Digital Signal Processing. An Introduction

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An Introduction

1.1 INTRODUCTION
1.2 APPLICATIONS OF DIGITAL SIGNAL PROCESSING
1.3 SIGNALS
1.4 CLASSIFICATION OF SIGNALS
1.5 SIGNAL PROCESSING SYSTEMS
1.6 SIGNAL PROCESSING
1.7 ADVANTAGES OF DIGITAL SIGNAL PROCESSING OVER
ANALOG SIGNAL PROCESSING
1.8 ELEMENTS OF DIGITAL SIGNAL PROCESSING SYSTEM
EXERCISES
2.1 INTRODUCTION
2.2 DISCRETE-TIME SIGNALS
T
0 < n < да
Transformation of the Dependent Variable (Signal Amplitude):
2.3
DISCRETE-TIME SYSTEMS
EXAMPLE 2. 1
EXAMPLE 2. 2
SOLUTION:
EXAMPLE 2. 3
EXAMPLE 2.4
= S A =
EXAMPLE 2.5
= SI A = 1+1A+1 Al2+...
2.4 CONVOLUTION OF TWO DISCRETE-TIME SIGNALS
EXAMPLE 2.6
t
t
t
t
t
t
EXAMPLE 2.7
A i
EXAMPLE 2.8
7 ^ 1 - A J
EXAMPLE 2.9
2.5 INVERSE SYSTEMS
= I — I u (n) 13 )
13 )
2.6 CORRELATION OF TWO DISCRETE-TIME SIGNALS
EXAMPLE 2.12
t
t
t
t
t
t
EXAMPLE 2.13
2.7 SIGNALS AND VECTORS
x = c 1 x + x 1
v ■ x = |x||u\ cos 0
v ■ x = 0.
d Ге t 2 2 / xj 1 d Г гt
И2 = lxl2 +1 x ’
= J^\х(t)|2 dt + J
EXAMPLE 2.14
—
2.8 REPRESENTATION OF SIGNALS ON ORTHOGONAL
BASIS
SAMPLING OF CONTINUOUS-TIME SIGNALS
= A cosl 2n max-n + 0 I
s I Fs J
EXAMPLE 2.15
EXAMPLE 2.16
F 3 = 2П
2.10 RECONSTRUCTION OF A SIGNAL FROM ITS SAMPLE VALUES
no. T
j s(nTs )
EXERCISES
NUMERICAL EXERCISES
9.
tt
t
13 J 14 J
3.1 INTRODUCTION
3.2 DEFINITION OF THE z -TRANSFORM
3.3 REGION OF CONVERGENCE (ROC)
t
= s ( -2 ) z2 + s (-1) z1 + s ( 0 ) z0 + s (1) z-1 + s ( 2 ) z 2
t
EXAMPLE 3.2
=z -° + z-1 + z-2 + ... + z -x=
1 - Az-1 - B-1 z + AB-1
B - ABz-1 - z + A ~ B+A - z - ABz-
PROPERTIES OF z -TRANSFORM
EXAMPLE 3.3
" [1, n > 0"
EXAMPLE 3.4
t
Ans(n) < ' > S f-^ IA )
EXAMPLE 3.5
Z [ u(-n)] = S ( z 1) = —^--1
EXAMPLE 3.6
EXAMPLE 3.7
t
t
EXAMPLE 3.8
= S[ Az-1 ] n
+
j = -~^
3.5 SOME COMMON z -TRANSFORM PAIRS
3.6 THE INVERSE z-TRANSFORM
dz = <
EXAMPLE 3.9
EXAMPLE 3.10
= У (z - z) -
+ +
EXAMPLE 3.11
2-3z-1+z-2
2 - 3 z-1
1.3 -1.7 42 .
1 ч— z ч— z +....
24
7 J - 3 z-3
7
-4
15 3
4
3-17-
+2
2 z2 + 6 z3 +14 z4 +...
