Fast Transforms Algorithms Analyses Applications 1st Edition by Douglas Elliott, Ramamohan Rao ISBN 9780080918068 0080918069

Fast Transforms Algorithms Analyses Applications 1st Edition by Douglas Elliott, Ramamohan Rao – Ebook PDF Instant Download/Delivery. 9780080918068 ,0080918069
Full download Fast Transforms Algorithms Analyses Applications 1st Edition after payment

Product details:
ISBN 10: 0080918069
ISBN 13: 9780080918068
Author: Douglas Elliott, Ramamohan Rao

Fast Transforms Algorithms Analyses Applications 1st Edition Table of contents:

Chapter 1. Introduction

1.0 Transform Domain Representations

1.1 Fast Transform Algorithms

1.2 Fast Transform Analyses

1.3 Fast Transform Applications

1.4 Organization of the Book

Chapter 2. Fourier Series and the Fourier Transform

2.0 Introduction

2.1 Fourier Series with Real Coefficients

2.2 Fourier Series with Complex Coefficients

2.3 Existence of Fourier Series

2.4 The Fourier Transform

2.5 Some Fourier Transforms and Transform Pairs

2.6 Applications of Convolution

2.7 Table of Fourier Transform Properties

2.8 Summary

Problems

Chapter 3. Discrete Fourier Transforms

3.0 Introduction

3.1 DFT Derivation

3.2 Periodic Property of the DFT

3.3 Folding Property for Discrete Time Systems with Real Inputs

3.4 Aliased Signals

3.5 Generating kn Tables for the DFT

3.6 DFT Matrix Representation

3.7 DFT Inversion—the IDFT

3.8 The DFT and IDFT—Unitary Matrices

3.9 Factorization of WE

3.10 Shorthand Notation

3.11 Table of DFT Properties

3.12 Summary

Problems

Chapter 4. Fast Fourier Transform Algorithms

4.0 Introduction

4.1 Power-of-2 FFT Algorithms

4.2 Matrix Representation of a Power-of-2 FFT

4.3 Bit Reversal to Obtain Frequency Ordered Outputs

4.4 Arithmetic Operations for a Power-of-2 FFT

4.5 Digit Reversal for Mixed Radix Transforms

4.6 More FFTs by Means of Matrix Transpose

4.7 More FFTs by Means of Matrix Inversion—the IFFT

4.8 Still More FFTs by Means of Factored Identity Matrix

4.9 Summary

Problems

Chapter 5. FFT Algorithms That Reduce Multiplications

5.0 Introduction

5.1 Results from Number Theory

5.2 Properties of Polynomials

5.3 Convolution Evaluation

5.4 Circular Convolution

5.5 Evaluation of Circular Convolution through the CRT

5.6 Computation of Small Ν DFT Algorithms

5.7 Matrix Representation of Small Ν DFTs

5.8 Kronecker Product Expansions

5.9 The Good FFT Algorithm

5.10 The Winograd Fourier Transform Algorithm

5.11 Multidimensional Processing

5.12 Multidimensional Convolution by Polynomial Transforms

5.13 Still More FFTs by Means of Polynomial Transforms

5.14 Comparison of Algorithms

5.15 Summary

Problems

Chapter 6. DFT Filter Shapes and Shaping

6.0 Introduction

6.1 DFT Filter Response

6.2 Impact of the DFT Filter Response

6.3 Changing the DFT Filter Shape

6.4 Triangular Weighting

6.5 Hanning Weighting and Hanning Window

6.6 Proportional Filters

6.7 Summary of Weightings and Windows

6.8 Shaped Filter Performance

6.9 Summary

Problems

Chapter 7. Spectral Analysis Using the FFT

7.0 Introduction

7.1 Analog and Digital Systems for Spectral Analysis

7.2 Complex Demodulation and More Efficient Use of the FFT

7.3 Spectral Relationships

7.4 Digital Filter Mechanizations

7.5 Simplifications of FIR Filters

7.6 Demodulator Mechanizations

7.7 Octave Spectral Analysis

7.8 Dynamic Range

7.9 Summary

Problems

Chapter 8. Walsh-Hadamard Transforms

8.0 Introduction

8.1 Rademacher Functions

8.2 Properties of Walsh Functions

8.3 Walsh or Sequency Ordered Transform (WHT)w

8.4 Hadamard or Natural Ordered Transform (WHT)h

8.5 Paley or Dyadic Ordered Transform (WHT)p

8.6 Cal-Sal Ordered Transform (WHT)cs

8.7 WHT Generation Using Bilinear Forms

8.8 Shift Invariant Power Spectra

8.9 Multidimensional WHT

8.10 Summary

Problems

Chapter 9. The Generalized Transform

9.0 Introduction

9.1 Generalized Transform Definition

9.2 Exponent Generation

9.3 Basis Function Frequency

9.4 Average Value of the Basis Functions

9.5 Orthonormality of the Basis Functions

9.6 Linearity Property of the Continuous Transform

9.7 Inversion of the Continuous Transform

9.8 Shifting Theorem for the Continuous Transform

9.9 Generalized Convolution

9.10 Limiting Transform

9.11 Discrete Transforms

9.12 Circular Shift Invariant Power Spectra

9.13 Summary

Problems

Chapter 10. Discrete Orthogonal Transforms

10.0 Introduction

10.1 Classification of Discrete Orthogonal Transforms

10.2 More Generalized Transforms

10.3 Generalized Power Spectra

10.4 Generalized Phase or Position Spectra

10.5 Modified Generalized Discrete Transform

10.6 (MGT), Power Spectra

10.7 The Optimal Transform: Karhunen-Loeve

10.8 Discrete Cosine Transform

10.9 Slant Transform

10.10 Haar Transform

10.11 Rationalized Haar Transform

10.12 Rapid Transform

10.13 Summary

Problems

Chapter 11. Number Theoretic Transforms

11.0 Introduction

11.1 Number Theoretic Transforms

11.2 Modulo Arithmetic

11.3 DFT Structure

11.4 Fermat Number Transform

11.5 Mersenne Number Transform

11.6 Rader Transform

11.7 Complex Fermat Number Transform

11.8 Complex Mersenne Number Transform

11.9 Pseudo-Fermat Number Transform

11.10 Complex Pseudo-Fermat Number Transform

11.11 Pseudo-Mersenne Number Transform

11.12 Relative Evaluation of the NTT

11.13 Summary

Problems

Appendix:

Direct or Kronecker Product of Matrices

Bit Reversal

Circular or Periodic Shift

Dyadic Translation or Dyadic Shift

modulo or mod

Gray Code

Correlation

Convolution

Special Matrices

Dyadic or Paley Ordering of a Sequence

References

Index

People also search for Fast Transforms Algorithms Analyses Applications 1st Edition:

application of algorithm in real life

ram model for algorithm analysis

fast fourier transform and convolution algorithms

fast fourier transform algorithm explained