اسم المؤلف
Steven T. Karris
التاريخ
23 فبراير 2024
المشاهدات
106
التقييم
(لا توجد تقييمات)

Signals and Systems with MATLAB Computing and Simulink Modeling – Fourth Edition
Steven T. Karris
Elementary Signals 1-1
1.1 Signals Described in Math Form 1-1
1.2 The Unit Step Function 1-2
1.3 The Unit Ramp Function 1-10
1.4 The Delta Function 1-11
1.4.1 The Sampling Property of the Delta Function 1-12
1.4.2 The Sifting Property of the Delta Function 1-13
1.5 Higher Order Delta Functions 1-14
1.6 Summary 1-22
1.7 Exercises 1-23
1.8 Solutions to End-of-Chapter Exercises 1-24
MATLAB Computing
Pages 1-20, 1-21
Page 1-18
The Laplace Transformation 2-1
2.1 Definition of the Laplace Transformation 2-1
2.2 Properties and Theorems of the Laplace Transform 2-2
2.2.1 Linearity Property 2-3
2.2.2 Time Shifting Property 2-3
2.2.3 Frequency Shifting Property 2-4
2.2.4 Scaling Property 2-4
2.2.5 Differentiation in Time Domain Property 2-4
2.2.6 Differentiation in Complex Frequency Domain Property 2-6
2.2.7 Integration in Time Domain Property 2-6
2.2.8 Integration in Complex Frequency Domain Property 2-8
2.2.9 Time Periodicity Property 2-8
2.2.10 Initial Value Theorem 2-9
2.2.11 Final Value Theorem 2-10
2.2.12 Convolution in Time Domain Property 2-11
2.2.13 Convolution in Complex Frequency Domain Property 2-12
2.3 The Laplace Transform of Common Functions of Time 2-14
2.3.1 The Laplace Transform of the Unit Step Function u0(t) 2-14
2.3.2 The Laplace Transform of the Ramp Function u1(t) 2-14
2.3.3 The Laplace Transform of tnu0(t) 2-152.3.4 The LaplaceTransform of the Delta Function 8(t) 2-18
2.3.5 The LaplaceTransformof the Delayed DeltaFunction 5(t – a) 2-18
2.3.6 The LaplaceTransform of e-atu0(t) 2-19
2.3.7 The LaplaceTransformof t ne-a u0(t) . 2-19
2.3.8 The LaplaceTransform of sino t u0t .2-20
2.3.9 The LaplaceTransform of cosot u0t .2-20
2.3.10 The LaplaceTransformof e-atsinot u0(t) .2-21
2.3.11 The LaplaceTransformof e-atcosot u0(t) . 2-22
2.4 The Laplace Transform of Common Waveforms . 2-23
2.4.1 The Laplace Transform of a Pulse 2-23
2.4.2 The Laplace Transform of a Linear Segment 2-23
2.4.3 The Laplace Transform of a Triangular Waveform . 2-24
2.4.4 The Laplace Transform of a Rectangular Periodic Waveform 2-25
2.4.5 The Laplace Transform of a Half-Rectified Sine Waveform . 2-26
2.5 Using MATLAB for Finding the Laplace Transforms of Time Functions . 2-27
2.6 Summary 2-28
2.7 Exercises . 2-31
The Laplace Transform of a Sawtooth Periodic Waveform . 2-32
The Laplace Transform of a Full-Rectified Sine Waveform . 2-32
2.8 Solutions to End-of-Chapter Exercises . 2-33
3 The Inverse Laplace Transform 3-1
3.1 The Inverse Laplace Transform Integral 3-1
3.2 Partial Fraction Expansion 3-1
3.2.1 Distinct Poles . 3-2
3.2.2 Complex Poles .3-5
3.2.3 Multiple (Repeated) Poles 3-8
3.3 Case where F(s) is Improper Rational Function 3-13
3.4 Alternate Method of Partial Fraction Expansion 3-15
3.5 Summary .3-19
3.6 Exercises 3-21
3.7 Solutions to End-of-Chapter Exercises . 3-22
MATLAB Computing
Pages 3-3, 3-4, 3-5, 3-6, 3-8, 3-10, 3-12, 3-13, 3-14, 3-22
4 Circuit Analysis with Laplace Transforms 4-1
4.1 Circuit Transformation from Time to Complex Frequency 4-1
4.1.1 Resistive Network Transformation . 4-1
4.1.2 Inductive Network Transformation 4-1
4.1.3 Capacitive Network Transformation 4-14.2 Complex Impedance Z(s) .
4.4 Transfer Functions
4.5 Using the Simulink Transfer Fcn Block .
4.6 Summary .
4.7 Exercises .
4.8 Solutions to End-of-Chapter Exercises .
. 4-8
.4-11
.4-13
.4-17
.4-20
.4-21
.4-24
MATLAB Computing
Pages 4-6, 4-8, 4-12, 4-16, 4-17, 4-18, 4-26, 4-27, 4-28, 4-29, 4-34
Page 4-17
5 State Variables and State Equations 5-1
5.1 Expressing Differential Equations in State Equation Form
5.2 Solution of Single State Equations
5.3 The State Transition Matrix
5.4 Computation of the State Transition Matrix .
5.4.1 Distinct Eigenvalues
5.4.2 Multiple (Repeated) Eigenvalues
5.5 Eigenvectors
5.6 Circuit Analysis with State Variables
5.7 Relationship between State Equations and Laplace Transform
5.8 Summary .
5.9 Exercises .
5.10 Solutions to End-of-Chapter Exercises .
5-1
5-6
5-9
5-11
5-11
5-15
5-18
5-22
5-30
5-38
5-41
5-43
MATLAB Computing
Pages 5-14, 5-15, 5-18, 5-26, 5-36, 5-48, 5-51
Pages 5-27, 5-37, 5-45
6 The Impulse Response and Convolution 6-1
6.1 The Impulse Response in Time Domain .
6.2 Even and Odd Functions of Time
6.3 Convolution .
6.4 Graphical Evaluation of the Convolution Integral .
6.5 Circuit Analysis with the Convolution Integral .
6.6 Summary
6.7 Exercises .
6-1
6-4
6-7
6-8
6-18
6-21
6-236.8 Solutions to End-of-Chapter Exercises 6-25
MATLAB Applications
Pages 6-12, 6-15, 6-30
7 Fourier Series 7-1
7.1 Wave Analysis 7-1
7.2 Evaluation of the Coefficients 7-2
7.3 Symmetry in Trigonometric Fourier Series 7-6
