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Chapter 1. Signals and Systems 1
% r$ A5 u; w# G' @% o8 v! m1.1 Introduction 1
/ Y, P6 \% ~' s. E, V1.2 Discrete-Time Signals 1
% h2 C1 q }9 ]$ K. S, o5 Q5 v1.2.1 Complex Sequences 2: R% Z# j/ i# L X; D4 b' K2 }
1.2.2 Some Fundamental Sequences 2
$ q7 O# F; ?1 c# l1 B; G1.2.3 Signal Duration 3' L( m( k* Y6 O& ~9 |
1.2.4 Periodic and Aperiodic Sequences 3+ c. ]0 p0 |' v1 `8 X4 y! v
1.2.5 Symmetric Sequences 42 w' j& J: y, _: }' l
1.2.6 Signal Manipulations 4/ w q: Q8 z' }( [, g1 l; l' @5 ?
1.2.7 Signal Decomposition 66 g; S- z: ?) R9 ~
1.3 Discrete-Time Systems 73 d2 |* F7 C v2 G- i& k
1.3.1 Systems Properties 7
* ?; M0 U0 T9 z" e1.4 Convolution 11
- A( z; }) ^. }( N" b' M5 ~. k- A$ J1.4.1 Convolution Properties 11. V; O" O3 Y) g8 }) M. C L/ q2 J
1.4.2 PeRForming Convolutions 12
9 _7 X3 F+ |6 g9 P1.5 Difference Equations 15
2 h) t+ S4 l, \" tSolved Problems 18
* H" f# L( Y4 w& k% q( R7 U4 f# uChapter 2. Fourier Analysis 55
% e( a+ [3 R: F2 e. M: Q% X4 {2.1 Introduction 551 r! t0 i' F, Z6 a; c- f
2.2 Frequency Response 55
# x$ c. i- a( g+ _2.3 Filters 58' P) |: U& U: S6 }" v* ]
2.4 Interconnection of Systems 599 }5 I' G6 e! B+ n: R) m
2.5 The Discrete-Time Fourier Transform 61
, c% o+ w5 `+ v: k5 |2.6 DTFT Properties 62
4 P+ R3 p8 e7 Y e1 V9 @) @ Y2.7 Applications 64
5 G+ u/ y* y( r8 ?. E* |2.7.1 LSI Systems and LCCDEs 64
* p7 ?9 \; r4 r. E2.7.2 Performing Convolutions 65
: M$ [6 j7 M: o2.7.3 Solving Difference Equations 66
( h2 g1 _& j' t" |* X$ R2.7.4 Inverse Systems 66" u" W+ m& m$ ~9 B. d2 R
Solved Problems 67
* C! Q+ E( I& nChapter 3. Sampling 101
5 ]. I# ?; E7 Z% O) _6 P* a3 U3.1 Introduction 101
; T) U# c1 T* v! [( y3.2 Analog-to-Digital Conversion 101
, L1 H, @' w9 i) E! `* d6 p3.2.1 Periodic Sampling 101
& |! ~' x. `+ F/ {7 g3.2.2 Quantization and Encoding 1043 a3 g8 D% a1 Q2 |$ g
3.3 Digital-to-Analog Conversion 1061 z/ k/ Q9 B4 _6 C. e4 s$ e
3.4 Discrete-Time Processing of Analog Signals 108
5 o) o9 X& m8 x1 y2 \- Z% L3.5 Sample Rate Conversion 110
+ K% f* _- @" }3.5.1 Sample Rate Reduction by an Integer Factor 1105 ?+ n' D! d. n8 R1 {2 ~1 A