- 4 z2
-18 z2 +12 z3
30z3 - 28z4
EXAMPLE 3.12
/з - 6 z -2 -12 z 43
+ + +
+ 6 z -2 + 12 z 43
- 6 z -2 +12 z 43
+ + +
+ 6 z ~2 + 12 z 43
- 8 z -3 -16 z -4
+ + +
6 z -2 + 20 z 43 + 16 z -4
EXAMPLE 3.13
14 )
EXAMPLE 3.14
z 3 X ;t - 4 •
a a a 11
a2 =
+ Z-1
3.7 SYSTEM FUNCTION
EXAMPLE 3.15
3.8 POLES AND ZEROS OF RATIONAL z -TRANSFORMS
EXAMPLE 3.16
3.9 SOLUTION OF DIFFERENCE EQUATIONS USING
z-TRANSFORM
EXAMPLE 3.17
Y (z) [1 - Az-1 ] = A +1—r
() 1 - Az-1 (1 - z-1 )(1 - Az-1)
A A A L1 - A ) L1 - A ) Y (n) = + + + f-
I (1 - A) I
1 - A L -
EXAMPLE 3.18
EXAMPLE 3.19
3.10 ANALYSIS OF LINEAR TIME-INVARIANT (LTI) SYSTEMS
IN THE z -DOMAIN
EXAMPLE 3.20
p TT.
\ 3 )
EXAMPLE 3.2 1
I 4 )
or —— =
(1 - 0.5z 1) 1 -72z 1 + z 2
+ ( jp A +
I 1 - e 4 z-1 I
14 J
Z h(n)| X
EXAMPLE 3.2 2
■
\ 2 J
EXAMPLE 3.2 3
EXAMPLE 3.2 4
I 1 -1 z-1 II 1 -1 z-1 I
(1 ^ n , ч y(n) = I — I u(n)
\ 2 J
EXAMPLE 3.25
EXAMPLE 3.26
z
a1 =
a =—1—
h (n) = Z-1 [ H ( z )]
D *
+ T
EXERCISES
NUMERICAL EXERCISES
4.1 INTRODUCTION TO DISCRETE-TIME FOURIER
TRANSFORM (DTFT)
4.2 DEVELOPMENT OF THE DISCRETE-TIME FOURIER
TRANSFORM (DTFT)
4.3 CONVERGENCE OF THE DTFT
EXAMPLE 4. 1
EXAMPLE 4. 2
EXAMPLE 4.3
z
s(ew)=y e-jwn =
4.4 FOURIER TRANSFORM OF DISCRETE-TIME PERIODIC
SIGNALS
S(e )= X 2pAkd w~~n~
EXAMPLE 4.4
- 2nm)+ X 2%d (w + w0
“ 7 Q-n-
^
7
2 p A f 2 p A
— + pd w + , -p < w < p
EXAMPLE 4.5
4.5 PROPERTIES OF THE DTFT
If s(n) < DTFT > {s (ew)}
if «(n) < DTFT s s (ew)
EXAMPLE 4.6
S ( e )=(1 - e - jw ) + p ^ d (w - wp k )
if s(n) < DTFT s s (ew)
EXAMPLE 4.7
[1 - e-w ]
(kw '1 к 2 )
= e4w I sin ( 5w ) , sin (w)
ds (ejw) d Г-A
jdS (ejw) “
jdS ( e jw )
EXAMPLE 4.8
EXAMPLE 4.9
1p
1 1 1 1 "
EXAMPLE 4.10
s (ew )=td^
S A 7
a 2 =7 T
1 - A1' B J
Y(ejw)=
f_B-'
J- +A —
( A ^
= X ■ n) t J si(ej )
EXAMPLE 4.11
p
4.6 TABULATION OF PROPERTIES OF DTFT
4.7 TABULATION OF DTFT PAIRS
Discrete-time signal s (n)
4.8 DUALITY
мn)=7т X s2(-k)j0n
EXAMPLE 4.12
Ak = <
Ak =
p
p
4.9 DISCRETE-TIME LTI SYSTEMS CHARACTERIZED BY LINEAR CONSTANT-COEFFICIENT DIFFERENCE
EQUATIONS
EXAMPLE 4.14
Y(ejw)
H (ew )=id?? (4)
EXAMPLE 4.15
H (ejw ) = rj- ( ) s (ew)
I 4 JI
a,
= -2
: 1 ”4
.,. .(1^. J1^n ,.