7.3.1 Symmetry in Square Waveform 7-8
7.3.2 Symmetry in Square Waveform with Ordinate Axis Shifted 7-8
7.3.3 Symmetry in Sawtooth Waveform 7-9
7.3.4 Symmetry in Triangular Waveform 7-9
7.3.5 Symmetry in Fundamental, Second, and Third Harmonics 7-10
7.4 Trigonometric Form of Fourier Series for Common Waveforms 7-10
7.4.1 Trigonometric Fourier Series for Square Waveform 7-11
7.4.2 Trigonometric Fourier Series for Sawtooth Waveform 7-14
7.4.3 Trigonometric Fourier Series for Triangular Waveform 7-16
7.4.4 Trigonometric Fourier Series for Half-Wave Rectifier Waveform . 7-17
7.4.5 Trigonometric Fourier Series for Full-Wave Rectifier Waveform 7-20
7.5 Gibbs Phenomenon . 7-24
7.6 Alternate Forms of the Trigonometric Fourier Series . 7-24
7.7 Circuit Analysis with Trigonometric Fourier Series 7-28
7.8 The Exponential Form of the Fourier Series 7-31
7.9 Symmetry in Exponential Fourier Series 7-33
7.9.1 Even Functions . 7-33
7.9.2 Odd Functions 7-34
7.9.3 Half-Wave Symmetry . 7-34
7.9.4 No Symmetry . 7-34
7.9.5 Relation of C-n toCn . 7-34
7.10 Line Spectra . 7-36
7.11 Computation of RMS Values from Fourier Series 7-41
7.12 Computation of Average Power from Fourier Series . 7-44
7.13 Evaluation of Fourier Coefficients Using Excel® 7-46
7.14 Evaluation of Fourier Coefficients Using MATLAB® . 7-47
7.15 Summary . 7-50
7.16 Exercises 7-53
7.17 Solutions to End-of-Chapter Exercises 7-55
MATLAB Computing
Page 7-31
8 The Fourier Transform 8-1
8.1 Definition and Special Forms 8-1
8.2 Special Forms of the Fourier Transform 8-2
8.2.1 Real Time Functions 8-3
8.2.2 Imaginary Time Functions 8-6
8.3 Properties and Theorems of the Fourier Transform 8-9
8.3.1 Linearity . 8-9
8.3.2 Symmetry . 8-9
8.3.3 Time Scaling 8-10
8.3.4 Time Shifting . 8-11
8.3.5 Frequency Shifting . 8-11
8.3.6 Time Differentiation 8-12
8.3.7 Frequency Differentiation . 8-13
8.3.8 Time Integration 8-13
8.3.9 Conjugate Time and Frequency Functions . 8-13
8.3.10 Time Convolution 8-14
8.3.11 Frequency Convolution . 8-15
8.3.12 Area Under f(t) 8-15
8.3.13 Area Under F(ro) .8-15
8.3.14 Parseval’s Theorem . 8-16
8.4 Fourier Transform Pairs of Common Functions 8-18
8.4.1 The Delta Function Pair . 8-18
8.4.2 The Constant Function Pair . 8-18
8.4.3 The Cosine Function Pair . 8-19
8.4.4 The Sine Function Pair 8-20
8.4.5 The Signum Function Pair . 8-20
8.4.6 The Unit Step Function Pair . 8-22
8.4.7 The e jra0tu0(t) Function Pair 8-24
8.4.8 The (coso0t)(u0t) FunctionPair 8-24
8.4.9 The (sino0t)(u0t) FunctionPair 8-25
8.5 Derivation of the Fourier Transform from the Laplace Transform . 8-25
8.6 Fourier Transforms of Common Waveforms . 8-27
8.6.1 The Transform of f(t) = A[u0(t + T) – u0(t – T)] .8-27
8.6.2 The Transform of f(t) = A[u0(t) – u0(t – 2T)] 8-28
8.6.3 The Transform of f(t) = A[u0(t + T) + u0(t) – u0(t – T) – u0(t – 2T)] .8-298.6.4 The Transform of f(t) = Acos©0t[u0(t + T) -u0(t- T)] 8-30
8.6.5 The Transform of a Periodic Time Function with Period T 8-31
8.6.6
TO
The Transform of the Periodic Time Function f(t) = A ^ S(t- nT) 8-32
n = -TO
9
8.7 Using MATLAB for Finding the Fourier Transform of Time Functions 8-33
8.8 The System Function and Applications to Circuit Analysis 8-34
8.9 Summary 8-42
8.10 Exercises 8-47
8.11 Solutions to End-of-Chapter Exercises . 8-49
MATLAB Computing
Pages 8-33, 8-34, 8-50, 8-54, 8-55, 8-56, 8-59, 8-60
Discrete-Time Systems and the Z Transform 9-1
9.1 Definition and Special Forms of the Z Transform 9-1
9.2 Properties and Theorems of the Z Transform 9-3
9.2.1 Linearity 9-3
9.2.2 Shift of f[n]u0[n] in the Discrete-Time Domain . 9-3
9.2.3 Right Shift in the Discrete-Time Domain . 9-4
9.2.4 Left Shift in the Discrete-Time Domain 9-5
9.2.5 Multiplication by an in the Discrete-Time Domain . 9-6
-naT
9.2.6 Multiplication by e in the Discrete-Time Domain . 9-6
9.2.7 Multiplication by n and n2 in the Discrete-Time Domain . 9-6
9.2.8 Summation in the Discrete-Time Domain 9-7
9.2.9 Convolution in the Discrete-Time Domain . 9-8
9.2.10 Convolution in the Discrete-Frequency Domain 9-9
9.2.11 Initial Value Theorem 9-9
9.2.12 Final Value Theorem 9-10
9.3 The Z Transform of Common Discrete-Time Functions . 9-11
9.3.1 The Transform of the Geometric Sequence . 9-11
9.3.2 The Transform of the Discrete-Time Unit Step Function 9-14
9.3.3 The Transform of the Discrete-Time Exponential Sequence .9-16
9.3.4 The Transform of the Discrete-Time Cosine and Sine Functions .9-16
9.3.5 The Transform of the Discrete-Time Unit Ramp Function 9-18
9.4 Computation of the Z Transform with Contour Integration 9-20
9.5 Transformation Between s- and z-Domains .9-22
9.6 The Inverse Z Transform .9-259.6.1 Partial Fraction Expansion .9-25
9.6.2 The Inversion Integral . .9-32
9.6.3 Long Division of Polynomials .9-36
