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Math Help - Find an efficient procedure to compute the discrete cosine & sin transforms using fft

  1. #1
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    Find an efficient procedure to compute the discrete cosine & sin transforms using fft

    Can't figure this out to save my life. Please help if possible

    Consider the discrete cosine and sine transforms of a real sequence of numbers
    {x_j, j=0,....,2N-1}

    C_k = \sum_{j=0}^{2N-1} x_j cos(\frac{jk\pi}{N}),
    S_k = \sum_{j=0}^{2N-1} x_j sin(\frac{jk\pi}{N})

    Find an efficient procedure to compute C_k, S_k using a Fast Fourier Transform of \{x_j, j=0,...2N-1\}.

    Can someone give me a hint/explain to me the way to go about doing this problem? I am completely lost. Thanks!
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  2. #2
    Grand Panjandrum
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    Re: Find an efficient procedure to compute the discrete cosine & sin transforms using

    Quote Originally Posted by drewprogden View Post
    Can't figure this out to save my life. Please help if possible

    Consider the discrete cosine and sine transforms of a real sequence of numbers
    {x_j, j=0,....,2N-1}

    C_k = \sum_{j=0}^{2N-1} x_j cos(\frac{jk\pi}{N}),
    S_k = \sum_{j=0}^{2N-1} x_j sin(\frac{jk\pi}{N})

    Find an efficient procedure to compute C_k, S_k using a Fast Fourier Transform of \{x_j, j=0,...2N-1\}.

    Can someone give me a hint/explain to me the way to go about doing this problem? I am completely lost. Thanks!


    What is the real part of the DFT of a real sequence? What is the imaginary part?

    CB
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