except zero) by 2. Then we scale the value by the number of sample points, take the magnitude, convert to dB, and plot it.

[Amanda Botelho Amaral]

Thank you for the answer!

That part is missing some detail.

XdB = 10 * log10 (abs ([X (1) 2 * X (2: nfftx / 2 + 1) '] ./ nfftx));

i dont get it

[Amanda Botelho Amaral]

My curve is coming out like this.

But it should look like this.

[Tyler F]

It is important to understand the output of the fft function in relation to frequency bins. For a real input signal like yours, the ouput is conjugate symmetric that is, the first half of the points are identical to the second half.

Maybe it will be helpful to split up that single line into multiple chunks:

[X(1) 2*X(2:nfftx/2+1)']

This line is taking the first element of your fft output, X(1), which corresponds to the 0 Hz frequency bin, and concatenating it with the next expression:

2*X(2:nfftx/2+1)'

This is taking the the remainder of the first half of the unique points and multiplying them by 2. Because the input signal was real, we effectively got the output split in half and mirrored. We only want the first half, and we want to multiply it by 2 to make up for the fact it was split in half (power wise). The transpose is just to make it concatenate.

./nfftx

This is just scaling the output of the fft by the number of points in it. Each data point in the fft output is taken by a summation over the length of your fft (nfftx) so we are essentially scaling here. Some people leave this out depending on the type of analysis you are doing or use other values. You can search around and find some philosophical discussions (https://www.mathworks.com/matlabcentral/answers/15770-scaling-the-fft-and-the-ifft for example)

10*log10()

This just converts from linear to dB

[Amanda Botelho Amaral]

this message appears when you add this equation.

XdB = 10 * log10 (abs ([X (1) 2 * X (2: nfftx / 2 + 1) '] ./ nfftx));

"A quoted character vector is unterminated."

[Tyler F]

Remove the space between the apostrophe and the close parenthesis

[Amanda Botelho Amaral]

Sorry, the message is: "Dimensions of arrays being concatenated are not consistent."

[Tyler F]

Remove all of the spaces except the one between X(1) and 2. Not sure why it inserted spaces if you copy/pasted.

XdB = 10*log10(abs([X(1) 2*X(2:nfftx/2+1)']./nfftx)

[Amanda Botelho Amaral]

I modified my code using your suggestions. The answer comes out almost similar to what I expect, but mirrored. Any idea what it might be?

C = corrente;% n = length(t);%NUMERO DE AMOSTRAS

V = tensao;

Cinput_freq = fft(exp(-c*tfreq).*C)*dt;

Vinput_freq = fft(exp(-c*tfreq).*V)*dt;

% %SINGLE-SIDED AMPLITUDE

Cinput_freq = Cinput_freq(1:n/2+1);

Cinput_freq(2:end-1) = 2*Cinput_freq(2:end-1);

%SINGLE-SIDED AMPLITUDE

Vinput_freq = Vinput_freq(1:n/2+1);

Vinput_freq(2:end-1) = 2*Vinput_freq(2:end-1);

Za = Vinput_freq./Cinput_freq;