Mathematical Representation of Waveforms

Mathematical Representation of Waveforms

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Waveforms normally encountered in radar are essentially time-limited and band-limited. (With proper interpretation, this characterization also applies to CW radar systems.) Those familiar with Fourier transform theory will realize, of course, that a waveform cannot be simultaneously time and band-limited. But in many practical cases this approximation permits a better understanding of radar performance and simplifies calculations. Hence we shall be interested in approximate mathematical representations based on this assumption.

Chapter Contents:

  • 2.1 Introduction
  • 2.2 Fourier Integral Representations
  • 2.3 Fourier Series Representations
  • 2.4 Low-Frequency (Video) Sampling Theorem
  • 2.5 Real and Complex (Analog) Representations of Narrowband Waveforms
  • 2.6 High-Frequency Sampling Theorem
  • 2.7 Representation in Terms of Orthogonal Functions
  • 2.8 Some Useful Relations
  • Problems
  • References

Inspec keywords: Fourier transforms; radar theory; approximation theory

Other keywords: mathematical representation; Fourier transform theory; approximation theory; time-limited waveform; CW radar system; band-limited waveform

Subjects: Radar theory; Interpolation and function approximation (numerical analysis); Integral transforms in numerical analysis

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