9.7 The Transfer Function of Discrete-Time Systems . .9-38
9.8 State Equations for Discrete-Time Systems .9-45
9.9 Summary . .9-48
9.10 Exercises . .9-53
9.11 Solutions to End-of-Chapter Exercises . .9-55
MATLAB Computing
Pages 9-35, 9-37, 9-38, 9-41, 9-42, 9-59, 9-61
Page 9-44
Excel Plots
Pages 9-35, 9-44
10
11
The DFT and the FFT Algorithm 10-1
10.1 The Discrete Fourier Transform (DFT) . . 10-1
10.2 Even and Odd Properties of the DFT . 10-9
10.3 Common Properties and Theorems of the DFT . 10-10
10.3.1 Linearity . . 10-10
10.3.2 Time Shift . 10-11
10.3.3 Frequency Shift . . 10-12
10.3.4 Time Convolution . 10-12
10.3.5 Frequency Convolution . . 10-13
10.4 The Sampling Theorem . 10-13
10.5 Number of Operations Required to Compute the DFT . . 10-16
10.6 The Fast Fourier Transform (FFT) . 10-17
10.7 Summary . 10-28
10.8 Exercises . 10-31
10.9 Solutions to End-of-Chapter Exercises . 10-33
MATLAB Computing
Pages 10-5, 10-7, 10-34
Excel Analysis ToolPak
Pages 10-6, 10-8
Analog and Digital Filters
11.1 Filter Types and Classifications 11-1
11.2 Basic Analog Filters 11-211.2.1 RC Low-Pass Filter 11-2
11.2.2 RC High-Pass Filter 11-4
11.2.3 RLC Band-Pass Filter 11-7
11.2.4 RLC Band-Elimination Filter 11-8
11.3 Low-Pass Analog Filter Prototypes 11-10
11.3.1 Butterworth Analog Low-Pass Filter Design 11-14
11.3.2 Chebyshev Type I Analog Low-Pass Filter Design 11-25
11.3.3 Chebyshev Type II Analog Low-Pass Filter Design 11-38
11.3.4 Elliptic Analog Low-Pass Filter Design 11-39
11.4 High-Pass, Band-Pass, and Band-Elimination Filter Design 11-41
11.5 Digital Filters 11-51
11.6 Digital Filter Design with Simulink 11-70
11.6.1 The Direct Form I Realization of a Digital Filter 11-70
11.6.2 The Direct Form II Realization of a Digital Filter 11-71
11.6.3 The Series Form Realization of a Digital Filter 11-73
11.6.4 The Parallel Form Realization of a Digital Filter 11-75
11.6.5 The Digital Filter Design Block 11-78
11.7 Summary 11-87
11.8 Exercises 11-91
11.9 Solutions to End-of-Chapter Exercises 11-97
MATLAB Computing
Pages 11-3, 11-4, 11-6, 11-7, 11-9, 11-15, 11-19, 11-23, 11-24, 11-31,
11-35, 11-36, 11-37, 11-38, 11-40, 11-41, 11-42, 11-43, 11-45, 11-46,
11-48, 11-50, 11-55, 11-56, 11-57, 11-60, 11-62, 11-64, 11-67, 11-68,
and 11-97 through 11-106
Pages 11-71, 11-74, 11-77, 11-78, 11-80, 11-82, 11-83, 11-84
A Introduction to MATLAB A-1
A.1 MATLAB® and Simulink® . A-1
A.2 Command Window A-1
A.3 Roots of Polynomials A-3
A.4 Polynomial Construction from Known Roots . A-4
A.5 Evaluation of a Polynomial at SpecifiedValues . A-6
A.6 Rational Polynomials A-8
A.7 Using MATLAB to Make Plots . A-10
A.8 Subplots A-18
A.9 Multiplication, Division, and Exponentiation A-18
A.10 Script and Function Files . A-26
A.11 Display Formats . A-31MATLAB Computing
Pages A-3 through A-8, A-10, A-13, A-14, A-16, A-17,
A-21, A-22, A-24, A-27
B.1 Simulink and its Relation to MATLAB B-1
MATLAB Computing
Page B-4
Pages B-7, B-12, B-14, B-18
C A Review of Complex Numbers C-1
C.1 Definition of a Complex Number C-1
C.2 Addition and Subtraction of Complex Numbers C-2
C.3 Multiplication of Complex Numbers C-3
C.4 Division of Complex Numbers C-4
C.5 Exponential and Polar Forms of Complex Numbers C-4
MATLAB Computing
Pages C-6, C-7, C-8
Page C-7
D Matrices and Determinants D-1
D.1 Matrix Definition . D-1
D.2 Matrix Operations D-2
D.3 Special Forms of Matrices . D-6
D.4 Determinants . D-10
D.5 Minors and Cofactors . D-12
D.6 Cramer’s Rule D-17
D.7 Gaussian Elimination Method . D-19
D.8 The Adjoint of a Matrix . D-21
D.9 Singular and Non-Singular Matrices . D-21
D.10 The Inverse of a Matrix D-22
D.11 Solution of Simultaneous Equations with Matrices . D-24
D.12 Exercises D-31E
MATLAB Computing
Pages D-3, D-4, D-5, D-7, D-8, D-9, D-10,
D-12, D-19, D-23, D-27, D-29
Page D-3
Page D-28
Window Functions E-1
E.1 Window Function Defined E-1
E.2 Common Window Functions E-1
E.2.1 Rectangular Window Function E-2
E.2.2 Triangular Window Function E-5
E.2.3 Hanning Window Function E-7
E.2.4 Hamming Window Function E-9
E.2.5 Blackman Window Function E-12
E.2.6 Kaiser Family of Window Functions E-14
E.3 Other Window Functions E-15
E.4 Fourier Series Method for Approximating an FIR Amplitude Response E-17
References R-1
Index IN-1
Index
Symbols
% (percent) symbol in MATLAB A-2
A
abs(z) in MATLAB A-23
active analog filter – see filter
adjoint of a matrix – see matrix
capacitive 4-2
inductive 4-2
complex input 4-11
algebraic constrain block in Simulink B-18
aliasing 10-14
all-pass filter – see filter
all-pole approximation 11-21
all-pole low-pass filter
see filter – low-pass
alternate form of the trigonometric
Fourier series – see Fourier series
alternate method of partial
fraction expansion – see partial
fraction expansion
angle(z) MATLAB function A-23
argument 11-2
