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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