Shift Operator

The shift operator is defined by

and denotes the entire shifted signal. Note that since indexing is modulo , the shift is circular (or ``cyclic''). However, we normally use it to represent time delay by samples. We often use the shift operator in conjunction with zero padding (appending zeros to the signal , §7.2.7) in order to avoid the ``wrap-around'' associated with a circular shift.

Figure 7.2 illustrates successive one-sample delays of a periodic signal having first period given by .

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Subsections

• Examples

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Order a Hardcopy of Mathematics of the DFT

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.