attenuation rate 11-12
axis MATLAB command A-16
B
band-elimination filter – see filter
band-elimination filter design
see filter design
band-limited signal 10-13
band-pass filter – see filter
band-pass filter design
see filter design
band-stop filter – see filter
Bessel filter – see filter
bilinear MATLAB function 11-59
bilinear transformation – see
transformation methods for mapping
analog prototype filters to digital filters
bode MATLAB function 11-24
box MATLAB command A-12
buttap MATLAB function 11-17
buttefly operation 10-23
Butterworth analog low-pass
filter design – see filter design
C
c2d MATLAB function 9-46
capacitive impedance – see impedance
cascade form realization – see digital filter
Category I FFT algorithm – see
FFT algorithm
Category II FFT algorithm – see
FFT algorithm
Cauchy’s residue theorem
see residue theorem
Cauer filter – see elliptic filter
Cayley-Hamilton theorem 5-11
characteristic equation 5-19
cheb1ap MATLAB function 11-35
cheb2ap MATLAB function 11-38
Chebyshev filters – see filter
Chebyshev Type I analog low-pass
filter design – see filter design
Chebyshev Type I filters – see filter
Chebyshev Type I low-pass filter
magnitude-square function 11-26

• see filter
Chebyshev Type II analog low-pass
filter design – see filter design
Chebyshev Type II filters – see filter
circuit analysis with Laplace transforms 4-1
circuit analysis with state variables 5-22
circuit transformation from time
to complex frequency 4-1
clc MATLAB command A-2
clear MATLAB command A-2
cofactor of a matrix – see matrix
collect(s) MATLAB symbolic function 3-12
column vector in MATLAB A-19
command screen in MATLAB A-1
Command Window in MATLAB A-1
commas in MATLAB A-8
comment line in MATLAB A-2
Commonly Used Blocks in Simulink B-7
complex conjugate in MATLAB A-4
complex conjugate pairs 3-5
complex impedance – see impedance
complex number C-2
complex numbers in MATLAB A-3
complex poles 3-5
Complex to Magnitude-Angle
computation of the state
transition matrix 5-11
computation of the Z Transform with
contour integration – see Z transform
Configuration Parameters
congugate of a matrix – see matrix
conj(A) MATLAB function D-9
conjugate of a complex number C-3
conjugate time and frequency functions
of the Fourier transform – see
Fourier transform – properties of
constant function – Fourier transform of
see Fourier transform – properties of
contour integral 9-20
conv MATLAB function A-7
convolution in the complex frequency
domain – see Laplace transform
properties of
convolution in the discrete-frequency
domain – see Z transform – properties of
convolution in the discrete-time
domain – see Z transform – properties of
convolution in the time domain property
of the Laplace transform – see
Laplace transform – properties of
convolution integral defined 6-8
graphical evaluation of 6-8
convolution property of the Fourier
transform – see Fourier transform
properties of
Cooley and Tukey 10-18
cosine function – Fourier transform of
see Fourier transform of
common functions
cosa>0t u0(t) function – Fourier transform of
see Fourier transform of
common functions
Cramer’s rule D-17
D
d2c MATLAB function 9-47
data points in MATLAB A-14
decimation in frequency – see FFT algorithm
decimation in time – see FFT algorithm
deconv MATLAB function A-6
default color in MATLAB A-15
default line in MATLAB A-15
default marker in MATLAB A-15
default values in MATLAB A-12
delta (impulse) function
definition of 1-11
doublet 1-14
Fourier transform of – see Fourier
transform of common functions
higher order 1-14
nth-order 1-14
sampling property of 1-12
sifting property of 1-13
triplet 1-14
demo in MATLAB A-2
DeMoivre’s theorem 11-15
derivation of the Fourier transform from
the Laplace Transform 8-25
determinant of a matrix – see matrix
determinant of order 2 – see matrix
DFT – common properties of
even time function 10-9
even frequency function 10-9
frequency convolution 10-13
frequency shift 10-12
linearity 10-10
odd time function 10-9
odd frequency function 10-9
time convolution 10-12
time shift 10-11
DFT – definition of 10-1
N-point 10-2, 10-16
diagonal elements of a matrix – see matrix
diagonal matrix – see matrix
IN-1differentiation in complex frequency
domain property of the Laplace
transform – see Laplace transform
• properties of
differentiation in time domain property
of the Laplace transform – see
Laplace transform – properties of
differentiation property of the Fourier
transform 8-12 – see Fourier
transform – properties of
digital filter 11-1, 11-51, 11-70
Finite Impulse Response (FIR) 11-52
FIR 11-52
IIR 11-51
Infinite Impulse Response (IIR) 11-51
realization of
Direct Form I 11-70
Direct Form II 11-71
non-recursive 11-52
parallel form 11-70
recursive 11-52
Digital Filter Design Simulink block 11-78