12 J 12 J
EXAMPLE 4.16
7
y (ew)
EXERCISES
NUMERICAL EXERCISES
M ... .
w+—
I 2 Л1
H1 (j )= 1 1 1
12 J
An . .
V 2 J
5.1 INTRODUCTION
5.2 DEFINITION OF DFT
EXAMPLE 5.1
EXAMPLE 5.2
EXAMPLE 5.3
5.3 THE DFT AS A LINEAR TRANSFORMATION TOOL
sN =
■ s(0) ’
EXAMPLE 5.4
5.4 PROPERTIES OF DFT
Step in computation of circular convolution.
EXAMPLE 5.5
EXAMPLE 5.6
5.5 TABULATION OF PROPERTIES OF DFT
5.6 RELATIONSHIP BETWEEN DFT AND z -TRANSFORM
LINEAR CONVOLUTION USING DFT
EXAMPLE 5.7
5.8 PITFALLS IN USING DFT
EXAMPLE 5.8
( N ^
\ 2 )
= - eJ + — eJ eJ + e J
EXAMPLE 5.9
EXAMPLE 5.1 0
EXAMPLE 5.1 1
b. SI K\ = S |—+ K
\ 2 J
11 2 J
EXAMPLE 5.13
|Д m )) 1Д m ))
(I F J) (I M ))
EXERCISES
NUMERICAL EXERCISES
t
t
6.1 INTRODUCTION
6.2 GOERTZEL ALGORITHM
(1 - WKz-1 )(1 - WKz-1)
.
(2 p K A l~
6.3 FAST FOURIER TRANSFORM ALGORITHMS
EXAMPLE 6.1
n „ N \
o/n 1 V / / . . N ^
V 2 2
(N -11 12 )
IZ 4 / 4 ( . N ^
EXAMPLE 6.2
EXERCISES
7.1 INTRODUCTION
EXAMPLE 7.1
7.2 MAJOR FACTORS INFLUENCING OUR CHOICE OF
SPECIFIC REALIZATION
7.3 NETWORK STRUCTURES FOR IIR SYSTEMS
EXAMPLE 7.2
EXAMPLE 7.3
EXAMPLE 7.5
1 — 1
NETWORK STRUCTURE FOR FIR SYSTEMS
H (z) = T1
=z
+x
EXAMPLE 7. 6
EXAMPLE 7. 7
Yh(°)
Yh(2) Yh<6) Yh<7)
EXAMPLE 7. 8
or Y(z) [1 - b z-1 ] = Y‘(z) [z-1 - b ]
EXAMPLE 7.9
(1+ 55
55
55
(1 — a z ) (1 — b z )
1 - a z = 0
EXAMPLE 7.10
EXAMPLE 7.11
EXAMPLE 7.12
EXERCISES
NUMERICAL EXERCISES
8.1 INTRODUCTION
Review of Analog Filter Design
Z-1 [ H (z) = Z-1 ]
1 + e Q
8.2 MAJOR CONSIDERATIONS IN USING DIGITAL FILTERS
8.3 COMPARISON BETWEEN DIGITAL AND ANALOG FILTERS
8.4 COMPARISON BETWEEN IIR AND FIR DIGITAL FILTERS
8.5 REALIZATION PROCEDURES FOR DIGITAL FILTERS
8.6 NOTCH FILTERS
8.7 COMB FILTERS
8.8 ALL-PASS FILTERS
8.9 DIGITAL SINUSOIDAL OSCILLATORS
8.10 DIGITAL RESONATORS
H ( z) =
EXERCISES
9.1 INTRODUCTION
9.2 APPROXIMATION OF IIR DIGITAL FILTERS FROM
ANALOG FILTERS
EXAMPLE 9.1
1
Step II.
