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wav file dft without fft

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Min Soo
Min Soo on 8 Jun 2020
Commented: Rena Berman on 12 Oct 2020
I want wav audio file to dft conversion without fft


Geoff Hayes
Geoff Hayes on 8 Jun 2020
Seung - to be clear you don't want to use the MATLAB fft function but want to implement your own DFT function? Is this the case? Please provide some more details.
Rik on 10 Jun 2020
(retrieved from Google Cache)
Question title:
wav file dft without fft
Question body:
I want wav audio file to dft conversion without fft
Deleted comment (posted on 9 Jun 2020 at 3:31):
yes I want to use only DFT function don't use fft function
Rena Berman
Rena Berman on 12 Oct 2020
(Answers Dev) Restored edit

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Accepted Answer

Ron Fredericks
Ron Fredericks on 10 Jun 2020
Edited: Ron Fredericks on 11 Jun 2020
Hi Seung Hoon LEE:
I produced this MATLAB script to demonstrate calculation of a DFT starting from an mp3 file. Audio files typically have a large number of data points and my DFT function is very slow. So I use a loop reduction factor to speed up the DFT calculation. This parameter and frequency range can be adjusted near top of code. The audio file I use is an mp3 bird call that can be downloaded from
% PURPOSE: Compare fft with dft loop for an audio file
% AUDIO FILE: Use a public domain birdcall from
% RESULT: Produce 3 plots: 1) Time domain, 2) FFT, and 3) DFT
% DATE: June 6, 2020
% "Signal Processing Problems" hosted on
% by Dr. Mike X Cohen, sigprocMXC_SpectBirdcall.m
% "Master the Fourier transform and its applications" hosted on
% by Dr. Mike X Cohen, Fourier_DTFT.m
% Load in birdcall (source:
[bc,fs] = audioread('XC403881.mp3');
% Configuration params for Fourier transforms.
freq_range = [0 8000]; % Hz
dft_loop_reduction = 100; % set to 1 for no reduction (Hint: takes a long time)
% let's hear it!
% soundsc(bc,fs)
n = length(bc);
hz = linspace(0,fs/2,floor(n/2)+1);
% Smooth birdcall audio audio for fft & dft
signal = detrend(bc(:,1))'; % transpose here for DFT loop later
% Create a time vector based on the data sampling rate.
timevec = (0:n-1)/fs;
% Plot the data from the two audio file channels.
figure(1), clf
% Include a small offset for left and right audio channels.
plot(timevec,bsxfun(@plus,bc,[.2 0]))
xlabel('Time (sec.)')
title('Time domain')
set(gca,'ytick',[],'xlim',timevec([1 end]))
%% Compute & plot the power spectrum using MATLAB fft function.
bcpow_fft = abs(fft( signal )/n).^2;
xlabel('Frequency (Hz)')
title(['Frequency domain using FFT with ' num2str(length(bcpow_fft)) ' points']);
% Make fft and dft y-limits be the same for comparison.
ylim_fft = get(gca,'ylim');
%% Compute & plot the power spectrum using DFT loop.
fourTime = (0:n-1)/n;
fCoefs = zeros(size(signal));
h = waitbar(0,'Please wait for DFT loop...');
% DFT loop is very inefficient, it is used here for demonstration only.
for fi=1:dft_loop_reduction:n
% Create complex sine wave.
csw = exp( -1i*2*pi*(fi-1)*fourTime );
% Compute dot product between sine wave and signal (Fourier coefficients).
fCoefs(fi) = sum( signal.*csw );
% GUI to show progress for long calculation times.
bcpow_dft = abs(fCoefs / n).^2;
xlabel('Frequency (Hz)')
title(['Frequency domain using DFT loop with ' ...
num2str(floor(length(bcpow_dft)/dft_loop_reduction)) ' points']);
%% done.


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