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linearity in DFT matrix multiplication in MATLAB - see matrix polar plot in MATLAB A-24see DFT - common properties of matrix power series - see matrix polar(theta,r) MATLAB function A-23linearity in discrete-time domain maximally flat filter - see filter poles 3-1see Z transform - properties of mesh(x,y,z) MATLAB function A-17 complex 3-5linearity property in Fourier transform meshgrid(x,y) MATLAB command A-17 distinct 3-2see Fourier transform - properties of m-file in MATLAB A-2, A-26 multiple (repeated) 3-8linearity property in Laplace transform minor of determinant - see matrix poly MATLAB function A-4see Laplace transform - properties of MINVERSE Excel function D-27 polyder MATLAB function A-7linspace MATLAB command A-14 MMULT Excel function D-27 polynomial construction fromln (natural log) A-13 modulated signals 8-12 known roots in MATLAB A-4log in MATLAB A-13 multiple eigenvalues - see eigenvalues polyval MATLAB function A-6log(x) MATLAB function A-13 multiple poles - see poles pre-sampling filter 10-13log10(x) MATLAB function A-13 multiplication by an in discrete-time domain pre-warping 11-55log2(x) MATLAB function A-13 see Z transform - properties of proper rational function -loglog MATLAB command A-13 multiplication by e -naT in discrete-time definition of 3-1, 11-11long division of polynomials 9-36 domain - see Z transform - properties of properties of the DFTlower triangular matrix - see matrix multiplication by n in discrete-time domain see DFT - common properties oflow-pass analog filter prototypes - see filter see Z transform - properties of properties of the Fourier Transformlow-pass filter - see filter multiplication by n 2 indiscrete-time domain see Fourier transform - properties oflp2bp MATLAB function 11-43 see Z transform - properties of properties of the Laplace Transformlp2bs MATLAB function 11-43 multiplication of complex numbers C-3 see Laplace transform - properties oflp2hp MATLAB function 11-43properties of the Z Transformlp2lp MATLAB function 11-43 N see Z transform - properties ofM NaN in MATLAB A-26 Qnatural input-output FFT algorithmmagnitude-squared function 11-10 see FFT algorithm quarter-wave symmetry 7-7 (footnote)main diagonal of a matrix - see matrix network transformation quit MATLAB command A-2Math Operations in Simulink B-10 resistive 4-1MATLAB Demos A-2 capacitive 4-1 RMATLAB’s Editor/Debugger A-1 inductive 4-1matrix (matrices) non-recursive realization digital filter radius of absolute convergence 9-3adjoint of D-21 see digital filter ramp function 1-9cofactor of D-13 non-singular determinant - see matrix randn MATLAB function 11-68conformable for addition D-2 normalized cutoff frequency 11-15 Random Source Simulink block 11-80conformable for subtraction D-2 notch filter - see filter rationalization of the quotient C-4conformable for multiplication D-4 N-point DFT - see DFT - definition of RC high-pass filter - see filtercongugate of D-8 nth-order delta function - see delta function RC low-pass filter - see filterdefinition of D-1 numerical evaluation of Fourier coefficients real axis C-2determinant D-10 see Fourier series coefficients real number C-2minor of D-13 Nyquist frequency 10-13 real(z) MATLAB function A-23non-singular D-21 rectangular form C-5singular D-21 O rectangular pulse expressed in termsdiagonal D-2, D-6 of the unit step function 1-4diagonal elements of D-2 octave defined 11-12 recursive realization digital filterelements of D-1 odd functions 6-5, 7-34 see digital filterHermitian D-9 odd symmetry - see Fourier region ofidentity D-7 series - symmetry convergence 9-3inverse of D-22 orthogonal functions 7-2 divergence 9-3left division in MATLAB D-25 orthogonal vectors 5-19 relationship between state equationsmultiplication in MATLAB A-18 orthonormal basis 5-19 and