digital filter design with Simulink 11-70
dimpulse MATLAB function 9-29
Dirac MATLAB function 1-20
Direct Form I realization – see digital filter
realization of
Direct Form II realization – see digital filter
realization of
direct term in MATLAB 3-4
discontinuous function – definition of 1-2
Discrete Fourier Transform (DFT) 10-1
discrete impulse response 9-40
discrete-time system transfer function 9-40
discrete unit step function 9-3
discrete-time exponential sequence 9-16
discrete-time systems 9-1
discrete-time unit ramp function 9-18
discrete-time unit step function 9-14
display formats in MATLAB A-31
distinct eigenvalues – see eigenvalues
distinct poles – see poles
division of complex numbers C-4
dot operator in MATLAB
division with A-21
exponentiation with A-21
multiplication with A-20
double-memory technique
see FFT Algorithm
doublet – see delta function
E
Editor Window in MATLAB A-1
Editor/Debugger in MATLAB A-1
eig(x) MATLAB function 5-17
eigenvalues
distinct 15-1
multiple (repeated) 5-15
eigenvector 5-19
e-j“t u0(t) Fourier transform of – see Fourier
transform of common functions
element-by-element operation in MATLAB
division A-21
exponentiation A-21
multiplication A-20
elements of the matrix – see matrix
ellip MATLAB function 11-40
elliptic filter – see filter
elliptic filter design – see filter design
eps in MATLAB A-22
Euler’s identities C-5
even functions 6-4, 7-33
even symmetry – see Fourier
series – symmetry
Excel’s Analysis ToolPak 10-5
exit MATLAB command A-2
expand MATLAB symbolic function 3-10
exponential form of complex numbers C-5
exponential form of the Fourier series –
see Fourier series
exponential order function –
definition of 2-2
eye(n) MATLAB function D-7
eye(size(A)) MATLAB function D-7
F
factor(s) MATLAB symbolic function 3-4
Fast Fourier Transform (FFT) 10-1, 10-17
FDA Tool Digital Filter Design
FFT algorithm
Category I 10-19
Category II 10-20
decimation in frequency 10-20
decimation in time 10-20
double-memory technique 10-20
in-place 10-20
natural input-output 10-20
FFT definition of 10-1, 10-17
fft(x) MATLAB function 10-5, 11-68
Figure Window in MATLAB A-13
active
high-pass 4-22, 4-32
low-pass 4-22, 4-32, 4-23, 4-35
all-pass 11-1, 11-94
all-pole 11-21
band-elimination 11-1, 11-8
band-pass 11-1, 11-7
band-stop – see band-elimination
Bessel 11-95
Chebyshev 11-10
Inverted 11-38
magnitude-square function 11-26
prototype 11-10
Type I 11-25
Type II 11-38
elliptic 11-39
high-pass 4-22, 4-30, 11-1, 11-4
low-pass 4-22, 4-30, 11-1, 11-2
low-pass analog filter
prototypes 11-10
maximally flat 11-14 (footnote)
notch (band-elimination) 11-8
phase shift 11-1, 11-94
RC high-pass 11-4
RC low-pass 11-2
RLC band-elimination 4-22, 4-31, 11-8
RLC band-pass 4-22, 4-31, 11-7
band-elimination 11-41
band-pass 11-41
Butterworth analog low-pass 11-14
Chebyshev
Type I 11-25
Type II 11-38
elliptic 11-39
high-pass 11-41
low-pass 11-14
filter MATLAB function 11-63
final value theorem in Z transform
see Z transform – properties of
final value theorem in Laplace transform
see Laplace transform – properties of
find MATLAB function 11-68
Finite Impulse Response (FIR) digital filter
see digital filter
FIR – see digital filter
first harmonic – see Fourier series
harmonics of
first-order circuit 5-1
first-order simultaneous
differential equations 5-1
Flip Block command in Simulink B-11
format in MATLAB A-31
fourier MATLAB command 8-33
Fourier series
exponential form of 7-31
method used in window functions E-17
trigonometric form of 7-2, 7-10
alternate form of 7-25
Fourier series coefficients – evaluation of
numerical evaluation using Excel 7-46
numerical evaluation using MATLAB® 7-47
Fourier series of common waveforms
full-wave rectifier 7-20, 7-24
half-wave rectifier 7-17, 7-20
square waveform
with even symmetry 7-9, 7-13
with odd symmetry 7-8, 7-12
sawtooth 7-9, 7-15
triangular 7-9, 7-16
Fourier series – harmonics of
first 7-1, 7-10
second 7-1, 7-10
third 7-1, 7-10
Fourier series – symmetry
even 7-7
half-wave 7-7, 7-34
odd 7-7
quarter-wave 7-7 (footnote)
types of 7-7
Fourier integral – see Fourier transform
Fourier transform
definition of 8-1
inverse of 8-1
special forms of 8-2
IN-2Fourier transform – properties of
area under f(t) 8-15
area under F(ro) 8-15
conjugate time and frequency
functions 8-13
constant function 8-18
frequency convolution 8-15
frequency differentiation 8-13
frequency shifting 8-11
imaginary time functions – Fourier
transform of 8-6
linearity 8-9
Parseval’s theorem 8-16
real time functions – Fourier
transform of 8-3
symmetry 8-9
time convolution 8-14
time differentiation 8-12
time integration 8-13
time scaling 8-10
time shifting 8-11
Fourier Transform derivation from
Laplace transform 8-25
Fourier transform of common functions
cosro 0t 8-19
cosro0t u0(t) 8-24
