NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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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Multiplication of Decimal Numbers
Since decimal numbers are implicitly just polynomials in the powers of 10, e.g.,
it follows that multiplying two numbers convolves their digits. The only twist is that, unlike normal polynomial multiplication, we havecarries. That is, when a convolution result exceeds 10, we subtract 10 from the result and add 1 to the digit in the next higher place.