الهندسة الكهربية برامج هندسية ميكاترونيكس هندسة الإنتاج والتصميم الميكانيكى

Signals and Systems with MATLAB Computing and Simulink Modeling – Fourth Edition

اسم المؤلف

Steven T. Karris

التاريخ

تاريخ النشر23 فبراير 2024

التصنيف

فيالهندسة الكهربيةبرامج هندسيةميكاترونيكسهندسة الإنتاج والتصميم الميكانيكى

المشاهدات

886

التقييم

(لا توجد تقييمات)

التحميل

Signals and Systems with MATLAB Computing and Simulink Modeling – Fourth Edition
Steven T. Karris
Table of Contents
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
Simulink Modeling
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) .
4.3 Complex Admittance Y(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
Simulink Modeling
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
Simulink Modeling
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
Pages 7-38, 7-47Simulink Modeling
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
Simulink Modeling
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
Simulink Modeling
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 Introduction to Simulink B-1
B.1 Simulink and its Relation to MATLAB B-1
B.2 Simulink Demos B-20
MATLAB Computing
Page B-4
Simulink Modeling
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
Simulink Modeling
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
Simulink Modeling
Page D-3
Excel Spreadsheet
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
admittance
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
autoscale icon in Simulink B-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 admittance – see admittance
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 admittance – see admittance
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
block in Simulink C-7
computation of the state
transition matrix 5-11
computation of the Z Transform with
contour integration – see Z transform
Configuration Parameters
in Simulink B-12
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
Contents Pane in Simulink B-7
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
decade – definition of 11-12
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
cascade (series) form 11-73
non-recursive 11-52
parallel form 11-70
recursive 11-52
series (cascade) form 11-73
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 block in Simulink B-18
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
Simulink block 11-82
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
filter – see also digital filter
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
filter design – see also digital filter
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 admittance – see admittance
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 in MATLAB 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
Math Operations in Simulink B-10
MATLAB Demos A-2
MATLAB’s Editor/Debugger A-1
matrix (matrices)
adjoint of D-21
cofactor of D-13
conformable for addition D-2
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
radius of absolute convergence 9-3
ramp function 1-9
randn MATLAB function 11-68
Random Source Simulink block 11-80
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
running Simulink B-7
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
Scope block in Simulink B-12
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
in Simulink B-12
simple MATLAB symbolic function 3-7
Simulation drop menu in Simulink B-12
simulation start icon in Simulink B-12
Simulink icon B-7
Simulink Library Browser B-8
sine function – Fourier transform of
see Fourier transform of
common functions
singular determinant – see matrix
Sinks library in Simulink B-18
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
start simulation in Simulink B-12
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 block in Simulink B-12
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
Simulink block 11-71
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
Tree Pane in Simulink B-7
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
Vector Scope Simulink block 11-84
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