Amplitude spectrum concentrated around the wrong frequency

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.

[Star Strider]

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.

Answer 1

[Mathieu NOE]

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