Notation and Terminology

GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. Notation and Terminology

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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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Notation and Terminology

If $X$ is the DFT of $x$, we say that $x$ and $X$ form a transform pair and write

\

Another notation we'll use is
\


As we've already seen, time-domain signals are consistently denoted using lowercase symbols such as ''$x$,'' while frequency-domainsignals (spectra), are denoted in uppercase (''$X$'').

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