Fourier Theory

Fourier Theory

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The most familiar way of representing signals is in the time domain (i.e., a voltage or current represented as functions of time). An alternative representation which is extremely powerful and is inherent in spectrum and network measurements is the frequency domain representation, which describes the signal or system in terms of its frequency content (i.e., how much energy is present at each particular frequency). The frequency domain is related to the time domain by a body of knowledge generally known as Fourier theory, named for Jean Baptiste Joseph Fourier (1768-1830). This includes the series representation know as the Fourier series and the transform techniques known as the Fourier transform. Discrete (digitized) signals can be transformed into the frequency domain using the discrete Fourier transform.

Chapter Contents:

  • 3.1 Periodicity
  • 3.2 Fourier Series
  • 3.3 Fourier Series of a Square Wave
  • 3.4 Fourier Series of Other Waveforms
  • 3.5 Fourier Transform
  • 3.6 Fourier Transform of a Pulse
  • 3.7 Inverse Fourier Transform
  • 3.8 Fourier Transform Relationships
  • 3.9 Discrete Fourier Transform
  • 3.10 Limitations of the DFT
  • 3.11 Fast Fourier Transform
  • 3.12 Relating Theory to Measurements
  • 3.13 Finite Measurement Time
  • References

Inspec keywords: frequency-domain analysis; Fourier series; discrete Fourier transforms; signal representation; time-domain analysis

Other keywords: network measurements; series representation; signal representation; Jean Baptiste Joseph Fourier; frequency content; discrete signals; spectrum measurements; frequency domain representation; time domain; discrete Fourier transform; Fourier series; Fourier theory

Subjects: Signal processing and detection; Mathematical analysis; Integral transforms; Integral transforms; Mathematical analysis; Signal processing theory

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