3.5.2 Sample Rate Increase by an Integer Factor 111, `2 y: E, \' T
3.5.3 Sample Rate Conversion by a Rational Factor 113
# r. u9 U/ }+ ~1 [# u* q, i9 h8 QSolved Problems 114) b9 k. R. R, F4 ^4 j
Chapter 4. The Z-Transform 142, H' z* Y3 i$ A
4.1 Introduction 142
) X( `8 t: W# Q! o4.2 Definition of the z-Transform 142
, G) S; j$ C% A1 g4.3 Properties 1465 ^; D# {5 p9 ~7 `4 U
vii# Z9 s3 Z9 c }: m% N
4.4 The Inverse z-Transform 149; L' e4 f+ U" x! q; e9 V
4.4.1 Partial Fraction Expansion 1491 D$ \: t3 C+ X9 C$ z' `4 ?
4.4.2 Power Series 150
6 r9 t) J( \( O( h9 S4.4.3 Contour Integration 151* h: K3 [3 w) a* |) k: k% r! B
4.5 The One-Sided z-Transform 151
0 N/ B/ J& n0 O3 b$ I$ vSolved Problems 152% V" G5 j$ n/ f; k2 p) i
Chapter 5. Transform Analysis of Systems 183
. J' ^, E7 `' d! j9 t: E( ~ w5.1 Introduction 183
7 y. |4 k9 W! ]5.2 System Function 1838 h9 A# L" P8 T$ E! C, h6 C
5.2.1 Stability and Causality 1845 t. ^/ t* J N* |3 l( ^ S
5.2.2 Inverse Systems 1860 Z2 n# }# ^# Y' q+ a' y& b' h
5.2.3 Unit Sample Response for Rational System Functions 187) O6 @& M& e% n
5.2.4 Frequency Response for Rational System Functions 188. ]& F) B- S) h/ |+ S# i3 {
5.3 Systems with Linear Phase 189
" b" v! Z& Y! `) w, s( V+ U5.4 Allpass Filters 193
' Q+ f; B1 ?% [6 u+ E! m5.5 Minimum Phase Systems 1943 E- m/ X1 ?. ]9 ~( y
5.6 Feedback Systems 195, A5 x$ O4 n) Q" F+ A
Solved Problems 1966 y5 f5 ^6 d( m( z
Chapter 6. The DFT 223
- h- K' Z; i6 i i* W, @6.1 Introduction 223
7 j+ A9 L2 ^7 x! [) z$ ~2 s2 G& h6.2 Discrete Fourier Series 223
, \9 G# E( Y7 Q6.3 Discrete Fourier Transform 226; O. l+ D9 d4 L$ M0 S) n( X* s
6.4 DFT Properties 227, U8 o; ? C. S/ p9 s7 ]9 c, T9 b
6.5 Sampling the DTFT 231/ j5 W9 ~- s2 y' O- x3 u
6.6 Linear Convolution Using the DFT 232) b+ s/ e8 N# ?- H+ o
Solved Problems 235/ a0 P# Q, ^5 ]! V
Chapter 7. The Fast Fourier Transform 262$ ]1 h/ r; |- ?* Z
7.1 Introduction 262
8 C8 u1 b2 n. j7.2 Radix-2 FFT Algorithms 262( u M0 M7 G! {* F
7.2.1 Decimation-in-Time FFT 262& E- G( D# ?& s* q d
7.2.2 Decimation-in-Frequency FFT 266
# W8 r$ W5 a) H1 }0 W7.3 FFT Algorithms for Composite N 267
% x" j+ C3 d$ l; H( u5 U/ h4 g7.4 Prime Factor FFT 271) ^0 A* S6 A: F! h. U& ]" _
Solved Problems 273
; L8 k) p0 `; `# v6 Z4 X7 mChapter 8. Implementation of Discrete-Time Systems 287
% w* ]6 W9 H+ g- E% f$ F! _2 A8.1 Introduction 287
! l7 A3 w& u* }1 @: P: T# {: I9 ~8.2 Digital Networks 287+ n* X9 Q: s6 l& W! j
8.3 Structures for FIR Systems 289
8 ]0 h8 t1 @. e5 y# }8.3.1 Direct Form 289
: W, h: O/ J( F0 Z8.3.2 Cascade Form 289
* C+ K! W1 c& _4 e3 |( c8.3.3 Linear Phase Filters 2895 B1 d/ |$ U- }" x0 t! E V& l) E/ {
8.3.4 Frequency Sampling 2911 ?4 S) v) j& o( w; G$ ]( f
8.4 Structures for IIR Systems 291
( e! z* {$ u/ g8 _" \8.4.1 Direct Form 2922 T4 z' L) U6 ^. o! E. x; |; L
8.4.2 Cascade Form 2942 s& F4 s" y& D9 u$ \
8.4.3 Parallel Structure 295- Z" B) Y P& w( y& O7 X! Q" h/ [
8.4.4 Transposed Structures 296$ a% k% V; L B. ~
8.4.5 Allpass Filters 2968 K4 M% a7 g6 g/ x/ B* |" O
8.5 Lattice Filters 2983 e: R, i }. k. E l# O
8.5.1 FIR Lattice Filters 298$ y0 M) ]$ e$ k0 e5 k: l7 l
8.5.2 All-Pole Lattice Filters 3007 e6 \. f! O8 f; Q1 M. F) \, _
viii' k9 q) N7 ?: e
8.5.3 IIR Lattice Filters 301
( }/ q3 H! b1 }3 o6 N0 P8.6 Finite Word-Length Effects 3022 p6 F9 _ o" @. f$ [5 Z
8.6.1 Binary Representation of Numbers 302
+ {: r$ Y8 Z, k9 Z8 o0 x8.6.2 Quantization of Filter Coefficients 304( ~3 R% O% ^( N. C, p
8.6.3 Round-Off Noise 3062 e" x, c% t" R, K+ E
8.6.4 Pairing and Ordering 309- o) P; W# P1 W! O2 T, S
8.6.5 Overflow 309
% Q4 L: X/ u$ g+ G3 JSolved Problems 3103 c5 @) |9 a. e5 Q# V
Chapter 9. Filter Design 358, B2 E8 p6 r- |+ t
9.1 Introduction 358. Y$ B, ^, @. o8 W6 d
9.2 Filter Specifications 358
$ g: A9 t& S& k! c5 R; B9.3 FIR Filter Design 359
9 p9 |! L9 Y% ^0 n s3 a9.3.1 Linear Phase FIR Design Using Windows 359
: v+ k7 y4 d& G7 u5 g% ^: J# @ ?9.3.2 Frequency Sampling Filter Design 363- W+ m: m. h5 W. ^! v5 x
9.3.3 Equiripple Linear Phase Filters 363 {7 b* G, L8 B4 I* g
9.4 IIR Filter Design 366/ k8 V- [+ |4 o/ {9 k/ i: Z
9.4.1 Analog Low-Pass Filter Prototypes 367! W7 t( l" e7 k" H2 v9 J( I" t
9.4.2 Design of IIR Filters from Analog Filters 373
2 b6 Y6 n' x, k2 S. N9.4.3 Frequency Transformations 376
% b# ^. H/ w. P2 E6 q) N9.5 Filter Design Based on a Least Squares Approach 376
6 v6 m7 ^6 H* T% n" ]5 @# A9.5.1 Pade Approximation 377
5 o. R, \2 k! G" M0 Z# t3 L9.5.2 Prony's Method 378
/ s5 w- L4 O S V4 C9.5.3 FIR Least-Squares Inverse 379* @2 A! T1 `) s6 A: q4 I
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