Polynomial Multiplication

GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. Polynomial Multiplication

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Polynomial Multiplication

Note that when you multiply two polynomials together, their coefficients are convolved. To see this, let $p(x)$ denote the $m$th-order polynomial

\

with coefficients $p_i$, and let $q(x)$ denote the $n$th-order polynomial
\

with coefficients $q_i$. Then we have [17]
\

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