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Fourier Transform-Related Operations

Fourier Transform-Related Operations

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In this chapter, the operations discussed will be related to the Fourier transform and especially to the discrete Fourier transform (DFT) or fast Fourier transform (FFT). Some of these operations are useful to receiver design and some of these techniques can improve the results of the FFT. The discussion includes zero padding, better localization of FFT peaks, digital convolution, parallel FFT operations to increase overall speed, performing real FFT by using complex FFT operations, and a phase sampling scheme to increase the bandwidth of the receiver.

Chapter Contents:

  • 5.1 Introduction
  • 5.2 Zero Padding
  • 5.3 Periodic and Linear Convolutions
  • 5.4 Peak Position Estimation for Rectangular Window
  • 5.5 Peak Position Estimation for Hanning Window
  • 5.6 Peak Position Estimation Through Iteration
  • 5.7 Actual Frequency Determination by Fast Fourier Transform
  • 5.8 Real Input Computed by a Complex FFT Operator
  • 5.9 Autocorrelation
  • 5.10 Autocorrelation (Blackman-Tukey) Spectrum Estimation
  • 5.11 Application of FFT to Spectrum Estimation From Autocorrelation Function
  • 5.12 Basic Idea of Sub-Nyquist Sampling Scheme
  • 5.13 Phase Relation in a Sub-Nyquist Sampling System
  • 5.14 Problems and Potential Solutions of Sub-Nyquist Sampling Scheme
  • 5.15 Discrete Fourier Transform Through Decimation
  • 5.16 Applications of Decimation Method to EW Receivers
  • 5.17 Simplified Decimation Method
  • References

Inspec keywords: discrete Fourier transforms; convolution; signal sampling; fast Fourier transforms

Other keywords: parallel FFT operations; digital convolution; zero padding; receiver design; discrete Fourier transform; DFT; complex FFT operations; receiver; fast Fourier transform; phase sampling scheme

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

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