Digital Processing of Signals Theory and Practice

by Bellanger, Maurice

• ISBN13: 9780471976738
• ISBN10: 0471976733
• Edition: 3rd
• Format: Hardcover
• Copyright: 2000-04-14
• Publisher: WILEY
• More Book Details
• Purchase Benefits

Summary

The latest, completely revised edition of this highly successful volume outlines the techniques for the digital processing of signals (DSP) providing a clear discussion of the technical problems. Essential theories of DSP are discussed in a clear and concise manner and the merits of the various techniques are also compared. New developments such as Fourier transforms, filter banks, and applications of DSP in telecommunications are covered in detail. Special features include: * exercises which enable the reader to have a more pragmatic understanding of the topics discussed * a new chapter on filter banks * updated information on finite impulse response (FIR) filters It will prove an invaluable text for practising development engineers, researchers and students working in advanced electronic and electrical engineering.

Author Biography

Maurice Bellanger is the author of Digital Processing of Signals: Theory and Practice, 3rd Edition, published by Wiley.

Table of Contents

Foreword	xi
Preface	xiii
Introduction	xv
Signal Digitizing---Sampling and Coding	1	(40)
Fourier analysis	1	(4)
Fourier series expansion of a periodic function	1	(2)
Fourier transform of a function	3	(2)
Distributions	5	(3)
Definition	5	(1)
Differentiation of distributions	6	(1)
The Fourier transform of a distribution	7	(1)
Some commonly studied signals	8	(6)
Determinist signals	8	(1)
Random signals	9	(2)
Gaussian signals	11	(3)
Peak factor of a random signal	14	(1)
The norms of a function	14	(1)
Sampling	15	(2)
Frequency sampling	17	(1)
The sampling theorem	18	(2)
Sampling of sinusoidal and random signals	20	(4)
Sinusoidal signals	20	(2)
Discrete random signals	22	(1)
Discrete noise generation	23	(1)
Quantization	24	(3)
The coding dynamic range	27	(3)
Non-linear coding with the 13-segment A-law	30	(2)
Optimal coding	32	(2)
Quantity of information and channel capacity	34	(1)
Binary representations	35	(6)
Appendix 1 The function I(x)	36	(1)
Appendix 2 The reduced normal distribution	37	(1)
References	37	(1)
Exercises	38	(3)
The Discrete Fourier Transform	41	(31)
Definition and properties of the discrete Fourier transform (DFT)	42	(1)
Fast Fourier transform (FFT)	43	(10)
Decimation-in-time fast Fourier transform	44	(4)
Decimation-in-frequency fast Fourier transform	48	(1)
Radix 4 FFT algorithm	49	(3)
Split radix FFT algorithm	52	(1)
Degradation arising from worldength-limitation effects	53	(4)
Effects of coefficient quantization	53	(1)
Round-off noise in the FFT	54	(3)
Calculation of a spectrum using the DFT	57	(4)
The filtering function of the DFT	58	(2)
Spectral resolution	60	(1)
Fast convolution	61	(2)
Calculation of a DFT using convolution	63	(1)
Implementation	64	(8)
Appendix 1 FFT Program (with binary inversion)	66	(2)
Appendix 2 FFT Program (without binary inversion)	68	(1)
References	69	(1)
Exercises	70	(2)
Other Fast Algorithms for the FFT	72	(21)
Kronecker product of matrices	72	(1)
Factorizing the matrix of a decimation-in-frequency algorithm	73	(3)
Partial transforms	76	(9)
Transform of real data and odd DFT	77	(2)
The odd-time odd-frequency DFT	79	(3)
Sine and cosine transforms	82	(2)
The two-dimensional DCT	84	(1)
Other fast algorithms	85	(3)
Number-theoretic transforms	88	(5)
References	91	(1)
Exercises	91	(2)
Time-Invariant Discrete Linear Systems	93	(12)
Definition and properties	93	(2)
The Z-transform	95	(2)
Energy and power of discrete signals	97	(1)
Filtering of random signals	98	(2)
Systems defined by difference equations	100	(2)
State variable analysis	102	(3)
References	103	(1)
Exercises	104	(1)
Finite Impulse Response (FIR) Filters	105	(48)
FIR filters	105	(4)
Practical transfer functions and linear phase filters	109	(3)
Calculation of coefficients by Fourier series expansion for frequency specifications	112	(5)
Calculation of coefficients by the method of least squares	117	(3)
Calculation of coefficients by discrete Fourier transform	120	(1)
Calculation of coefficients by Chebyshev approximation	121	(3)
Relationships between the number of coefficients and the filter characteristic	124	(3)
Raised cosine transition filter	127	(1)
Structures for implementing FIR filters	128	(2)
Limitation of the number of bits for coefficients	130	(3)
Limitation of the number of bits in internal memories	133	(3)
Z-transfer function of an FIR filter	136	(1)
Minimum phase filters	137	(3)
Design of filters with a large number of coefficients	140	(2)
