[picture of book]

The Scientist and Engineer's
Guide to Digital Signal Processing

by Steven W. Smith
California Technical Publishing

ISBN 0-9660176-3-3 (1997)



Chapter 10. Fourier Transform Properties
  • Linearity of the Fourier Transform
  • Characteristics of the Phase
  • Periodic Nature of the DFT
  • Compression and Expansion
  • Multiplying Signals (Amplitude Modulation)
  • The Discrete Time Fourier Transform
  • Parseval's Relation
The time and frequency domains are alternative ways of representing signals. The Fourier transform is the mathematical relationship between these two representations. If a signal is modified in one domain, it will also be changed in the other domain, although usually not in the same way. For example, it was shown in the last chapter that convolving time domain signals results in their frequency spectra being multiplied. Other mathematical operations, such as addition, scaling and shifting, also have a matching operation in the opposite domain. These relationships are called properties of the Fourier Transform, how a mathematical change in one domain results in a mathematical change in the other domain.



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