delta (8(t) and 8(t-a)) 8-18
e-jro0t 8-19
e-jro0t u0(t) 8-24
signum (sgn(t)) 8-20
sinro0t 8-20
sinro0t u0(t) 8-25
unit step (u0(t)) 8-22
Fourier transform of common waveforms
combined rectangular pulses 8-29
cosine within a rectangular pulse 8-30
shifted rectangular pulse 8-28
symmetrical rectangular pulse 8-27
periodic time functions 8-31, 8-32
fourth-order all-pole low-pass filter
see filter, low-pass
fplot in MATLAB A-27
frequency convolution in DFT
see DFT – common properties of
frequency convolution in Fourier
transform of – see Fourier transform
• properties of
frequency differentiation in Fourier
transform of – see Fourier transform
• properties of
frequency shift in DFT
see DFT – common properties of
frequency shift in Fourier transform
see Fourier transform – properties of
frequency shift in Laplace transform
see Laplace transform – properties of
freqz MATLAB function 11-57
full rectification waveform – Laplace
transform of – see Laplace transform
of common waveforms
full-wave rectifier – Fourier series of – see
Fourier series of common waveforms
Function Block Parameters in Simulink B-10
function files in MATLAB A-26
fundamental frequency 7-1
fzero MATLAB function A-26
G
Gain block in Simulink B-9, B-18
gamma function 2-15
Gaussian elimination method D-19
generalized factorial function 2-15
Gibbs phenomenon 7-24
grid MATLAB command A-12
gtext MATLAB command A-13
H
half-wave rectifier – Fourier series of – see
Fourier series of common waveforms
half-wave symmetry
see Fourier series – symmetry
Heavyside MATLAB function 1-14
help in MATLAB A-2
Hermitian matrix – see matrix
higher order delta functions – see delta
function
high-pass filter – see filter
high-pass filter design – see filter design
I
identity matrix – see matrix
ifft(x) MATLAB function 10-5
ifourier MATLAB function 8-33
IIR – see digital filter
ilaplace MATLAB function 3-4
imag(z) MATLAB function A-23
imaginary axis – definition of C-2
imaginary number – definition of C-2
imaginary time functions 8-6
see Fourier transform – properties of
impedance
capacitive 4-2
inductive 4-2
complex input 4-8, 4-9
improper integral – definition of 2-15
improper rational function –
definition of 3-1, 3-13
impulse function – see delta function
impulse invariant method – see
transformation methods for mapping
analog prototype filters to
digital filters
increments between points
in MATLAB A-14
inductive impedance – see impedance
infinite impulse response – see digital filter
initial value theorem in Z transform
see Z transform – properties of
initial value theorem in Laplace transform
see Laplace transform – properties of
in-place FFT algorithm 10-20
see FFT algorithm
integration in frequency in Laplace transform
see Laplace transform – properties of
integration in time in Laplace transform
see Laplace transform – properties of
Inverse Fourier transform
see Fourier transform
Inverse Laplace transform 2-1
see Laplace transform
inverse of a matrix – see matrix
Inverse Z transform – see Z transform
inversion integral 9-32
Inverted Chebyshev filter – see filter
J j
operator C-1
L L
’ Hopital’s rule 2-16
laplace MATLAB function 2-27
Laplace integral – see Laplace transform
Laplace transform
definition of 2-1
Inverse of 2-1, 3-1
Laplace transform – properties of
convolution in the complex
frequency domain 2-12
convolution in the time domain 2-11
differentiation in complex
frequency domain 2-6
differentiation in time domain 2-4
final value theorem 2-10
frequency shift 2-4
initial value theorem 2-9
integration in
complex frequency domain 2-8
time domain 2-6
linearity 2-3
scaling 2-4
time periodicity 2-8
time shift 2-3
Laplace transform of common waveforms
full-rectified 2-32
half-rectified 2-26
linear segment 2-23
pulse 2-23
rectangular periodic 2-25
sawtooth 2-32
triangular 2-24
Laplace transform of common functions
transform of e-at cosrot u0(t) 2-22
transform of e-at sinrot u0(t) 2-21
transform of e-at u0(t) 2-19
transform of cosrot u0(t) 2-20
transform of 8(t) 2-18
transform of 8(t-a) 2-18
transform of sinrot u0(t) 2-20
transform of tn u0(t) function 2-15
transform of tn e-at u0(t) 2-19
transform of u0(t) 2-14
transform of u1(t) 2-14
leakage 10-13
left shift in discrete-time domain
see Z transform – properties of
Leibnitz’s rule 6
lims= MATLAB command A-27
line spectra 7-36
linear difference equation 9-38
IN-3linearity in DFT
see DFT – common properties of
linearity in discrete-time domain
see Z transform – properties of
linearity property in Fourier transform
see Fourier transform – properties of
linearity property in Laplace transform
see Laplace transform – properties of
linspace MATLAB command A-14
ln (natural log) A-13
log(x) MATLAB function A-13
log10(x) MATLAB function A-13
log2(x) MATLAB function A-13
