The fast Fourier transform / E. Oran Brigham.
Editor: Englewood Cliffs, N.J. : Prentice-Hall, c1974Descripción: xiii, 252 p. : il. ; 24 cmISBN: 013307496XOtra clasificación: 65T50 (42A38)CHAPTER 1 INTRODUCTION [1] 1-1 Transform Analysis [1] 1-2 Basic Fourier Transform Analysis [3] 1-3 The Ubiquitous Fourier Transform [7] 1-4 Digital Computer Fourier Analysis [7] 1- 5 Historical Summary of the Fast Fourier Transform [8] CHAPTER 2 THE FOURIER TRANSFORM [11] 2- 1 The Fourier Integral [11] 2-2 The Inverse Fourier Transform [13] 2-3 Existence of the Fourier Integral [15] 2-4 Alternate Fourier Transform Definitions [23] 2- 5 Fourier Transform Pairs [28] CHAPTER 3 FOURIER TRANSFORM PROPERTIES [31] 3-1 Linearity [31] 3-2 Symmetry [32] 3-3 Time Scaling [32] 3-4 Frequency Scaling [35] 3-5 Time Shifting [37] 3-6 Frequency Shifting [37] 3-7 Alternate Inversion Formula [40] 3-8 Even Functions [40] 3-9 Odd Functions [41] 3-10 Waveform Decomposition [42] 3-11 Complex Time Functions [43] 3-12 Summary of Properties [46] CHAPTER 4 CONVOLUTION AND CORRELATION [50] 4- 1 Convolution Integral [50] 4- 2 Graphical Evaluation of the Convolution Integral [50] 4-3 Alternate Form of the Convolution Integral [54] 4-4 Convolution Involving Impulse Functions [57] 4-5 Convolution Theorem [58] 4-6 Frequency Convolution Theorem [61] 4-7 Proof of Parseval’s Theorem [64] 4-8 Correlation [64] 4- 9 Correlation Theorem [66] CHAPTER 5 FOURIER SERIES AND SAMPLED WAVEFORMS [75] 5- 1 Fourier Series [75] 5-2 Fourier Series as a Special Case of the Fourier Integral [78] 5-3 Waveform Sampling [80] 5-4 Sampling Theorem [83] 5- 5 Frequency Sampling Theorem [87] CHAPTER 6 THE DISCRETE FOURIER TRANSFORM [91] 6- 1 A Graphical Development [91] 6-2 Theoretical Development [94] 6-3 Discrete Inverse Fourier Transform [98] 6- 4 Relationship Between the Discrete and Continuous Fourier Transform [99] CHAPTER 7 DISCRETE CONVOLUTION AND CORRELATION [110] 7- 1 Discrete Convolution [110] 7-2 Graphical Discrete Convolution [111] 7-3 Relationship Between Discrete and Continuous Convolution [113] 7-4 Discrete Convolution Theorem [118] 7-5 Discrete Correlation [119] 7-6 Graphical Discrete Correlation [119] 3-6 Frequency Shifting [37] 3-7 Alternate Inversion Formula [40] 3-8 Even Functions [40] 3-9 Odd Functions [41] 3-10 Waveform Decomposition [42] 3- 11 Complex Time Functions [43] 3- 12 Summary of Properties [46] CHAPTER 4 CONVOLUTION AND CORRELATION [50] 4- 1 Convolution Integral [50] 4- 2 Graphical Evaluation of the Convolution Integral [50] 4-3 Alternate Form of the Convolution Integral [54] 4-4 Convolution Involving Impulse Functions [57] 4-5 Convolution Theorem [58] 4-6 Frequency Convolution Theorem [61] 4-7 Proof of Parseval’s Theorem [64] 4-8 Correlation [64] 4- 9 Correlation Theorem [66] CHAPTER 5 FOURIER SERIES AND SAMPLED WAVEFORMS [75] 5- 1 Fourier Series [75] 5-2 Fourier Series as a Special Case of the Fourier Integral [78] 5-3 Waveform Sampling [80] 5-4 Sampling Theorem [83] 5- 5 Frequency Sampling Theorem [87] CHAPTER 6 THE DISCRETE FOURIER TRANSFORM [91] 6- 1 A Graphical Development [91] 6-2 Theoretical Development [94] 6-3 Discrete Inverse Fourier Transform [98] 6- 4 Relationship Between the Discrete and Continuous Fourier Transform [99] CHAPTER 7 DISCRETE CONVOLUTION AND CORRELATION [110] 7- 1 Discrete Convolution [110] 7-2 Graphical Discrete Convolution [111] 7-3 Relationship Between Discrete and Continuous Convolution [113] 7-4 Discrete Convolution Theorem [118] 7-5 Discrete Correlation [119] 7-6 Graphical Discrete Correlation [119] CHAPTER 8 DISCRETE FOURIER TRANSFORM PROPERTIES [123] 8-1 Linearity [123] 8-2 Symmetry [123] 8-3 Time Shifting [124] 8-4 Frequency Shifting [124] 8-5 Alternate Inversion Formula [124] 8-6 Even Functions [125] 8-7 Odd Functions [126] 8-8 Waveform Decomposition [126] 8- 9 Complex Time Functions [127] 8-10 Frequency Convolution Theorem [127] 8-11 Discrete Correlation Theorem [128] 8-12 Parseval’s Theorem [130] 8-13 Summary of Properties [130] CHAPTER 9 APPLYING THE DISCRETE FOURIER TRANSFORM [132] 9- 1 Fourier Transforms [132] 9-2 Inverse Fourier Transform Approximation [135] 9-3 Fourier Series Harmonic Analysis [137] 9-4 Fourier Series Harmonic Synthesis [140] 9-5 Leakage Reduction [140] CHAPTER 10 THE FAST FOURIER TRANSFORM (FFT) [148] 10-1 Matrix Formulation [148] 10-2 Intuitive Development [149] 10-3 Signal Flow Graph [153] 10-4 Dual Nodes [154] 10-5 Wp Determination [156] 10-6 Unscrambling the FFT [158] 10-7 FFT Computation Flow Chart [160] 10-8 FFT FORTRAN Program [163] 10-9 FFT ALGOL Program [163] 10- 10 FFT Algorithms for Real Data [163] CHAPTER 11 THEORETICAL DEVELOPMENT OF THE BASE 2 FFT ALGORITHM [172] 11- 1 Definition of Notation [172] 11-2 Factorization of Wp [173] 11-3 Derivation of the Cooley-Tukey Algorithm for N=2y [176] 11-4 Canonic Forms of the FFT [177] CHAPTER 12 FFT ALGORITHMS FOR ARBITRARY FACTORS [184] 12-1 FFT Algorithm for N = r1r2 [184] 12-2 Cooley-Tukey Algorithm for N = r1 r2 ... rm [188] 12-3 Sande-Tukey Algorithm for N = r1r2 ... rm [190] 12-4 Twiddle Factor FFT Algorithms [191] 12-5 Computations Required by Base 2, Base 4, Base 8, and Base 16 Algorithms [193] 12-6 Summary of FFT Algorithms [195] CHAPTER 13 FFT CONVOLUTION AND CORRELATION [198] 13-1 FFT Convolution of Finite Duration Waveforms [199] 13-2 FFT Correlation of Finite Duration Waveforms [202] 13-3 FFT Convolution of an Infinite and a Finite Duration Waveform [206] 13-4 Efficient FFT Convolution [217] 13-5 Applications Summary [221] APPENDIX A THE IMPULSE FUNCTION: A DISTRIBUTION [224] A-l Impulse Function Definitions [224] A-2 Distribution Concepts [226] A-3 Properties of Impulse Functions [228]
Item type | Home library | Shelving location | Call number | Materials specified | Copy number | Status | Date due | Barcode | Course reserves |
---|---|---|---|---|---|---|---|---|---|
Libros | Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 65 B855 (Browse shelf) | Available | A-3788 | ||||
Libros | Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 65 B855 (Browse shelf) | Ej. 2 | Available | A-6678 |
Bibliografía: p. 231-246.