S
S
= V" Rm
9.2.3.1 Derivations of Formula for Bilinear Transformation Method
У (nTB)- У (nTs - Ts) = —[s(nTs- Ts) + s(nTs)] 2
Ts к z +1J
9.2.3.2 Properties of Mapping of Bilinear Transformation
2 ( z -1 ^ s = I I
) + w2
Case III:
(2/Ts + s )
. . _ . , (0T '
I 2 J
9.2.3.3 Warping Effect
9.2.3.4 Influence of the Warping Effect on the Amplitude Response of
a Digital Filter
9.2.3.5 Influence of the Warping Effect on the Phase Response of
a Derived Digital Filter
EXAMPLE 9.2
1
1
s
EXAMPLE 9.3
Cs v CsJ
+
of h ( nTs) = Z |j
EXAMPLE 9.4
( z — 1 ^ I — 1 + 0.1
I z +1)
I 1 + 0.1
I z +1)
s = I I
T I z +1J
( T j
1 + | ~ 15
< T j
1 + (T J) (s + jQ)
z = (T ^
T ^ fQTл
=1 2 JI 2 >
( AA ‘ + B2) + jB( A + A ‘)
B2 - B2 - B2
C=
D=
, ^1T 1 +-^-s-
EXAMPLE 9.6
o=^3
1 + I -x-
(9)2 +(^/3)2 \ 84
I 7 I
(s +1)2 (s2 + s +1)
4l 1 +1 Ml 1^ + 4l 1 +1
^ 1 +1) J [ ^ z +1 )^ z +1)
к 2 J
I 2 J
Pole Locations for Chebyshev Filters
r = 1
( M1 n - M -1/ n ^
R = 1 1
I 2 J
EXAMPLE 9.7
R = =
I 2 ) L 2 J
= - P1 X - P 2 X - P 2
(S - P1 )(S - P2 )(S - P2)
— 1 1
2. Design using Bilinear Transformation Method
Q = 2 tan | w2 | = 2 tan | — x — p | = 0.65
Q2 = 2tan| w2- | = 2tan| — x — p | = 1.02
( z -1 YI2 Г ( z -1 ^1 -
I z +1)
H ( ep1) = H ( e 02p ) = 0.9421-164°
ECN [Ji j
1 + ECN IO j
= ^7^^ d •• l--Q c
i+e 2 CN f l J
E=
N=
9.3 FREQUENCY TRANSFORMATION
s >Q s(O2 -QJ
H(s) = Hp fo/2 +^^^
(O2 -Al)
s >O C
/4 ( s (О2-О,)С
H (s) = H I О- -M 1 I
EXAMPLE 9.8
CI s J
EXAMPLE 9.9
Q C QC
s + Q C
Q C QC
C C +Q C
QCs + (s + QC ) = s + QC '
= 1 f ( e - w )|
Transformation
Design Parameters
A=
z 2 - A1 z 1 + A 2
EXERCISES
s = — I I
Ts I z +1J
NUMERICAL EXERCISES
10
10.1 INTRODUCTION
10.2 PROPERTIES OF FIR DIGITAL FILTERS
ф(а} = -та = tan
IA J
^h(nTs)sin(aT - anTs) = 0
0(0) = ^ h ( nTs) sin(aT - anTs)
S h(mTs )
+ £ /г(пТ5)е^и[(^1)/21т'
j27i(nTs)[e->[f(^1)/2)’"ffi
®\ n |T
10.3 DESIGN OF FIR DIGITAL FILTERS USING FOURIER
SERIES METHOD
h (nTs )=L j h (eaT) e^da
( N -1 ^ ( N -1 ^
I —-— l> n >1 —-— I
Ways to reduce Gibb’s oscillations
10.3.2.1. Rectangular Window Function
w ( nTs )=<
—-— I < n <1 —-—
Spectrum of Rectangular Window Function
M=
I e s - s I
I 2j J
10.3.2.2. Hann and Hamming Window Functions
a + (1 - a)cos , for-I l< n <1-
< N -1 ^ 2 J ^
= awR (nTs) + (1 - a)
(nT ) = awR (nT ) + N 1-O- J(A-1) nwR (nT )
+N 12a 1( A)-nwR (nTs)
f 12Г^( A-1) wR (nTs)
к 2 у
WH (e- ) = aW, (e-) + ^W, (ej■"-1)"■ )
WH(e )
2n A N
। 1 - a A
+1 I
I 2 J .
