MATLAB: Hanning window Frequency Domain Graph

frequency domain

Hello,

I have calculated the time domain of the hanning window through the formula.

But now I have to find the frequency domain by using fft and fft shift which i have calculated but I want to know is this graph correct or not?

M = 40;
n = -M / 2: M / 2;
window = 0.5 + 0.5 * cos (2 * pi * n / M);
figure;
plot (n, window);
L = length (window); 
NFFT = 1024;
X1 = fftshift (fft (window, NFFT) / length (window));
Freq = (-NFFT / 2: NFFT / 2-1) / NFFT;     % Frequency vector
figure; 
plot (Freq, X1 (1: length (Freq)) / max (X1), 'r' );

Best Answer

The graph for frequency response is correct. In case you want to generate a plot for magnitude response in decibels, make the following changes to the code:

Y1 = X1 (1: length (Freq)) / max (X1);
mag_dB =  10*log10(Y1);
plot(Freq,mag_dB);

The following link to the documentation might be helpful ofr generating frequency response for Hanning window using the 'hann' function available in the Signal Processing Toolbox in MATLAB.

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

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hello

see below (myspecgram)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% data
[data,Fs] = audioread('myWAVaudiofile.wav');
channel = 1;
signal = data(:,channel);
samples = length(signal);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 4096;    % 
OVERLAP = 0.75;
% spectrogram dB scale
spectrogram_dB_scale = 100;  % dB range scale (means , the lowest displayed level is XX dB below the max level)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% options 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% decimate (if needed)
% NB : decim = 1 will do nothing (output = input)
decim = 2;
if decim>1
    signal = decimate(signal,decim);
    Fs = Fs/decim;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% display 2 : time / frequency analysis : spectrogram demo
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% [sg,fsg,tsg] = specgram(signal,NFFT,Fs,hanning(NFFT),floor(NFFT*OVERLAP));  
[sg,fsg,tsg] = myspecgram(signal,NFFT,Fs,OVERLAP);  
% FFT normalisation and conversion amplitude from linear to dB (peak)
sg_dBpeak = 20*log10(abs(sg))+20*log10(2/length(fsg));     % NB : X=fft(x.*hanning(N))*4/N; % hanning only
% saturation of the dB range : 
% saturation_dB = 60;  % dB range scale (means , the lowest displayed level is XX dB below the max level)
min_disp_dB = round(max(max(sg_dBpeak))) - spectrogram_dB_scale;
sg_dBpeak(sg_dBpeak<min_disp_dB) = min_disp_dB;
% plots spectrogram
figure(2);
imagesc(tsg,fsg,sg_dBpeak);colormap('jet');
axis('xy');colorbar('vert');grid
title([' Spectrogram / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(fsg(2)-fsg(1)) ' Hz ']);
xlabel('Time (s)');ylabel('Frequency (Hz)');
function  [sg,freq_vector,time] = myspecgram(signal,nfft,Fs,Overlap)
% [sg,freq_vector,time] = myspecgram(signal,NFFT,Fs,hanning(NFFT),floor(NFFT*OVERLAP));
% FFT peak spectrogram 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)
dt = 1/Fs;
signal = signal(:);
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;
    samples = nfft;
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
    sg = [];
    for i=1:spectnum
        start = (i-1)*offset;
        sw = signal((1+start):(start+nfft)).*window;
        sg = [sg (abs(fft(sw))*4/nfft)];     % X=fft(x.*hanning(N))*4/N; % hanning only 
        time(i) = (start+nfft/2)*dt; % time defined as in the middle of the data buffer
    end
% 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
    
sg = sg(select,:);
freq_vector = (select - 1)*Fs/nfft;
end

Best Answer

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