CHAPTER 1 INTRODUCTION [1] --
1-1 Transform Analysis [1] --
1-2 Basic Fourier Transform Analysis [3] --
1-3 The Ubiquitous Fourier Transform [7] --
1-4 Digital Computer Fourier Analysis [7] --
1- 5 Historical Summary of the Fast Fourier Transform [8] --
CHAPTER 2 THE FOURIER TRANSFORM [11] --
2- 1 The Fourier Integral [11] --
2-2 The Inverse Fourier Transform [13] --
2-3 Existence of the Fourier Integral [15] --
2-4 Alternate Fourier Transform Definitions [23] --
2- 5 Fourier Transform Pairs [28] --
CHAPTER 3 FOURIER TRANSFORM PROPERTIES [31] --
3-1 Linearity [31] --
3-2 Symmetry [32] --
3-3 Time Scaling [32] --
3-4 Frequency Scaling [35] --
3-5 Time Shifting [37] --
3-6 Frequency Shifting [37] --
3-7 Alternate Inversion Formula [40] --
3-8 Even Functions [40] --
3-9 Odd Functions [41] --
3-10 Waveform Decomposition [42] --
3-11 Complex Time Functions [43] --
3-12 Summary of Properties [46] --
CHAPTER 4 CONVOLUTION AND CORRELATION [50] --
4- 1 Convolution Integral [50] --
4- 2 Graphical Evaluation of the Convolution Integral [50] --
4-3 Alternate Form of the Convolution Integral [54] --
4-4 Convolution Involving Impulse Functions [57] --
4-5 Convolution Theorem [58] --
4-6 Frequency Convolution Theorem [61] --
4-7 Proof of Parseval’s Theorem [64] --
4-8 Correlation [64] --
4- 9 Correlation Theorem [66] --
CHAPTER 5 FOURIER SERIES AND SAMPLED WAVEFORMS [75] --
5- 1 Fourier Series [75] --
5-2 Fourier Series as a Special Case of the Fourier Integral [78] --
5-3 Waveform Sampling [80] --
5-4 Sampling Theorem [83] --
5- 5 Frequency Sampling Theorem [87] --
CHAPTER 6 THE DISCRETE FOURIER TRANSFORM [91] --
6- 1 A Graphical Development [91] --
6-2 Theoretical Development [94] --
6-3 Discrete Inverse Fourier Transform [98] --
6- 4 Relationship Between the Discrete and Continuous Fourier Transform [99] --
CHAPTER 7 DISCRETE CONVOLUTION AND CORRELATION [110] --
7- 1 Discrete Convolution [110] --
7-2 Graphical Discrete Convolution [111] --
7-3 Relationship Between Discrete and Continuous Convolution [113] --
7-4 Discrete Convolution Theorem [118] --
7-5 Discrete Correlation [119] --
7-6 Graphical Discrete Correlation [119] --
3-6 Frequency Shifting [37] --
3-7 Alternate Inversion Formula [40] --
3-8 Even Functions [40] --
3-9 Odd Functions [41] --
3-10 Waveform Decomposition [42] --
3- 11 Complex Time Functions [43] --
3- 12 Summary of Properties [46] --
CHAPTER 4 CONVOLUTION AND CORRELATION [50] --
4- 1 Convolution Integral [50] --
4- 2 Graphical Evaluation of the Convolution Integral [50] --
4-3 Alternate Form of the Convolution Integral [54] --
4-4 Convolution Involving Impulse Functions [57] --
4-5 Convolution Theorem [58] --
4-6 Frequency Convolution Theorem [61] --
4-7 Proof of Parseval’s Theorem [64] --
4-8 Correlation [64] --
4- 9 Correlation Theorem [66] --
CHAPTER 5 FOURIER SERIES AND SAMPLED WAVEFORMS [75] --
5- 1 Fourier Series [75] --
5-2 Fourier Series as a Special Case of the Fourier Integral [78] --
5-3 Waveform Sampling [80] --