loglog MATLAB command A-13
long division of polynomials 9-36
lower triangular matrix – see matrix
low-pass analog filter prototypes – see filter
low-pass filter – see filter
lp2bp MATLAB function 11-43
lp2bs MATLAB function 11-43
lp2hp MATLAB function 11-43
lp2lp MATLAB function 11-43
M
magnitude-squared function 11-10
main diagonal of a matrix – see matrix
MATLAB Demos A-2
MATLAB’s Editor/Debugger A-1
matrix (matrices)
cofactor of D-13
conformable for subtraction D-2
conformable for multiplication D-4
congugate of D-8
definition of D-1
determinant D-10
minor of D-13
non-singular D-21
singular D-21
diagonal D-2, D-6
diagonal elements of D-2
elements of D-1
Hermitian D-9
identity D-7
inverse of D-22
left division in MATLAB D-25
multiplication in MATLAB A-18
power series of 5-9
scalar D-7
size of D-7
skew-Hermitian D-9
skew-symmetric D-9
square D-1
symmetric D-8
trace of D-2
transpose of D-8
triangular
lower D-6
upper D-6
zero D-2
matrix left division in MATLAB – see matrix
matrix multiplication in MATLAB – see matrix
matrix power series – see matrix
maximally flat filter – see filter
mesh(x,y,z) MATLAB function A-17
meshgrid(x,y) MATLAB command A-17
m-file in MATLAB A-2, A-26
minor of determinant – see matrix
MINVERSE Excel function D-27
MMULT Excel function D-27
modulated signals 8-12
multiple eigenvalues – see eigenvalues
multiple poles – see poles
multiplication by an in discrete-time domain
see Z transform – properties of
multiplication by e-naT in discrete-time
domain – see Z transform – properties of
multiplication by n in discrete-time domain
see Z transform – properties of
multiplication by n2 indiscrete-time domain
see Z transform – properties of
multiplication of complex numbers C-3
N
NaN in MATLAB A-26
natural input-output FFT algorithm
see FFT algorithm
network transformation
resistive 4-1
capacitive 4-1
inductive 4-1
non-recursive realization digital filter
see digital filter
non-singular determinant – see matrix
normalized cutoff frequency 11-15
notch filter – see filter
N-point DFT – see DFT – definition of
nth-order delta function – see delta function
numerical evaluation of Fourier coefficients
see Fourier series coefficients
Nyquist frequency 10-13
O
octave defined 11-12
odd functions 6-5, 7-34
odd symmetry – see Fourier
series – symmetry
orthogonal functions 7-2
orthogonal vectors 5-19
orthonormal basis 5-19
P
parallel form realization – see digital filter
Parseval’s theorem – see
Fourier transform – properties of
partial fraction expansion 3-1, 3-2, 9-25
alternate method of 3-15
method of clearing the fractions 3-15
phase angle 11-2
phase shift filter – see filter
picket-fence effect 10-14
plot MATLAB command A-10
polar form of complex numbers C-6
polar plot in MATLAB A-24
polar(theta,r) MATLAB function A-23
poles 3-1
complex 3-5
distinct 3-2
multiple (repeated) 3-8
poly MATLAB function A-4
polyder MATLAB function A-7
polynomial construction from
known roots in MATLAB A-4
polyval MATLAB function A-6
pre-sampling filter 10-13
pre-warping 11-55
proper rational function –
definition of 3-1, 11-11
properties of the DFT
see DFT – common properties of
properties of the Fourier Transform
see Fourier transform – properties of
properties of the Laplace Transform
see Laplace transform – properties of
properties of the Z Transform
see Z transform – properties of
Q
quarter-wave symmetry 7-7 (footnote)
quit MATLAB command A-2
R
ramp function 1-9
randn MATLAB function 11-68
rationalization of the quotient C-4
RC high-pass filter – see filter
RC low-pass filter – see filter
real axis C-2
real number C-2
real(z) MATLAB function A-23
rectangular form C-5
rectangular pulse expressed in terms
of the unit step function 1-4
recursive realization digital filter
see digital filter
region of
convergence 9-3
divergence 9-3
relationship between state equations
and Laplace Transform 5-30
residue 3-2, 9-41
residue MATLAB function 3-3, 3-12
residue theorem 9-20, 9-21
right shift in the discrete-time domain
see Z transform – properties of
RLC band-elimination filter – see filter
RLC band-pass filter – see filter
roots of polynomials in MATLAB A-3
roots(p) MATLAB function 3-6, A-3
round(n) MATLAB function A-24
row vector in MATLAB A-3
Runge-Kutta method 5-1
IN-4S
sampling property of the delta function
see delta function
sampling theorem 10-13
sawtooth waveform – see Laplace
transform of common waveforms
sawtooth waveform – Fourier series of
see Fourier series of
common waveforms
scalar matrix – see matrix
scaling property of the Laplace transform
see Laplace transform – properties of
script file in MATLAB A-2, A-26
second harmonic – see Fourier series
harmonics of
semicolons in MATLAB A-8
semilogx MATLAB command A-12
semilogy MATLAB command A-12
series form realization – see digital filter