Two-dimensional FIR filters	142	(3)
Coefficients of two-dimensional FIR filters by the method of least squares	145	(8)
Appendix Example of FIR filter design	150	(1)
References	150	(1)
Exercises	151	(2)
Infinite Impulse Response (IIR) Filter Sections	153	(30)
First-order section	153	(5)
Purely recursive second-order section	158	(9)
General second-order section	167	(4)
Structures for implementation	171	(4)
Coefficient wordlength limitation	175	(2)
Internal data wordlength limitation	177	(1)
Stability and limit-cycles	178	(5)
References	181	(1)
Exercises	181	(2)
Infinite Impulse Response Filters	183	(55)
General expressions for the properties of IIR filters	183	(2)
Direct calculation of the coefficients using model functions	185	(12)
Impulse invariance	185	(1)
Bilinear transformation	186	(2)
Butterworth filters	188	(3)
Elliptic filters	191	(4)
Calculating any filter by transformation of a low-pass filter	195	(2)
Iterative techniques for calculating IIR filters with frequency specifications	197	(3)
Minimizing the mean square error	197	(2)
Chebyshev approximation	199	(1)
Filters based on spheroidal sequences	200	(2)
Structures representing the transfer function	202	(6)
Direct structures	202	(2)
Decomposed structures	204	(2)
Basic structure of phase shifters	206	(2)
Limiting the coefficient wordlength	208	(4)
Coefficient wordlength for the cascade structure	212	(2)
Round-off noise	214	(7)
Determining internal data wordlength	221	(4)
Auto-oscillations	225	(1)
Comparison of IIR and FIR filters	225	(13)
Appendix Program to determine the coefficients of an elliptic filter (CERII)	228	(7)
References	235	(2)
Exercises	237	(1)
Digital Ladder Filters	238	(26)
Properties of two-port circuits	238	(4)
Simulated ladder filters	242	(5)
Switched-capacitor filters	247	(3)
Wave filters	250	(5)
Lattice filters	255	(6)
Comparison elements	261	(3)
References	262	(1)
Exercises	263	(1)
Complex Signals and Minimum Phase Filters	264	(16)
The Fourier transform of a real and causal set	264	(3)
Analytic signals	267	(4)
Calculating the coefficents of an FIR quadrature filter	271	(3)
Recursive 90° phase shifters	274	(1)
Single side-band modulation	275	(2)
Minimum phase filters	277	(3)
References	278	(1)
Exercises	278	(2)
Multirate Filtering	280	(29)
Complements in sampling theory	280	(3)
Decomposition of a low-pass FIR filter	283	(3)
Half-band FIR filters	286	(3)
Decomposition with half-band filters	289	(6)
Implementation structures	295	(3)
Advantages of the phase shift function	298	(4)
Multirate filtering with IIR elements	302	(3)
Filter banks using polyphase networks and DFT	305	(1)
Conclusion	306	(3)
References	307	(1)
Exercises	308	(1)
Filter Banks	309	(27)
Decomposition and reconstruction	309	(2)
Analysing the elements of the polyphase network	311	(2)
Determining the inverse functions	313	(3)
QMF filters	316	(4)
Banks of paseudo-QMF filters	320	(5)
Determining the coefficients of the prototype filter	325	(5)
Realizing a bank of real filters	330	(3)
Filter banks with perfect decomposition and reconstruction	333	(3)
References	335	(1)
Adaptive Filtering	336	(36)
Calculation of the coefficients of an FIR filter for specifications in time	336	(2)
Autocorrelation and intercorrelation	338	(3)
Autocorrelation matrix---eigenvalues	341	(2)
Recursive estimation	343	(2)
The gradient algorithm	345	(2)
Convergence conditions	347	(2)
Time constant	349	(3)
Residual error	352	(3)
Parameters of complexity	355	(2)
Normalized algorithms and sign algorithms	357	(2)
Adaptive FIR filtering in cascade form	359	(2)
Adaptive IIR filtering	361	(3)
Linear prediction	364	(4)
Conclusions	368	(4)
References	369	(1)
Exercises	370	(2)
Circuits and Factors of Complexity	372	(22)
Binary representations	372	(3)
Types of circuit	375	(2)
Serial multipliers	377	(2)
Serial-parallel multipliers	379	(2)
Parallel multipliers	381	(2)
Comparison of distributed and residue arithmetic	383	(3)
Memories and auxiliary circuits	386	(1)
Processors	387	(1)
Choosing the complexity parameters	388	(2)
System architecture	390	(4)
References	392	(1)
Exercises	392	(2)
Applications in Telecommunications	394	(26)
Advantages and limitations of digital techniques	394	(2)
Frequency detection	396	(2)
Phase-locked loop	398	(1)
PCM time-division multiplexing	399	(2)
Adaptive differential PCM (ADPCM)	401	(4)
Frequency-division multiplexing---transmultiplexer	405	(2)
Coding of sound	407	(1)
Speech synthesizer	408	(2)
Modems	410	(1)
Echo cancellation	411	(1)
Television image processing	412	(2)
Multicarrier transmission---OFDM	414	(6)
References	418	(2)
Exercises: solutions and hints	420	(7)
Index	427