5-4 Sampling Theorem [83] --
5- 5 Frequency Sampling Theorem [87] --
CHAPTER 6 THE DISCRETE FOURIER TRANSFORM [91] --
6- 1 A Graphical Development [91] --
6-2 Theoretical Development [94] --
6-3 Discrete Inverse Fourier Transform [98] --
6- 4 Relationship Between the Discrete and Continuous Fourier Transform [99] --
CHAPTER 7 DISCRETE CONVOLUTION AND CORRELATION [110] --
7- 1 Discrete Convolution [110] --
7-2 Graphical Discrete Convolution [111] --
7-3 Relationship Between Discrete and Continuous Convolution [113] --
7-4 Discrete Convolution Theorem [118] --
7-5 Discrete Correlation [119] --
7-6 Graphical Discrete Correlation [119] --
CHAPTER 8 DISCRETE FOURIER TRANSFORM PROPERTIES [123] --
8-1 Linearity [123] --
8-2 Symmetry [123] --
8-3 Time Shifting [124] --
8-4 Frequency Shifting [124] --
8-5 Alternate Inversion Formula [124] --
8-6 Even Functions [125] --
8-7 Odd Functions [126] --
8-8 Waveform Decomposition [126] --
8- 9 Complex Time Functions [127] --
8-10 Frequency Convolution Theorem [127] --
8-11 Discrete Correlation Theorem [128] --
8-12 Parseval’s Theorem [130] --
8-13 Summary of Properties [130] --
CHAPTER 9 APPLYING THE DISCRETE FOURIER TRANSFORM [132] --
9- 1 Fourier Transforms [132] --
9-2 Inverse Fourier Transform Approximation [135] --
9-3 Fourier Series Harmonic Analysis [137] --
9-4 Fourier Series Harmonic Synthesis [140] --
9-5 Leakage Reduction [140] --
CHAPTER 10 THE FAST FOURIER TRANSFORM (FFT) [148] --
10-1 Matrix Formulation [148] --
10-2 Intuitive Development [149] --
10-3 Signal Flow Graph [153] --
10-4 Dual Nodes [154] --
10-5 Wp Determination [156] --
10-6 Unscrambling the FFT [158] --
10-7 FFT Computation Flow Chart [160] --
10-8 FFT FORTRAN Program [163] --
10-9 FFT ALGOL Program [163] --
10- 10 FFT Algorithms for Real Data [163] --
CHAPTER 11 THEORETICAL DEVELOPMENT OF THE BASE 2 FFT --
ALGORITHM [172] --
11- 1 Definition of Notation [172] --
11-2 Factorization of Wp [173] --
11-3 Derivation of the Cooley-Tukey Algorithm for N=2y [176] --
11-4 Canonic Forms of the FFT [177] --
CHAPTER 12 FFT ALGORITHMS FOR ARBITRARY FACTORS [184] --
12-1 FFT Algorithm for N = r1r2 [184] --
12-2 Cooley-Tukey Algorithm for N = r1 r2 ... rm [188] --
12-3 Sande-Tukey Algorithm for N = r1r2 ... rm [190] --
12-4 Twiddle Factor FFT Algorithms [191] --
12-5 Computations Required by Base 2, Base 4, Base 8, and Base 16 Algorithms [193] --
12-6 Summary of FFT Algorithms [195] --
CHAPTER 13 FFT CONVOLUTION AND CORRELATION [198] --
13-1 FFT Convolution of Finite Duration Waveforms [199] --
13-2 FFT Correlation of Finite Duration Waveforms [202] --
13-3 FFT Convolution of an Infinite and a Finite Duration Waveform [206] --
13-4 Efficient FFT Convolution [217] --
13-5 Applications Summary [221] --
APPENDIX A THE IMPULSE FUNCTION: A DISTRIBUTION [224] --
A-l Impulse Function Definitions [224] --
A-2 Distribution Concepts [226] --
A-3 Properties of Impulse Functions [228] --
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