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DSP Code Sharing > Discrete Fourier Transform (DFT)
Discrete Fourier Transform (DFT)
Language: Matlab
Processor: Not Relevant
Submitted by Miguel De Jesus on Oct 27 2010
Licensed under a Creative Commons Attribution 3.0 Unported License
Discrete Fourier Transform (DFT)
This is a basic Matlab implementation of the Discrete Fourier Transform also known as DFT. The function receives as input a discrete-time signal (a sequence of N real numbers)and returns the frequency spectrum (a sequence of N complex numbers).
function xdft=fdft(x)
N=length(x);
xdft(1,N)=0; % defining a 1xN sequence with all the elements equals to zero.
%*************THIS IS THE DFT IMPLEMENTATION**************
%For each value of k, the Summatory function is computed over the interval 0<n<N-1.
for k=0:N-1,
for n=0:N-1,
xdft(k+1)=xdft(k+1) + x(n+1)*exp(-j*2*pi*k*n/N);
end
end
%NOTE: You may skip the use of for-loops by defining k and n as two N-points sequences. This is:
% k=0:N-1; n=0:N-1;
%The DFT is now computed in matrix form (as a matrix multiplication of the N-points Fourier Matrix and the discrete-time sequence x).
N=length(x);
xdft(1,N)=0; % defining a 1xN sequence with all the elements equals to zero.
%*************THIS IS THE DFT IMPLEMENTATION**************
%For each value of k, the Summatory function is computed over the interval 0<n<N-1.
for k=0:N-1,
for n=0:N-1,
xdft(k+1)=xdft(k+1) + x(n+1)*exp(-j*2*pi*k*n/N);
end
end
%NOTE: You may skip the use of for-loops by defining k and n as two N-points sequences. This is:
% k=0:N-1; n=0:N-1;
%The DFT is now computed in matrix form (as a matrix multiplication of the N-points Fourier Matrix and the discrete-time sequence x).
posted by Miguel De Jesus Miguel De Jesus possessed a BS in Electrical Engineering. He also pursued graduate studies obtaining a MSEE with specialization in Digital Signal Processing from the Polytechnic University of Puerto Rico. He has experience in research and development in several DSP areas such as time/frequency analysis, array processing, and parallel processing.
Comments
Synbios wrote:
11/4/2010
mnentwig wrote:
11/5/2010
keep in mind, the "call for code snippets" explicitly mentioned "from the simplest filter implementation to the most complex DSP algorithm". Many *are* actually taking DSP 101, nothing wrong with that.
Besides, if more people would take the time to *understand* those five lines of code, the world (or at least comp.dsp) would be a better place :-)
mdejesus wrote:
11/19/2010
The DFT is one of the most fundamental and simplest concept in DSP. This code and other more complex codes will be useful for you, when enroll any DSP course.
You can't use something you don't understand.
gilgamash wrote:
11/29/2010
Regards,
G.
mdejesus wrote:
11/30/2010
Thanks for your observation.
stephaneb wrote:
11/30/2010
Not necessarily. This could be of some value to students or people learning DSP.
aerodude wrote:
12/15/2010
Any help on getting to this step would be great. Thanks in advance.
mdejesus wrote:
12/15/2010
Precisely, my objective here is help people in the dsp learning process. If you want to plot the spectrum (amplitude vs frequency) just add the following piece of code in the Matlab Command Window or in a m-file :
N=length(xdft); %N is the number of frequency samples
k=0:N-1; % k is a vector containing the dft index
faxis=k/N*fs; % mapping k-axis to f-axis (frequency axis in Hz) NOTE: fs is the sampling frequency used to sampling the signal x.
plot(faxis,abs(xdft)) % plot the frequency spectrum
lmorales wrote:
12/15/2010
aerodude wrote:
12/20/2010
Thanks for the help, really useful for people (like me) who come from a different background and have to use DFT. Thanks a lot.
mdejesus wrote:
12/20/2010
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