2 n 2n A 1
wT + I—
10.3.2.3. Blackman Window Function
2 ) I 2 )
EXAMPLE 10.1
h I I + 2 > h I - n I cos naT
I 2 J nS I 2 1 ’
Delay = т = ^ j T = ^ | T, = 3 T
h I I + 2 > h I - n I cos na
nn
nn
3n
2n
n
10.3.2.4. Kaiser Window Function
wk (nTs ) = <
I < n <1
4
t |
Ъ J
a 2a
2a
1 - Y
H (ejT) = <
" <|a|< '2
aC =
Op + aa
D=
EXAMPLE 10.2
2n
nn
nn
N > ^D +1
f F0.W f„. ( N - 1 U.,f N - 11
10.4 DESIGN OF FIR DIGITAL FILTER BASED ON NUMERICAL-ANALYSIS FORMULAE
Gregory-Newton Forward Difference Formula
Gregory-Newton Backward Difference Formula
1 + 8 2 + -
m Г f _ T 4 Г _ T 4
+— 8s I nT —- I + 8s I nT —s- I
m ( m2 -1) ( m2
+ 85sI nT + -
) ) f f T 4 f f T
f T 4
8s I nTs + "2“ 1 = s (nTs + Ts )- s (nTs )
= d'S (nTs + mTs )
y(nTs) =
EXAMPLE 10.3
y(nTs) =
— 1) ( m2 2(Z5)
+ d I nT
= 71- <
T 4 .( ds I nT I + d I nT
s- I + d3s I nT + -
. I T
+ d I nT
1 t f T 4 t f T 4
+ d5sI nT —- | + d5sI nT +■— I
T A
8s I nTs +T 1 = s (nTs + Ts )- s (nTs )
N 2 7
TA
N 2 7
.( _ T A Г _ T A
3s \nTs + Ф +83s\nTs -TH = s(nTs + Ts)-s(
8 8s I nT + 7T
( t t A Г t t s I nT + T + — I — s I nT + T + —
Г t AT
sI nTs — Ts + I — sI nTs
N 2 7 N
Г _ 3 T A Г _ T
s | nT + I — s | nT + -
Г _ T A Г _ 3 T
—s | nT + - I — s | nT + -
„ Г T A „ Г T
s| nT + | — s| nT + L
t A Г
s- I + s I nT
„з Г t A „з Г t
83s| nT + - I + 83s| nT — -
3 T A . Г T A . Г
+ | — 8s| nT + L I — 8s| nT
2 7 N s 2) N s
+ 8s I nTs
+^T [ s ( nTs + 3 Ts) — 4 s ( nTs + 2 Ts) + 5 s ( nTs + Ts) — 5 s ( nTs — Ts)
or y (nTs ) = 601t [ s (nTs + 3 Ts) — 9 s ( nTs + 2 Ts) + 45 s ( nTs + Ts)
10.5 DESIGN OF OPTIMAL LINEAR-PHASE FIR DIGITAL
FILTERS USING M-CLELLAN-PARKS METHOD
f Ss к Л
10.6 FINITE WORD LENGTH EFFECTS IN DIGITAL FILTERS
H (z) = — z-a
z - a
IM <£
I ■ j
Requirements for low coefficient sensitivity
Reduction of Product Round-off Error
Granular Limit Cycles
Overflow Limit Cycles
EXERCISES
NUMERICAL EXERCISES
a < a < a
0, ac <|a|< a
a <a<a
0, ac <|a|< a
^ h (nTs) sin (ar - aril's) = 0.
11.1 INTRODUCTION TO SPECTRAL ESTIMATION
11.2 ENERGY DENSITY SPECTRUM
11.3 ESTIMATION OF THE AUTOCORRELATION AND
POWER SPECTRUM OF RANDOM SIGNALS
Estimate 1
Mean and Variance for Estimate 1
Mean and Variance for Estimate 2
Estimate of Power Density Spectrum
Mean and Variance of Periodogram Estimate
=S
J
EXAMPLE 11.1
Rss (T) = E [ Ac cos(2nfc (t + t) + фф ■ Ac cos (2nfct + ф)^| = E|^A2 cos(2nfct + 2nfcT + ф) cos (2nfct + ф)]
cos (2nfT)
=-f [A f—f.)+A f+f.)]
