Amplitude spectrum concentrated around the wrong frequency

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Maria Zilidou
Maria Zilidou 2020-12-8
回答： Mathieu NOE 2020-12-8
I have an ultrasonic signal obtained by scanning a specimen using a 7.5 MHz probe (which is close to the resonance frequency of the material) with a spherical focus of 1.5 inches. I am calculating the fft of the signal, truncating to half the length, taking the magnitude and then I finally define the frequency step as follows:
Spectrum = fft(real(Signal));
Spectrum=Spectrum(1:length(Spectrum)/2+1);
AmplitudeSpectrum = abs(Spectrum);
fft_pts = 2^nextpow2(length(TimeInMicroSec)) ;
FreqIncInMHz = 1.0 / (TimeIncrementInMicroSec*fft_pts) ;
FreqInMHz = zeros(size(Spectrum));
for i = 1:length(FreqInMHz)
FreqInMHz(i) = double(i-1)*FreqIncInMHz;
end
I then plot the amplitude against the frequency (as shown in the figure below) but instead of getting a distribution concentrated around the centre frequency of the transducer, my results are off by a factor of 2 approximately. I am not sure what is causing this.
  1 个评论
Star Strider
Star Strider 2020-12-8
I strongly suspect that you are not calculating the frequency vector correctly. It should extend from 0 Hz (D-C) to the Nyquist frequency (half the sampling frequency). The ‘FreqIncInMHz’ calculation is a complete mystery.

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回答（1 个）

Mathieu NOE
Mathieu NOE 2020-12-8
hello
FYI, this is my fft code for doing averaging fft (works also for no averaging) :
function [freq_vector,fft_spectrum] = myfft_peak(signal, Fs, nfft, Overlap)
%FFT peak spectrum of signal (example sinus amplitude 1 = 0 dB after fft).
% signal - input signal,
% Fs - Sampling frequency (Hz).
% nfft - FFT window size
% Overlap - buffer overlap % (between 0 and 0.95)
samples = length(signal);
% fill signal with zeros if its length is lower than nfft
if samples<nfft
s_tmp = zeros(nfft,1);
s_tmp((1:samples)) = signal;
signal = s_tmp;
end
% window : hanning
window = hanning(nfft);
window = window(:);
% compute fft with overlap
offset = fix((1-Overlap)*nfft);
spectnum = 1+ fix((samples-nfft)/offset); % Number of windows
% % for info is equivalent to :
% noverlap = Overlap*nfft;
% spectnum = fix((samples-noverlap)/(nfft-noverlap)); % Number of windows
% main loop
fft_spectrum = 0;
for i=1:spectnum
start = (i-1)*offset;
sw = signal((1+start):(start+nfft)).*window;
fft_spectrum = fft_spectrum + (abs(fft(sw))*4/nfft); % X=fft(x.*hanning(N))*4/N; % hanning only
end
fft_spectrum = fft_spectrum/spectnum; % to do linear averaging scaling
% one sidded fft spectrum % Select first half
if rem(nfft,2) % nfft odd
select = (1:(nfft+1)/2)';
else
select = (1:nfft/2+1)';
end
fft_spectrum = fft_spectrum(select);
freq_vector = (select - 1)*Fs/nfft;
end

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