Laplace Transform 5-30power series of 5-9 residue 3-2, 9-41scalar D-7 P residue MATLAB function 3-3, 3-12size of D-7 residue theorem 9-20, 9-21skew-Hermitian D-9 parallel form realization - see digital filter right shift in the discrete-time domainskew-symmetric D-9 Parseval’s theorem - see see Z transform - properties ofsquare D-1 Fourier transform - properties of RLC band-elimination filter - see filtersymmetric D-8 partial fraction expansion 3-1, 3-2, 9-25 RLC band-pass filter - see filtertrace of D-2 alternate method of 3-15 roots of polynomials in MATLAB A-3transpose of D-8 method of clearing the fractions 3-15 roots(p) MATLAB function 3-6, A-3triangular phase angle 11-2 round(n) MATLAB function A-24lower D-6 phase shift filter - see filter row vector in MATLAB A-3upper D-6 picket-fence effect 10-14 Runge-Kutta method 5-1zero D-2 plot MATLAB command A-10 running Simulink B-7matrix left division in MATLAB - see matrix polar form of complex numbers C-6IN-4
S for discrete-time systems 9-45 Step Invariant Method 11-52State-Space block in Simulink B-12 Bilinear transformation 11-53sampling property of the delta function state-space equations transpose of a matrix - see matrixsee delta function for continuous-time systems 5-1 Tree Pane in Simulink B-7sampling theorem 10-13 for discrete-time systems 9-45 triangular waveform expressed in termssawtooth waveform - see Laplace step function - see unit step function of the unit step function 1-4transform of common waveforms step invariant method - see trans- triplet - see delta functionsawtooth waveform - Fourier series of formation methods for mapping analog Tukey - see Cooley and Tukeysee Fourier series ofprototype filters to digital filterscommon waveforms stop-band filter - see filter Uscalar matrix - see matrix string in MATLAB A-16scaling property of the Laplace transform subplots in MATLAB A-18 unit eigenvectors 5-19see Laplace transform - properties of summation in the discrete-time Domain unit impulse function (δ(t)) 1-8Scope block in Simulink B-12 see Z transform - properties of unit ramp function (u 1 (t)) 1-8script file in MATLAB A-2, A-26 symmetric matrix - see matrix unit step function (u 0 (t)) 1-2second harmonic - see Fourier series symmetric rectangular pulse expressed upper triangular matrix - see matrixharmonics of as sum of unit step functions 1-6 using MATLAB for finding the Laplacesemicolons in MATLAB A-8 symmetric triangular waveform expressed transforms of time functions 2-27semilogx MATLAB command A-12 as sum of unit step functions 1-6 using MATLAB for finding the Fouriersemilogy MATLAB command A-12 symmetry - see Fourier series - symmetry transforms of time function 8-33series form realization - see digital filter symmetry property of the Fourier transformShannon’s sampling theorem see Fourier transform - properties of Vsee sampling theorem system function - definition of 8-35shift of f[n] u 0 [n] in discrete-time domain Vandermonde matrix 10-18see Z transform - properties of T Vector Scope Simulink block 11-84sifting property of the delta functionsee delta function Taylor series 5-1 Wsignal flow graph 10-23 text MATLAB command A-14signals described in math form 1-1 tf2ss MATLAB function 5-33 warping 11-54signum function - see Fourier transform theorems of the DFT 10-10 window functionsof common functions theorems of the Fourier Transform 8-9 Blackman E-12simout To Workspace block theorems of the Laplace transform 2-2 Fourier series method for approximatingin Simulink B-12 theorems of the Z Transform 9-3 an FIR amplitude response E-17simple MATLAB symbolic function 3-7 third harmonic - see Fourier Hamming E-9, E-31Simulation drop menu in Simulink B-12 series - harmonics of Hanning E-7, E-27simulation start icon in Simulink B-12 time convolution in DFT Kaiser E-14, E-35Simulink icon B-7 see DFT - common