How to average values and get a one-sided spectrum from two-sided spectrum?

Hello Community! In this code i am doing a STFT on my WAV-File. If you look at the "parameter code-line", you can see, that i am defining three different frequency bands. Afterwards, if you look at the "for loop", here i am trying to find the values of indices from the signal "Ya" and try to get a single value, which is being put together through the function "mean". I am aware there is something missing, since it doesn't work like that. But this is, what i want. I am trying to average all values, which are being defined previously from my frequnecy bands and get every value until to the length of my signal. Another thing is, i seem to get a two-sided spectrum. How do i get rid of the second spectrum? If you can provide any solutions or tips, i would appreciate it.

 [y,fs]=audioread('UnchainMyHeart.wav');
 % audioread = Reading the WAV-File 
 % y = A vector, which contains our audio signal
 % fs = Sampling frequency
 % 'UnchainMyHeart' = Name of the WAV-File

 %PARAMETER FOR THE CODE
 %_________________________________________________________________________
 t_seg=0.05; %Length of the segment, on which we use the STFT

 fftlen = 4096; 
 % Length of the FFT

 % L,M,H bands
 % Start & Stop frequency defenition of bands
  fL = [  1,  250 ]; % Low frequencies
  fM = [  251,  600 ]; % Medium frequencies
  fH = [ 601, 1000 ]; % High frequencies
 %_________________________________________________________________________

 segl =floor(t_seg*fs); 
 % Length of the segment(50ms), which is being multiplied by the sampling frequency 
 % The result is rounded off with the function "floor"

 windowshift=segl/2; 
 % Defining the size of the window, which goes to next segment and so on, until to the 
 % end of the audio signal

 window=hann(segl); 
 % Hanning Function, which is being stored in a vraiable
 % Matlab usually works better with variables than actual numbers. Hence the
 % workspace. This way, you can avoid errors.  

 window=window.'; 
 % transpose vector from a line vector to a row vector
 % In the workspace, you can see, what kind of vector it is

 si=1; 
 % Start index

 ei=segl; 
 % End index

 AOS= length(y)/windowshift - 1;
 % Determining the numbers of segments in my audio signal

 f1=figure;
    % New figure is being openend

    f=0:1:fftlen-1;
    f=f/(fftlen-1)*fs;
    % Definig frequency vector
    Ya=zeros(1,fftlen);
    % The values between "1" and "fftlen" are being filled with zeros

 for m= 1:1:AOS

    y_a = y(si:ei);
    y_a= y_a.*window;
    Ya=fft(y_a, fftlen);

    % indices of bands
    LI = find((f>=fL(1))&(f<=fL(2))); 
    MI = find((f>=fM(1))&(f<=fM(2)));
    HI = find((f>=fH(1))&(f<=fH(2)));
    % mean values of bands
    ML = mean(Ya(LI));
    MM = mean(Ya(MI));
    MH = mean(Ya(HI));

    drawnow; 
    % Updates the graphical objects

    figure(f1);
    plot(f, 20*log10(abs(Ya)));    
    ylim([-90 50]);
    % Limiting the length of my y-axis
    title('Spectrum of audio signal');
    % Title
    xlabel('f(Hz)');
    % Name of x-axis
    ylabel('dB');
    % Name of y-axis
    grid on;
    % Generating grid raster

    si=si+windowshift; 
    %Startindex is being updated
    ei=ei+windowshift; 
    %Endindex is being updated

 end

Answer 1

[Vandana Rajan]

Hi,

Your code can be simplified a lot by using the MATLAB function 'spectrogram'. Please find the link below for details on this function.

https://www.mathworks.com/help/signal/ref/spectrogram.html

By taking mean values of frequency bands, I believe you wish to take average power in those bands. 'Ya=fft(y_a, fftlen);' returns complex vectors. You need to take the power spectrum '20*log10(abs(Ya)+eps)'.

Also, variables 'windowshift' and 'AOS' are not integers. You can use 'floor' or 'round' or 'ceil'.

The code snippet, % indices of bands LI = find((f>=fL(1))&(f<=fL(2))); MI = find((f>=fM(1))&(f<=fM(2))); HI = find((f>=fH(1))&(f<=fH(2))); can be taken out of the loop, since the values are not changing with each iteration of the loop.

For your query regarding single sided spectrum, you may read the contents here

https://www.mathworks.com/matlabcentral/answers/166697-plot-single-sided-amplitude-spectrum

[Denny Muttathil]

Regarding the single-sided-amplitude-spectrum: Wouln't the function "xlim" enough? Since the documentation says, that values are being "freezed" at the current values. For example "xlim ([0 fs/2]);". Or is it, that i just can't see the double-sided spectrum and only see half of that spectrum? But the imaginary values are still being used.

[Vandana Rajan]

Single sided spectrum displays only the positive half of the frequency spectrum because the spectrum of a real-world signal is symmetrical around DC. The negative frequency information is redundant. A two-sided power spectrum displays half the energy at the positive frequency and half the energy at the negative frequency. Therefore, to convert a two-sided spectrum to a single-sided spectrum, you discard the second half of the array and multiply every point except for DC by two. The height of the non-DC frequency components in the single-sided spectrum is twice the height of the non-DC frequency component in the two-sided power spectrum. Also, the single-sided spectrum stops at half the frequency of that in the two-sided power spectrum.