The discrete fourier transform : theory, algorithms and applications

The discrete fourier transform : theory, algorithms and applications / D. Sundararajan.

This book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Had...

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Bibliographic Details
Main Author: Sundararajan, D.
Format: eBook
Language:English
Published: Singapore ; River Edge, NJ : World Scientific, ©2001.
Subjects:
Fourier transformations.
SCIENCE > Physics > Mathematical & Computational.
Fourier transformations
FOURIER TRANSFORMATION.
DISCRETE FUNCTIONS.
FUNCTIONAL ANALYSIS.
WALSH FUNCTION.
DISCRETE COSINE TRANFORM.
Online Access:Click for online access
Table of Contents:
  • Ch. 1. Introduction. 1.1. The transform method. 1.2. The organization of this book
  • ch. 2. The discrete sinusoid. 2.1. Signal representation. 2.2. The discrete sinusoid. 2.3. Summary and discussion
  • ch. 3. The discrete Fourier transform. 3.1. The Fourier analysis and synthesis of waveforms. 3.2. The DFT and the IDFT. 3.3. DFT representation of some signals. 3.4. Direct computation of the DFT. 3.5. Advantages of sinusoidal representation of signals. 3.6. Summary
  • ch. 4. Properties of the DFT. 4.1. Linearity. 4.2. Periodicity. 4.3. Circular shift of a time sequence. 4.4. Circular shift of a spectrum. 4.5. Time-reversal property. 4.6. Symmetry properties. 4.7. Transform of complex conjugates. 4.8. Circular convolution and correlation. 4.9. Sum and difference of sequences. 4.10. Padding the data with zeros. 4.11. Parseval's theorem. 4.12. Summary
  • ch. 5. Fundamentals of the PM DFT algorithms. 5.1. Vector format of the DFT. 5.2. Direct computation of the DFT with vectors. 5.3. Vector format of the IDFT. 5.4. The computation of the IDFT. 5.5. Fundamentals of the PM DIT DFT algorithms. 5.6. Fundamentals of the PM DIF DFT algorithms. 5.7. The classification of the PM DFT algorithms. 5.8. Summary
  • ch. 6. The u x 1 PM DFT algorithms. 6.1. The u x 1 PM DIT DFT algorithms. 6.2. The 2 x 1 PM DIT DFT algorithm. 6.3. Reordering of the input data. 6.4. Computation of a single DFT coefficient. 6.5. The u x 1 PM DIF DFT algorithms. 6.6. The 2 x 1 PM DIF DFT algorithm. 6.7. Computational complexity of the 2 x 1 PM DFT algorithms. 6.8. The 6 x 1 PM DIT DFT algorithm. 6.9. Flow chart description of the 2 x 1 PM DIT DFT algorithm. 6.10. Summary
  • ch. 7. The 2 x 2 PM DFT algorithms. 7.1. The 2 x 2 PM DIT DFT algorithm. 7.2. The 2 x 2 PM DIF DFT algorithm. 7.3. Computational complexity of the 2 x 2 PM DFT algorithms. 7.4. Summary
  • ch. 8. DFT algorithms for real data
  • I. 8.1. The direct use of an algorithm for complex data. 8.2. Computation of the DFTs of two real data sets at a time. 8.3. Computation of the DFT of a single real data set. 8.4. Summary.
  • Ch. 9. DFT algorithms for real data
  • II. 9.1. The storage of data in PM RDFT and RIDFT algorithms. 9.2. The 2 x 1 PM DIT RDFT algorithm. 9.3. The 2 x 1 PM DIF RIDFT algorithm. 9.4. The 2 x 2 PM DIT RDFT algorithm. 9.5. The 2 x 2 PM DIF RIDFT algorithm. 9.6. Summary and discussion
  • ch. 10. Two-dimensional discrete Fourier transform. 10.1. The 2-D DFT and IDFT. 10.2. DFT representation of some 2-D signals. 10.3. Computation of the 2-D DFT. 10.4. Properties of the 2-D DFT. 10.5. The 2-D PM DFT algorithms. 10.6. Summary
  • ch. 11. Aliasing and other effects. 11.1. Aliasing effect. 11.2. Leakage effect. 11.3. Picket-fence effect. 11.4. Summary and discussion
  • ch. 12. The continuous-time Fourier series. 12.1. The 1-D continuous-time Fourier series. 12.2. The 2-D continuous-time Fourier series. 12.3. Summary
  • ch. 13. The continuous-time Fourier transform. 13.1. The 1-D continuous-time Fourier transform. 13.2. The 2-D continuous-time Fourier transform. 13.3. Summary
  • ch. 14. Convolution and correlation. 14.1. The direct convolution. 14.2. The indirect convolution. 14.3. Overlap-save method. 14.4. Two-dimensional convolution. 14.5. Computation of correlation. 14.6. Summary
  • ch. 15. Discrete cosine transform. 15.1. Orthogonality property revisited. 15.2. The 1-D discrete cosine transform. 15.3. The 2-D discrete cosine transform. 15.4. Summary
  • ch. 16. Discrete Walsh-Hadamard transform. 16.1. The discrete Walsh transform. 16.2. The naturally ordered discrete Hadamard transform. 16.3. The sequency ordered discrete Hadamard transform. 16.4. Summary.

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