Question on use of fft and using positive frequency values only

I have two outputs of an carried out fft from filtered signal. I now that there is only a 770 Hz sin signal left in x_filtered, sample frequency fs is 48000.

fft_xf_shift = fftshift(fft(x_filtered,fs));

m_sh = abs(fft_xf_shift);

Seems to me that fft gives out a double sided frequency spectrum. With fftshift I zero-center the spectrum. Next I calculate the absolute values and then save in m_pos only the positive values because the negative frequency values are of no intereset in this case.

Next I plot the 20*log10 magnitude over frequency:

m_pos = m_sh(fs/2+1:fs);

f=0:1:fs/2-1;

figure;

plot(f,20*log10(m_pos/max(m_pos)))

The plot give the correct magnitude at 770 Hz. Even if I have the highest magnitude reading at 770 Hz in the final plot, when I plot m_pos, which is the right snipped of the fft_shifted value, the highest reading is at 771 Hz or at position 771 of the vector.

I certainly have a misconception here. Can you help me? Thank you.

Answer 1

[Paul]

Is this just an indexing question? If I understand the code snippet correctly, the frequency vector starts at 0, and incremented by 1, so f(771) = 770. So the peak would also be at m_pos(771), corresponding to 770 Hz.