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Math Help - polynomial multiplication using FFT

  1. #1
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    polynomial multiplication using FFT

    I apologize if this is in the wrong section, wasnt positive.
    Im reviewing a problem to prepare myself for an exam and im having a hard time figuring out how my professor puts A(x) in the form (1+2x^2)+x(1+0+x^2) and how he calculates the roots. If anyone could give me some pointers on what methods he did I would be extremely grateful . Posted the original question and the solution below.

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  2. #2
    MHF Contributor chisigma's Avatar
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    Re: polynomial multiplication using FFT

    The two polynomial can be written as P_1(z)= \sum_{k=0}^{n_{1}} a_{k}\ z^{-k} and P_2(z)= \sum_{k=0}^{n_{2}} b_{k}\ z^{-k}. The product of P_{1}(z) and P_{2}(z) using FFT can be performed in the following steps...

    a) if n=\text{max} [n_{1},n_{2}], then trasform by inserting zeroes P_{1}(z) and P_{2}(z) into polynomial of degree 2n-1...

    b) perform the FFT of P_{1}(z) and P_{2}(z) calling \Pi_{1} (\omega) the FFT of P_{1}(z) and \Pi_{1} (\omega) the FFT of P_{2}(z) ...

    c) compute the product \Pi (\omega)= \Pi_{1} (\omega)\ \Pi_{2} (\omega)...

    d) perform the inverse FFT of \Pi (\omega) obtaining the product P(z)=P_{1}(z)\ P_{2}(z)...



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