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# V F* N! d. D5 t4 X* h8 ?9 \Chapter 1. Signals and Systems 1
: m& {0 I& ^! Y6 a5 ~8 r" \1.1 Introduction 16 h1 l: J. W J
1.2 Discrete-Time Signals 1
. M, D5 @* H; Q: d. m, N. K9 {7 @1.2.1 Complex Sequences 2- H, K; b. _/ z& c- T% w, c8 f
1.2.2 Some Fundamental Sequences 2! X" E$ K# Q3 u+ M5 g: B9 X
1.2.3 Signal Duration 3
" }$ N6 u4 @ V. U+ [+ C, i4 x1.2.4 Periodic and Aperiodic Sequences 3
, D- T z( U) ?% g4 \3 z1.2.5 Symmetric Sequences 4
1 ~6 C8 W) K! Y* S9 |1.2.6 Signal Manipulations 46 q3 Z$ ?( i _ T4 r
1.2.7 Signal Decomposition 67 x0 w, B$ U7 C+ F: g' b
1.3 Discrete-Time Systems 78 S' s7 _% Y7 f+ l) x( s4 F; P9 z
1.3.1 Systems Properties 76 Q2 \8 Z; g0 f% V
1.4 Convolution 11
. t) M, L% q: J6 [0 {& s, n1.4.1 Convolution Properties 11
, C- J. G8 l$ c% \( j1.4.2 PeRForming Convolutions 12' `; T% r! [& q2 V1 [8 W6 W v! w7 X
1.5 Difference Equations 155 [1 c& U5 T: N$ q
Solved Problems 181 D7 }% g. i7 Z" K ?5 d
Chapter 2. Fourier Analysis 55
# ^* d/ c7 V9 X# @. J4 b* u0 b2.1 Introduction 55
. K5 ~2 a0 _& l$ n# m2.2 Frequency Response 55, { ]/ _: k# x8 |- f
2.3 Filters 58
, M! c3 j" Z$ L2.4 Interconnection of Systems 596 u) V/ H6 _7 E* i: P
2.5 The Discrete-Time Fourier Transform 61
8 \- G9 o& a' v) \8 C: y0 R# ~* f2.6 DTFT Properties 629 _+ ]1 v3 {4 @- v
2.7 Applications 64
) o# E& O2 j {( q1 Z) |2 u6 Z$ I$ E* a2.7.1 LSI Systems and LCCDEs 64
7 e$ @1 A* z7 A4 H; I0 B7 ?8 k6 l2.7.2 Performing Convolutions 65: g+ m( ?' T' E0 X
2.7.3 Solving Difference Equations 661 @7 I5 s/ ~9 c1 Z m
2.7.4 Inverse Systems 66
% B' i+ `$ s% Y( E) V3 ?& k OSolved Problems 67
0 e; \: L; Q/ q. D. F, lChapter 3. Sampling 101
* q% `' q1 \/ U3.1 Introduction 101
4 [6 C) v2 G9 a; V: U3.2 Analog-to-Digital Conversion 101
& \: z" }; r+ ]! |1 ?/ d3.2.1 Periodic Sampling 101
2 X; A1 `6 x v% Y4 C T3.2.2 Quantization and Encoding 104
, w9 ^- t4 [2 Y$ Y3.3 Digital-to-Analog Conversion 106, B z4 V, K) k5 e/ w
3.4 Discrete-Time Processing of Analog Signals 108
) v5 n8 k" r' W3.5 Sample Rate Conversion 110
$ w3 p9 K& Y) E! y6 S. ^" \3.5.1 Sample Rate Reduction by an Integer Factor 110
" v4 M( H1 K8 J9 K0 O8 u3.5.2 Sample Rate Increase by an Integer Factor 1118 \; r5 c# y/ u% Z* U
3.5.3 Sample Rate Conversion by a Rational Factor 113
* i; [: o" _9 DSolved Problems 114
; H! V4 y) u7 v/ EChapter 4. The Z-Transform 1422 z/ m5 }* Y7 ^: Q
4.1 Introduction 1429 b, Z' c2 a- X) G$ {! {
4.2 Definition of the z-Transform 142
# Y1 e3 L3 \) N$ Y# f; H4.3 Properties 1469 p" z7 g: H; D& J1 v& @
vii. E$ P$ e: L4 f/ S3 W/ [/ a) j" t/ ~
4.4 The Inverse z-Transform 1494 P, E m% |# t4 f+ t. O0 X
4.4.1 Partial Fraction Expansion 149, K1 ^$ L. u3 w! L3 r6 ~
4.4.2 Power Series 150' ]* ?5 w- l' N. s$ w5 o
4.4.3 Contour Integration 151+ a4 R ?" l& l a" @ r7 v
4.5 The One-Sided z-Transform 1513 H4 {6 ~5 j1 D$ U0 a
Solved Problems 152
: R9 E" }8 P! T5 wChapter 5. Transform Analysis of Systems 183
- \& F* r" `: [% m5.1 Introduction 183: Z( a' C; l9 a7 o/ G
5.2 System Function 183+ S! U4 O& O5 g1 ^+ T! x$ O
5.2.1 Stability and Causality 184
2 W" s2 | d* a) z5.2.2 Inverse Systems 186
, O" T! E& `2 O5.2.3 Unit Sample Response for Rational System Functions 1874 {! U* l; x4 r
5.2.4 Frequency Response for Rational System Functions 188
4 o: o. r) ]$ I4 U5.3 Systems with Linear Phase 189