Shannon’s sampling theorem
see sampling theorem
shift of f[n] u0[n] in discrete-time domain
see Z transform – properties of
sifting property of the delta function
see delta function
signal flow graph 10-23
signals described in math form 1-1
signum function – see Fourier transform
of common functions
simout To Workspace block
simple MATLAB symbolic function 3-7
simulation start icon in Simulink B-12
sine function – Fourier transform of
see Fourier transform of
common functions
singular determinant – see matrix
sina>0t u0(t) Fourier transform of – see
Fourier transform of common functions
size of a matrix – see matrix
skew-Hermitian matrix – see matrix
skew-symmetric matrix – see matrix
special forms of the Fourier transform
see Fourier transform
spectrum analyzer 7-36
square matrix – see matrix
square waveform with even symmetry – see
Fourier series of common waveforms
square waveform with odd symmetry – see
Fourier series of common waveforms
ss2tf MATLAB function 5-33
stability 11-13
state equations
for continuous-time systems 5-1
for discrete-time systems 9-45
state transition matrix 5-9
state variables
for continuous-time systems 5-1
for discrete-time systems 9-45
state-space equations
for continuous-time systems 5-1
for discrete-time systems 9-45
step function – see unit step function
step invariant method – see transformation methods for mapping analog
prototype filters to digital filters
stop-band filter – see filter
string in MATLAB A-16
subplots in MATLAB A-18
summation in the discrete-time Domain
see Z transform – properties of
symmetric matrix – see matrix
symmetric rectangular pulse expressed
as sum of unit step functions 1-6
symmetric triangular waveform expressed
as sum of unit step functions 1-6
symmetry – see Fourier series – symmetry
symmetry property of the Fourier transform
see Fourier transform – properties of
system function – definition of 8-35
T
Taylor series 5-1
text MATLAB command A-14
tf2ss MATLAB function 5-33
theorems of the DFT 10-10
theorems of the Fourier Transform 8-9
theorems of the Laplace transform 2-2
theorems of the Z Transform 9-3
third harmonic – see Fourier
series – harmonics of
time convolution in DFT
see DFT – common properties of
time integration property of the Fourier
transform – see Fourier
transform – properties of
time periodicity property of the Laplace
transform 2-8 – see Laplace
transform – properties of
time scaling property of the Fourier
transform – see Fourier
transform – properties of
time shift in DFT
see DFT – common properties of
time shift property of the Fourier transform
see Fourier transform – properties of
time shift property of the Laplace transform
see Laplace transform – properties of
title(‘string’) MATLAB command A-12
trace of a matrix – see matrix
Transfer Fcn block in Simulink 4-17
Transfer Fcn Direct Form II
transfer function of
continuous-time systems 4-13
discrete-time systems 9-38
transformation between
s and z domains 9-22
transformation methods for mapping
analog prototype filters to digital filters
Impulse Invariant Method 11-52
Step Invariant Method 11-52
Bilinear transformation 11-53
transpose of a matrix – see matrix
triangular waveform expressed in terms
of the unit step function 1-4
triplet – see delta function
Tukey – see Cooley and Tukey
U
unit eigenvectors 5-19
unit impulse function (S(t)) 1-8
unit ramp function (u1(t)) 1-8
unit step function (u0(t)) 1-2
upper triangular matrix – see matrix
using MATLAB for finding the Laplace
transforms of time functions 2-27
using MATLAB for finding the Fourier
transforms of time function 8-33
V
Vandermonde matrix 10-18
W
warping 11-54
window functions
Blackman E-12
Fourier series method for approximating
an FIR amplitude response E-17
Hamming E-9, E-31
Hanning E-7, E-27
Kaiser E-14, E-35
other used as MATLAB functions E-15
rectangular E-2
triangular E-5, E-23
Window Visualization Tool in MATLAB E-4
X
xlabel MATLAB command A-12
Y
ylabel MATLAB command A-12
Z Z
transform
computation of with contour
integration 9-20
definition of 9-1
Inverse of 9-1, 9-25
Z transform – properties of
convolution in the discrete
frequency domain 9-9
convolution in the discrete
time domain 9-8
final value theorem 9-10
initial value theorem 9-9
left shift 9-5
linearity 9-3
IN-5multiplication by an 9-6
multiplication by e-naT 9-6
multiplication by n 9-6
multiplication by n2 9-6
right shift 9-4
shift of f[n] u0[n] 9-3
summation 9-7
Z Transform of discrete-time functions
cosine function cosnaT 9-16
exponential sequence e-naT u0[n]
9-16, 9-21
geometric sequence an 9-11
sine function sinnaT 9-16
unit ramp function nu0[n] 9-18, 9-21
unit step function u0[n] 9-14, 9-20
zero matrix – see matrix
zeros 3-1, 3-2
zp2tf MATLAB function 11-17

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