properties of other used as MATLAB functions E-15Simulink Library Browser B-8 time integration property of the Fourier rectangular E-2sine function - Fourier transform of transform - see Fourier triangular E-5, E-23see Fourier transform of transform - properties of Window Visualization Tool in MATLAB E-4common functionstime periodicity property of the Laplacesingular determinant - see matrix transform 2-8 - see Laplace XSinks library in Simulink B-18 transform - properties ofsinω 0 t u 0 (t) Fourier transform of - see time scaling property of the Fourier xlabel MATLAB command A-12Fourier transform of common functions transform - see Fouriersize of a matrix - see matrix transform - properties of Yskew-Hermitian matrix - see matrixtime shift in DFTskew-symmetric matrix - see matrix see DFT - common properties of ylabel MATLAB command A-12special forms of the Fourier transform time shift property of the Fourier transformsee Fourier transform see Fourier transform - properties of Zspectrum analyzer 7-36time shift property of the Laplace transformsquare matrix - see matrix see Laplace transform - properties of Z transformsquare waveform with even symmetry - see title(‘string’) MATLAB command A-12 computation of with contourFourier series of common waveforms trace of a matrix - see matrix integration 9-20square waveform with odd symmetry - see Transfer Fcn block in Simulink 4-17 definition of 9-1Fourier series of common waveforms Transfer Fcn Direct Form II Inverse of 9-1, 9-25ss2tf MATLAB function 5-33 Simulink block 11-71 Z transform - properties ofstability 11-13 transfer function of convolution in the discretestart simulation in Simulink B-12 continuous-time systems 4-13 frequency domain 9-9state equations discrete-time systems 9-38 convolution in the discretefor continuous-time systems 5-1 transformation between time domain 9-8for discrete-time systems 9-45 s and z domains 9-22 final value theorem 9-10state transition matrix 5-9 transformation methods for mapping initial value theorem 9-9state variables analog prototype filters to digital filters left shift 9-5for continuous-time systems 5-1 Impulse Invariant Method 11-52 linearity 9-3IN-5
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4.2 Complex Impedance Z(s).........
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8.6.4 The Transform of ft () = Acos
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11.2.1 RC Low−Pass Filter .......
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MATLAB ComputingPages D−3, D−4,
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The Unit Step FunctionThus, the pul
Page 18 and 19: Chapter 1 Elementary Signals6. To d
Page 20 and 21: Chapter 2 The Laplace Transformatio
Page 22 and 23: Chapter 2 The Laplace Transformatio
Page 24 and 25: Chapter 3 The Inverse Laplace Trans
Page 26 and 27: Chapter 4Circuit Analysis with Lapl
Page 28 and 29: Solutions to End−of−Chapter Exe
Page 30 and 31: Chapter 5 State Variables and State
Page 32 and 33: A: [−1 −1; 3/4 0]B: [1 0]’C:
Page 38 and 39: Chapter 7 Fourier Seriesthat is, th
Page 40 and 41: Chapter 8 The Fourier Transform8.2
Page 42 and 43: Chapter 8 The Fourier TransformExam
Page 44 and 45: Chapter 9 Discrete−Time Systems a
Page 46 and 47: num=[0 1 0 0];% The coefficients of
Page 48 and 49: Chapter 10 The DFT and the FFT Algo
Page 50 and 51: The Fast Fourier Transform (FFT)The
Page 52 and 53: Basic Analog Filters11.2.3 RLC Band
Page 54 and 55: Chapter 11 Analog and Digital Filte
Page 56 and 57: Digital Filters1Four signals separa
Page 58 and 59: Chapter 11 Analog and Digital Filte
Page 60: Appendix E Window Functionsh[n]A(f)
Page 63 and 64: Appendix E Window FunctionsMH 1 ( z
Page 65 and 66: IndexSymbols Cauchy’s residue the
Page 67: Fourier transform - properties of f
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