I+ ]% M! s1 u, L8 c; B& l% Z1 A' K5.4 Allpass Filters 1938 S I, R1 C, i; s
5.5 Minimum Phase Systems 1949 q! q( E7 W9 o2 _' z
5.6 Feedback Systems 195/ L* A! ^& H& Q! K0 Y
Solved Problems 196
7 V6 A5 D' a, Y* g) XChapter 6. The DFT 223# A4 i# W8 R$ m5 m
6.1 Introduction 223! W: Q1 o# \1 @- |9 m$ Y5 y
6.2 Discrete Fourier Series 2232 M) s4 ~5 F. G. x; n
6.3 Discrete Fourier Transform 226" \' R2 _/ X: r) y
6.4 DFT Properties 227
0 p( z3 ]" X5 Y$ y* j2 T+ n" `$ {6.5 Sampling the DTFT 231
& r7 ?2 J6 Z+ p) {. x. D0 A6.6 Linear Convolution Using the DFT 232
/ Z8 O+ S y2 l5 NSolved Problems 2352 }, e/ Z6 @0 b9 X* q
Chapter 7. The Fast Fourier Transform 262
: Q( |' Y% ]5 u- g" s7.1 Introduction 262' X8 l/ q" c+ W) s% C# m# P
7.2 Radix-2 FFT Algorithms 262
, S& m2 l- J% p4 X3 U: N8 T9 s7.2.1 Decimation-in-Time FFT 262
- E6 K( x# Y k. Q7.2.2 Decimation-in-Frequency FFT 266
0 O" l& [& t9 L) j5 G7.3 FFT Algorithms for Composite N 267! a" }. k+ b+ k/ q& U$ l; U
7.4 Prime Factor FFT 271
) E8 |+ m6 e# [( W: HSolved Problems 2738 q: K7 }2 {) A5 ~" [6 `' U
Chapter 8. Implementation of Discrete-Time Systems 287! K, K( @; u% O# W: f% I' Z
8.1 Introduction 2871 t, t; H) z5 I* u5 n1 p: ?
8.2 Digital Networks 287
5 ^8 S! N% {) M9 s. [8.3 Structures for FIR Systems 289& w2 U. H a2 t. i" \
8.3.1 Direct Form 2897 n; \7 f$ _( h1 p
8.3.2 Cascade Form 289
$ b" g. u! k! o7 A- k8 `8.3.3 Linear Phase Filters 2896 } g( {+ B/ y3 A0 q& @5 S" u c
8.3.4 Frequency Sampling 2913 i( M) z- ~, o: y. E z: z
8.4 Structures for IIR Systems 291
9 R' o* e. g% P8.4.1 Direct Form 292
$ i1 @, h+ \8 T) K+ s0 z8.4.2 Cascade Form 294" u/ R9 K* H! g1 H
8.4.3 Parallel Structure 295
P8 G Y% |1 E* F8.4.4 Transposed Structures 296+ o+ p Y6 I8 s; Y* \3 d
8.4.5 Allpass Filters 2964 n% T. E, q, W& T- }* C
8.5 Lattice Filters 298
1 V! u2 z" H0 `/ s8.5.1 FIR Lattice Filters 298
, V4 L: m: R& J+ H. l8.5.2 All-Pole Lattice Filters 300! L! T7 _8 |8 v0 U; H
viii
% n* z+ ~- l) Q8 o8.5.3 IIR Lattice Filters 301+ k7 r; @1 Q/ M$ P* n! \
8.6 Finite Word-Length Effects 302
* A5 A7 F7 R6 |& `! F) L8.6.1 Binary Representation of Numbers 302
. { \6 k9 u( g9 T& d8.6.2 Quantization of Filter Coefficients 304
4 F/ m! v" o) J$ ^8.6.3 Round-Off Noise 306- v) p* E" e) }1 }* E1 I- D
8.6.4 Pairing and Ordering 309
, _& }$ d0 \& I0 d8.6.5 Overflow 309
: M! }, i) j, D1 V# n$ C$ {Solved Problems 310
9 l$ W# L' G3 m9 @Chapter 9. Filter Design 358
) K/ }) A1 m% }' L, H$ m9.1 Introduction 358
% G1 ?7 U3 N9 }9.2 Filter Specifications 358& x" ]3 ^2 i) J( x4 J; w- |, R4 P N
9.3 FIR Filter Design 359
3 j9 ^) T/ Z/ f" @3 `+ W9.3.1 Linear Phase FIR Design Using Windows 359
1 |' x/ V# D9 E. X+ J2 R4 E9.3.2 Frequency Sampling Filter Design 363
3 |! Y$ d6 R8 J& C2 }0 g9.3.3 Equiripple Linear Phase Filters 363
/ G; N! x; ]* F9 C& R0 A! d9.4 IIR Filter Design 366
2 s0 Y4 i; f) b$ D9.4.1 Analog Low-Pass Filter Prototypes 3676 o7 f! v: q& h4 ^
9.4.2 Design of IIR Filters from Analog Filters 373" j& A$ [3 l! X8 ^: n5 K& m1 [
9.4.3 Frequency Transformations 376* H6 O$ V R3 W/ k" A7 z
9.5 Filter Design Based on a Least Squares Approach 376
5 b4 o+ H7 T. @% E( z5 N9.5.1 Pade Approximation 377* T! F7 D! S. x" t; `' k
9.5.2 Prony's Method 378
9 X- n l' C3 X; ?- S. p; b9.5.3 FIR Least-Squares Inverse 379
( O- ]/ J8 r, _3 x) z8 \4 v5 LSolved Problems |
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