December 2005
Intermediate to advanced
475 pages
12h 6m
English
Content preview from Signals and SystemsBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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11.6 PROPERTIES OF DISCRETE FOURIER TRANSFORM
There is similarity among most of the properties of DFT and z-transform due to existence of some relationship of each other. DFT also differs in some properties like circular convolution property. The following properties play an important role in practical techniques for processing a signal:
- Periodicity
- Linearity
- Circular symmetry of a sequence
- Symmetry properties
- Circular convolution of two sequences
- Time reversal of a sequence
- Circular frequency-shift of a sequence
- Circular correlation of two sequences
- Multiplication of two sequences
- Parseval’s theorem
11.6.1 Periodicity
If a discrete time signal x(n) is periodic, its DFT will also be periodic in nature. Let x(n) and X(k) be the DFT pair i.e., ...
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