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& w% e% f8 i6 p' ^Chapter 1. Signals and Systems 1
/ k- W7 x% K2 Z: P3 p( o1.1 Introduction 19 n9 `! {- _+ H2 V+ D; `7 ?( J
1.2 Discrete-Time Signals 1& k7 q7 q3 H+ c+ L0 r1 R" X2 O
1.2.1 Complex Sequences 2. ?' k+ A0 I# H9 q' ?# Y
1.2.2 Some Fundamental Sequences 2
' Z' c- c, K3 O6 n" a* ^; A1.2.3 Signal Duration 3# x$ W" g2 a- a$ q1 H5 h- I
1.2.4 Periodic and Aperiodic Sequences 3% w- J. L# g1 r, r& E( b
1.2.5 Symmetric Sequences 4' r$ u+ E- p( C
1.2.6 Signal Manipulations 49 X7 l' q6 G, O; e1 L$ }! J
1.2.7 Signal Decomposition 6
8 E* E, K* C, U% x1.3 Discrete-Time Systems 7
% x5 l9 r) o! L1.3.1 Systems Properties 7
9 ]" P& i4 h, O1.4 Convolution 11
: {4 A3 W/ i+ i! s7 D1.4.1 Convolution Properties 11
0 D; y, t! L3 k) t' h. w1.4.2 PeRForming Convolutions 12
3 a) v% I/ e3 S1.5 Difference Equations 15
! B# ~7 k3 \2 MSolved Problems 181 t/ _2 @# s. e) ~0 \9 _+ K
Chapter 2. Fourier Analysis 55 s8 \6 _- @* L5 T
2.1 Introduction 55
/ Q9 t& I* @, s& w3 l7 O, G2.2 Frequency Response 555 B0 ? D- @; T
2.3 Filters 58
7 \- M" p& e4 ?/ k, z2.4 Interconnection of Systems 59* d9 N9 {& o0 W( W( m5 b
2.5 The Discrete-Time Fourier Transform 61
# ^1 F! D# t' f9 d2.6 DTFT Properties 62
: O7 z4 V4 W% ?7 x2 u0 T5 i7 q2.7 Applications 64
7 w0 U) c3 S7 A+ X5 H3 P+ j8 {$ R F2.7.1 LSI Systems and LCCDEs 64
2 J" B0 M5 V) w( ]* v2.7.2 Performing Convolutions 65& T3 T# j0 Q' m4 e+ e# N( X. w1 b
2.7.3 Solving Difference Equations 66
% }3 F3 {; S2 @& R9 n6 [1 k% P2.7.4 Inverse Systems 66
- T' x! L1 ~+ Q( q& I+ q# l& hSolved Problems 67
5 W5 {1 D) M" @# M0 N8 _) tChapter 3. Sampling 101
6 c$ i& W7 H, o) U, Y1 i3.1 Introduction 101" ?' {# l" m: \# J' t5 ]
3.2 Analog-to-Digital Conversion 101
3 _- E( B* @8 _5 ~- A8 ~3.2.1 Periodic Sampling 101
, q+ w# s; q- q, D3.2.2 Quantization and Encoding 104
. t" H6 e$ j( Z% Z3.3 Digital-to-Analog Conversion 106, O2 c. K$ g) a0 t
3.4 Discrete-Time Processing of Analog Signals 108 L; L& t! B3 {2 {* z" B
3.5 Sample Rate Conversion 110. L9 R; r3 i9 H4 p( |
3.5.1 Sample Rate Reduction by an Integer Factor 110' g% ?8 l2 V5 i7 [$ q
3.5.2 Sample Rate Increase by an Integer Factor 1119 _( F, g: \2 \" x( K) P
3.5.3 Sample Rate Conversion by a Rational Factor 113+ A6 H7 ^/ B/ Q/ V6 _( S7 y
Solved Problems 1149 l' W& f# J9 T% H) B% V9 k
Chapter 4. The Z-Transform 142
; }1 J, |5 v+ U4.1 Introduction 142
- ]& I. B- a1 d2 C% _: `4.2 Definition of the z-Transform 142& q$ J) P& K1 {2 ]7 S% g- N7 X' e
