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., ...
Get Signals and Systems now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