11.4 DFT IN SPECTRAL ESTIMATION
f k 1 1
P I — I: ss IN ) N
EXAMPLE 11.2
11.5 NON-PARAMETRIC METHODS OF POWER SPECTRUM
ESTIMATION
Mean of Bartlett Power Spectral Estimate
Variance of Bartlett Power Spectral Estimate
Mean Value of the Welch Estimate
E Гp:( f Я = — У E ГP(i) (f Я
_ Pss (J ) J / / < _ Pss (J ) J
= j Yss(a)W(f — a)da
da
Variance of the Welch Estimate
var ГPw (f Я =—УУ e ГP(i)(f)P)(f Я - Ze ГPw (f Я12
Mean Value of Blackman-Tukey Estimate
E [Pss (a)]= f Yss (0)Wb (a - 0)d0
rnB (m) = •! N
1/2
Variance of the Blackman-Tukey Power Spectrum Estimate
1/2 1/2
,r„ / ,, /z-,41 /X /z-,x x Г sin n(0 + a) 12 [ sin n(0 - a) 12 Z11
E [ PSS (a) PSS (0)] = у (a)Y (0) l1 + _ 7 + _ 7 r (11.69)
xS
sin n(0 - a)N N sin n(0 - a)
2' ,
r dad0
Mean of Periodogram
Variance of Periodogram
QP =
Дf = =
Bartlett Power Spectrum Estimate
M L 2 82 J 2 82
Welch Power Spectrum Estimate (50% Overlap)
= M =
Blackman-Tukey Power Spectrum Estimate
= 21 I +1 ■ 1 = —
11.6 PARAMETRIC METHODS OF POWER
SPECTRUM ESTIMATION
ARMA Process
AR Process
MA Process
The Yule-Walker Method for the AR Model Parameters
a
MA Model
ARMA Model
Advantages of Burg’s Method
Disadvantages of Burg’s Method
=E Ifp(n) + |gp(n)
=E
Y (o) = a2 + V P.
EXAMPLE 11.3
a.
E [PSS ( f1) PSS ( f 2 )] = E
But, E [ S ( ni) S ( n 2) S ( n з) S ( n 4 )] = E [ S ( ni) S ( n 2)] E [ S ( n з) S ( n 4 )]
+E [ s ( ni) s ( n 3)] E [ s ( n 2) s ( n 4 )]
+E[[s(n1)s(n4)]]E[[s(n2)s(n3)]]
= N2 Ё Ё Ё Ё{E [s(n1)s(n2)]E [s(n3)s(n4)]
+E [ s ( n1) s ( n з) E [ s ( n 2) s ( n 4)]+ E ( s ( n1) s ( n 4)] E [ s ( n 2) s ( n 3
2 - 2cos2n(f1 - f2 )
] [Nsinn(f1 - f■)]
and E [ s ( n1) s ( n 2) s ( n 3) s ( n 4)] = E [ s ( n1) s ( n 2)] E [ s ( n 3) s ( n 4)]
+E [ s ( n1) s ( n 3) E [ s ( n 2) s ( n 4)]]
+E [ s ( ni) s ( n 4)] E [ s ( n 2) s ( n 3)]
, N4
EXAMPLE 11 .4
Bartlett method
Welch Method
Blackman-Tukey Method
EXAMPLE 11 .5
Mean:
Autocorrelation:
EXAMPLE 11 .6
ri -
1
EXERCISES
NUMERICAL EXERCISES
12
12.1 INTRODUCTION
Advantages of using MDSP
12.2 SAMPLING RATE CONVERSION
n
n
w = Da
a - 2nk
D ^ D J
12.3 INTERPOLATION OF SAMPLING RATE BY A INTEGER
FACTOR (I)
= L s Im Iz ■m
н
f/ , I I П
I m 1
=~ J I s (®vida
12.4 SAMPLING RATE ALTERNATION OR CONVERSION
BY A RATIONAL FACTOR (DJ
H (®u ) = <
2nF _ as
k=
mD -
mD -