4.3 Properties 146; @+ f, J/ Z9 j- H
vii! b1 n k8 h5 }8 i9 i/ I( P' ~" f
4.4 The Inverse z-Transform 149
! E7 e e' b6 \4.4.1 Partial Fraction Expansion 1493 l- u% M( m% G# Q' V. \" c
4.4.2 Power Series 150" w6 n) C4 I& h7 f% y. D% R( ?
4.4.3 Contour Integration 151; i" \0 t$ o6 x, V7 U B! j5 w- ^
4.5 The One-Sided z-Transform 151
9 E |+ A1 X" s8 c* [3 r" t* iSolved Problems 152; F: ]4 Y, J( B: P
Chapter 5. Transform Analysis of Systems 183
3 L( ~9 t/ @& t. ?& i5.1 Introduction 183& o' D( _/ r S- O, e% h! e) W
5.2 System Function 183( ~2 ~5 f3 q0 F) L. {
5.2.1 Stability and Causality 1847 D3 K) D% o* { {$ N
5.2.2 Inverse Systems 1860 Y& {- T4 @1 ]% b, \ W/ B
5.2.3 Unit Sample Response for Rational System Functions 187
! o% y1 J% ?) w5 h7 d" c5.2.4 Frequency Response for Rational System Functions 188, g. Y& V9 u3 w1 Z7 H* r
5.3 Systems with Linear Phase 189
* M/ _3 ^* P8 Q5.4 Allpass Filters 193" i0 s+ y, w7 X6 c' r
5.5 Minimum Phase Systems 194, r$ N8 c0 _, G( y3 X8 d7 Q! P
5.6 Feedback Systems 195
2 Y8 [) u% Q% vSolved Problems 196
y) h! U) r8 Z8 F* u9 bChapter 6. The DFT 223, X9 g% [; F; ]% A) g( N
6.1 Introduction 223
- C4 }; T" {6 `- b6.2 Discrete Fourier Series 2239 X. B1 H* G: u% r# x' e/ z
6.3 Discrete Fourier Transform 226
" ~) _/ K7 e% g' u4 v6 q8 n6.4 DFT Properties 227* O4 L- b; I* s) k4 v
6.5 Sampling the DTFT 2315 l* a w. R6 n7 H: X! O8 g5 k
6.6 Linear Convolution Using the DFT 232+ d# P' O, L7 t3 o
Solved Problems 235
1 c/ p2 g1 y; I+ XChapter 7. The Fast Fourier Transform 262
; w5 Q( @- g; T6 a4 @1 M* k7.1 Introduction 262
; z5 s. k7 G8 v! u" H# K7.2 Radix-2 FFT Algorithms 262
, E% M+ g1 t' U) g% D1 Y7.2.1 Decimation-in-Time FFT 262
; Q9 z- t7 E% @7.2.2 Decimation-in-Frequency FFT 266$ c" {1 G: G5 L4 T9 `
7.3 FFT Algorithms for Composite N 267
3 F) E! b+ r7 {% i2 X7.4 Prime Factor FFT 271) G# x0 a$ o7 M& _8 I
Solved Problems 273
+ [4 k& G( e# n" Y* z) yChapter 8. Implementation of Discrete-Time Systems 287
3 T% |% T7 P; V6 n" K/ B8.1 Introduction 287% Y0 R3 ?6 H$ f) T. y1 I5 ~
8.2 Digital Networks 287; L( L. p3 ~/ t
8.3 Structures for FIR Systems 289" N& q4 s0 y. u% U* ?, v7 @0 t
8.3.1 Direct Form 2899 h: Z' d. W: ~" K/ I
8.3.2 Cascade Form 289) o. H# \# |: j1 h. D4 s9 ^
8.3.3 Linear Phase Filters 289, b) x4 h2 W' x% I$ `$ J c; ?
8.3.4 Frequency Sampling 2910 S' r8 T0 x' e6 |* d
8.4 Structures for IIR Systems 291/ Z- e$ z& x* e X7 X% v/ B. q
8.4.1 Direct Form 292
. l1 l& G/ N4 t9 |9 ]$ f4 L8.4.2 Cascade Form 294
4 S1 v) }0 E b) ?8.4.3 Parallel Structure 295
( o, g! v1 k# y8.4.4 Transposed Structures 296
! B5 F1 P7 v8 c0 Q8.4.5 Allpass Filters 296
% B/ h# _( q: R: v1 |8.5 Lattice Filters 298
% h% e& A% o7 K1 j8 h8 D8.5.1 FIR Lattice Filters 298 p7 ~+ S2 T* h
8.5.2 All-Pole Lattice Filters 300
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: d, h: v0 k. ]$ C, _8.5.3 IIR Lattice Filters 301
( \0 @( J1 Z2 p+ b& q8.6 Finite Word-Length Effects 302- K- ?+ `' Z$ F- s0 p. x
8.6.1 Binary Representation of Numbers 3023 Z3 n# u4 E- H( A: n' w0 z
8.6.2 Quantization of Filter Coefficients 304
7 M- p: H; k9 j. R; n$ s9 {8.6.3 Round-Off Noise 3066 E# R: @! [( {6 a- C- K& Q
8.6.4 Pairing and Ordering 3095 q2 C4 \2 m1 h
8.6.5 Overflow 309& j- I, U3 n9 Z4 ]& i
Solved Problems 310
$ o' Y3 C0 b% N) q, v; d2 K9 FChapter 9. Filter Design 3582 g" f4 \+ J6 F/ `* u( I
9.1 Introduction 358) T* ^. z, m$ u7 s3 h8 N
9.2 Filter Specifications 3585 N5 J8 K1 V6 h. ~, M [' C
9.3 FIR Filter Design 359
8 j0 z3 e2 ]" S6 R3 t3 U# H9.3.1 Linear Phase FIR Design Using Windows 359. b% J5 ^( `# ^0 L9 f* Z; P
9.3.2 Frequency Sampling Filter Design 3631 G/ o& D5 I C! I' s+ z( `1 [. h
9.3.3 Equiripple Linear Phase Filters 3639 M: o. I/ n( t& [. I
9.4 IIR Filter Design 3667 {6 L8 a; x4 u* N; ^
9.4.1 Analog Low-Pass Filter Prototypes 3677 Y4 f) D) R9 \" T
9.4.2 Design of IIR Filters from Analog Filters 373
, ^$ C! }" a7 D2 f% o6 s: H& g9.4.3 Frequency Transformations 376; h8 ?& ~% I% U5 T4 @1 ?
9.5 Filter Design Based on a Least Squares Approach 376+ m# r$ X& ^2 z
9.5.1 Pade Approximation 377
/ f9 M" e% ~" n; _/ |' l/ p9.5.2 Prony's Method 378, u3 F/ x i& M& _" n
9.5.3 FIR Least-Squares Inverse 379' q6 B, k' Q' }+ v& ^7 r& P9 |2 ~
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