Program the following Digital Signal in MATLAB Discrete Fourier Transform (DFT)

Question

Program the following Digital Signal in MATLAB

Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) The DFT of a sequence x(n) with length N is defined: X[k] = sigma^N - 1_n = 0 x[n]W^kn for each k = 0, 1 ..., N - 1 Where W = e^-j(2 pi/N) The inverse DFT is given by: x[n] = 1/N sigma^N - 1/n =0 X[k]W^-kn for each n = 0, 1, ..., N - 1 The Fast Fourier transform (FFT) is an efficient algorithm to compute the DFT. Use 'fft' function to calculate the Fourier Transform of a sequence, x = [1, 2, 3, 4, 5, 6, 7, 8]. Use 'ifft' function to calculate the inverse Fourier Transform of the result you get in (a). Re-do (a) and (b) using your own DFT and inverse DFT functions.

Explanation / Answer

x=[1 2 3 4 5 6 7 8 ];
for n=1:2
y=fft(x);
disp('the fast fourier transform is'); disp(y);
g=ifft(y);
disp('the inverse fast fourier transform is'); disp(g);
if g==y
disp('Hence proved');
end
x=input('next sequence');
end

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