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Time Waveform

In digital signal processing, a signal's time-waveform is usually a real-valued function of an integer sample number, corresponding to continuous amplitude versus discrete time. This means that, at any sampling instant $ nT$, the amplitude may take on any real value. The time-waveform may be pictured as a bar graph that extends forever to the left and right.

By convention, a filter input signal is usually denoted by $ x(n)$, giving the signal's amplitude at time sample $ n$. Similarly, a filter output is usually called $ y(n)$. In both cases, $ n$ is an integer, while $ x(n)$ and $ y(n)$ are usually real numbers. This notation should be comfortable for anyone who has written a computer subroutine for processing samples of digitized sound.

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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (August 2006 Edition).
Copyright © 2007-02-02 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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