Block Wise FFT on Audio Signal

Let us take a audio signal. Divide the audio sequence into non-overlapping block each of 8 samples. Perform fft of each block and concatenate all the fft blocks. Plot the magnitude and phase spectrum.

To verify whether the implementation is correct, divide the fft coefficients into blocks of 8 samples and compute ifft. then compare the ifft with the audio signal. If they are equal then the algorithm is correct.

So, I've tried this code but it's not giving any output

[x,Fs] = audioread('amy.mp3');
x1 = x(:, 1);
a = x1.'; 
N=8;

for i= 1:27366
    
    temp =  a((8*i-7):(8*i));  
    X=zeros(1, N);
    for k = 0:N-1 
        for n = 0:N-1
            X(k+1) = X(k+1)+x(n+1)*exp((-1j*2*pi*k*n)/N);
        end
    end
    Y=zeros(1, N);
    for k = 0:N-1
        for n = 0:length(x)-1
            Y(k+1) = Y(k+1)+(x(n+1)*exp(1i*2*pi*n*k/N));
        end
    end
      
end
X;
Y = Y./N;
Z = a - Y

Answer 1

[Pramil]

Hi Sree,

You can use the built-in MATLAB functions “fft” and “ifft” to address the described problem.

Here is a code that works in MATLAB R2023b for your reference:

[x,Fs] = audioread('song.mp3'); % Load the audio file
x1 = x(:, 1); % Use only one channel if stereo
N = 8; % Block size

% Number of blocks
numBlocks = floor(length(x1)/N);

% Initialize an empty array for FFT results
fftBlocks = zeros(1,numBlocks*8);

% Divide the signal into non-overlapping blocks and compute FFT for each block
for i = 1:numBlocks
    block = x1((N*(i-1))+1:N*i); % Extract block
    fftBlock = fft(block); % Compute FFT of the block
    fftBlocks((N*(i-1))+1:N*i) = fftBlock; % Assign the FFT results
end

% Plot the magnitude and phase spectrum of the concatenated FFT blocks
figure;
subplot(2,1,1);
plot(abs(fftBlocks));
title('Magnitude Spectrum');
subplot(2,1,2);
plot(angle(fftBlocks));
title('Phase Spectrum');

% Verification by computing IFFT
ifftBlocks = zeros(1,numBlocks*8);
for i = 1:numBlocks
    block = fftBlocks((N*(i-1))+1:N*i); % Extract block
    ifftBlock = ifft(block); % Compute IFFT of the block
    ifftBlocks((N*(i-1))+1:N*i) = ifftBlock; % Assign the IFFT results
end

% Compare the original audio signal with the IFFT result (after reshaping it to match original signal length)
originalSignal = x1(1:N*numBlocks); % Original signal might need to be truncated to match the length
reconstructedSignal = reshape(ifftBlocks, [], 1);

% Check if they are equal
difference = originalSignal - reconstructedSignal;
disp(['Difference between original and reconstructed signal: ', num2str(sum(abs(difference)))]);

% A very small difference value indicates that the algorithm is correct.

You can know more about “fft” and “ifft” funtions through the following links:

https://www.mathworks.com/help/matlab/ref/fft.html

https://www.mathworks.com/help/matlab/ref/ifft.html

Hope it helps.