fft based dct and idct

Ericson

2015 9 27

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Write two MATLAB functions, called mydct.m and myidct.m, that implement the discrete cosine transform (DCT) and its inverse for a vector of length N. Your code should be short (4 lines or less per function, no loops), ecient (it should make use of the fft command), and match the output of MATLAB's dct and idct commands.

I really have problem in solving this simple question. Could anyone help me?

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John D'Errico 2015-9-27

I just used google. "dct from fft". surprisingly, I found much there. Ok, maybe not a surprise.

Ericson 2015-9-28

编辑：Walter Roberson 2015-9-28

在 MATLAB Online 中打开

Actually I found one, but when I do the inverse dct, I got a large difference. Could you point out my errors?

function w1 = myidct(y)
N=length(y);
x=[y;flipud(y)];
fi=ifft(x);
k=0:N-1;
w1=sqrt(2*N)*real(fi(1:N).*exp(1j.*k'.*pi./(2*N)));
w1(1)=sqrt(1/2)*w1(1);
end