= h nl + (mD ) I J
12.5 FILTER DESIGN AND IMPLEMENTATION FOR
SAMPLING RATE ALTERNATION OR CONVERSION
12.5.1.1 Efficient Implementation of a Decimator
Efficient Implementation of an Interpolator
( i ^
I I J
12.6 SAMPLING RATE CONVERSION BY AN ARBITRARY FACTOR
ID J
К ■k+в
0 < в <1
k1k+1 — < — <
P=п а и d°=
A2 f 0.5 Y a2 da
I I )
= emT (1 - a )[cosjt — 1sin jt ]
1 C1
1 - (1 - a ) cos jt - a cos j|—-1
j2 (1 - a ) ^m- m I2
j2 (1 - am ) ^m /2 dj
2П Е/ S (j)e
12.7 APPLICATION OF MULTIRATE DIGITAL SIGNAL PROCESSING
SOLVED EXAMPLES
EXAMPLE 12.1
EXAMPLE 12.2
EXAMPLE 12.3
EXAMPLE 12.4
Hfa) (1 -4'-) (1 -4" )(1 -5")
H () (1 + 5 -1) (1 + 5 -1 )(1 - 5 -1)
= Г1 + 20z-2 ^ -1 ( -9 ^
EXAMPLE 12.5
Two-Stage Realization
EXAMPLE 12.6
Two-stage realization
Three-Stage Realization
EXAMPLE 12.7
EXERCISES
13
13.1 INTRODUCTION
13.2 MODEL OF SPEECH PRODUCTION
13.3 SHORT-TIME FOURIER TRANSFORM (STFT)
13.3.1.1 Implementation of STFT
13.4 SPEECH ANALYSIS-SYNTHESIS USING STFT
13.5 ANALYSIS CONSIDERATIONS
13.6 OVERALL ANALYSIS-SYNTHESIS SYSTEM
13.7 CHANNEL VOCODER
13.8 PITCH DETECTION AND VOICED-UNVOICED
DECISIONS
13.9 VOICED-UNVOICED (BUZZ-HISS) DETECTION
13.10 VOICED-UNVOICED (BUZZ-HISS) DETECTION
Homomorphic Vocoder
Formant Synthesis
13.11 VOICED FRICATIVE EXCITATION NETWORK
13.12 RANDOM NUMBER GENERATOR
13.13 PRINCIPLES OF DIGITAL OPERATION
13.14 LINEAR PREDICTION OF SPEECH
< E 2( n)> = E
13.15 A COMPUTER VOICE RESPONSE SYSTEM
EXERCISES
14
14.1 INTRODUCTION
14.2 APPLICATIONS AND ADVANTAGES OF RADARS
Advantages of Using Radar
14.3 LIMITATIONS OF USING RADAR
14.4 CHIRP z -TRANSFORM (CZT) ALGORITHM
S (zk ) = £ s(n) [AW-k ] n
nk = ~[ n2 + k2 —( k — n )2 ] (14.7)
EXAMPLE 14.1
14.5 RADAR SYSTEM AND RADAR PARAMETERS
, „ , vT ,
2
14.6 RADAR SIGNAL DESIGN AND AMBIGUITY FUNCTIONS
= £ S J 5 ( nTs + Т ) s ( nT ) s ( mTs + T ) s ( mTs ) n=-X m=-X -X
14.7 AMBIGUITY FUNCTIONS OF CHIRPS AND
SINUSOIDAL PULSES
Z ,<
“ I n 1
“I n 1
14.8 AMBIGUITY FUNCTION OF A CW PULSE
14.9 AMBIGUITY FUNCTIONS OF A BURST
14.10 OTHER SIGNALS
2v
T
14.11 AIRBORNE SURVEILLANCE RADAR FOR AIR TRAFFIC
CONTROL (ATC)
14.12 LONG-RANGE DEMONSTRATION RADAR (LRDR)
14.13 DIGITAL MATCHED FILTER FOR A
HIGH-PERFORMANCE RADAR (HPR)
\ 2 J \ 2 J
EXAMPLE 14.2
EXERCISES
A
C
D
E
F
G
H
I
L
M
N
P
R
S
T
U
V
Z