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Signals and Systems by Smarajit Ghosh

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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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