Record Nr.

UNINA9910782389603321

Autore

Sundararajan D

Titolo

The discrete fourier transform [[electronic resource] ] : theory, algorithms and applications / / D. Sundararajan

Pubbl/distr/stampa


Singapore ; ; River Edge, NJ, : World Scientific, c2001

ISBN

1-281-95180-3

9786611951801

981-281-029-3

Descrizione fisica

1 online resource (392 p.)

Disciplina

530.15/5723

Soggetti

Fourier transformations

Mathematical physics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Preface; Contents; Abbreviations; Chapter 1 Introduction; 1.1 The Transform Method; 1.2 The Organization of this Book; Chapter 2 The Discrete Sinusoid; 2.1 Signal Representation; 2.2 The Discrete Sinusoid; 2.3 Summary and Discussion; Chapter 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; Chapter 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; Chapter 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; Chapter 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; Chapter 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; Chapter 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; Chapter 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 Chapter 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; Chapter 11 Aliasing and Other Effects; 11.1 Aliasing Effect; 11.2 Leakage Effect; 11.3 Picket-Fence Effect; 11.4 Summary and Discussion; Chapter 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

Chapter 13 The Continuous-Time Fourier Transform

Sommario/riassunto

This authoritative 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-Hadamard transforms. The large number of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and