**NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW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 denote the th-order polynomial

with coefficients , and let denote the th-order polynomial

with coefficients . Then we have [17]