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Fourier transform - properties of fzero MATLAB function A-26 Inverse Fourier transformarea under f(t) 8-15 see Fourier transformarea under F(ω) 8-15 G Inverse Laplace transform 2-1conjugate time and frequency see Laplace transformfunctions 8-13 Gain block in Simulink B-9, B-18 inverse of a matrix - see matrixconstant function 8-18 gamma function 2-15 Inverse Z transform - see Z transformfrequency convolution 8-15 Gaussian elimination method D-19 inversion integral 9-32frequency differentiation 8-13 generalized factorial function 2-15 Inverted Chebyshev filter - see filterfrequency shifting 8-11 Gibbs phenomenon 7-24imaginary time functions - Fourier grid MATLAB command A-12 Jtransform of 8-6 gtext MATLAB command A-13linearity 8-9 j operator C-1Parseval's theorem 8-16Hreal time functions - FourierLtransform of 8-3half-wave rectifier - Fourier series of - seesymmetry 8-9 Fourier series of common waveforms L’ Hôpital’s rule 2-16time convolution 8-14 half-wave symmetry laplace MATLAB function 2-27time differentiation 8-12 see Fourier series - symmetry Laplace integral - see Laplace transformtime integration 8-13 Heavyside MATLAB function 1-14 Laplace transformtime scaling 8-10 help in MATLAB A-2 definition of 2-1time shifting 8-11 Hermitian matrix - see matrix Inverse of 2-1, 3-1Fourier Transform derivation from higher order delta functions - see delta Laplace transform - properties ofLaplace transform 8-25 function convolution in the complexFourier transform of common functions high-pass filter - see filter frequency domain 2-12cosω 0 t 8-19 high-pass filter design - see filter design convolution in the time domain 2-11cosω 0 t u 0 (t) 8-24 differentiation in complexdelta (δ(t) and δ(t-a)) 8-18 I frequency domain 2-6e -jω0t 8-19 differentiation in time domain 2-4e -jω0t u 0 (t) 8-24 identity matrix - see matrix final value theorem 2-10signum (sgn(t)) 8-20 ifft(x) MATLAB function 10-5 frequency shift 2-4sinω 0 t 8-20 ifourier MATLAB function 8-33 initial value theorem 2-9sinω 0 t u 0 (t) 8-25 IIR - see digital filter integration inunit step (u 0 (t)) 8-22 ilaplace MATLAB function 3-4 complex frequency domain 2-8Fourier transform of common waveforms imag(z) MATLAB function A-23 time domain 2-6combined rectangular pulses 8-29 imaginary axis - definition of C-2 linearity 2-3cosine within a rectangular pulse 8-30 imaginary number - definition of C-2 scaling 2-4shifted rectangular pulse 8-28 imaginary time functions 8-6 time periodicity 2-8symmetrical rectangular pulse 8-27 see Fourier transform - properties of time shift 2-3periodic time functions 8-31, 8-32 impedance Laplace transform of common waveformsfourth-order all-pole low-pass filter capacitive 4-2 full-rectified 2-32see filter, low-pass inductive 4-2 half-rectified 2-26fplot in MATLAB A-27 complex input 4-8, 4-9 linear segment 2-23frequency convolution in DFT improper integral - definition of 2-15 pulse 2-23see DFT - common properties of improper rational function - rectangular periodic 2-25frequency convolution in Fourier definition of 3-1, 3-13 sawtooth 2-32transform of - see Fourier transform impulse function - see delta function triangular 2-24- properties of impulse invariant method - see Laplace transform of common functionsfrequency differentiation in Fourier transformation methods for mapping transform of e -at cosωt u 0 (t) 2-22transform of - see Fourier transform analog prototype filters to transform of e -at sinωt u 0 (t) 2-21- properties of digital filters transform of e -at u 0 (t) 2-19frequency shift in DFT increments between points transform of cosωt u 0 (t) 2-20see DFT - common properties of in MATLAB A-14 transform of δ(t) 2-18frequency shift in Fourier transform inductive admittance - see admittance transform of δ(t-a) 2-18see Fourier transform - properties of inductive impedance - see impedance transform of sinωt u 0 (t) 2-20frequency shift in Laplace transform infinite impulse response - see digital filter transform of t n u 0 (t) function 2-15see Laplace transform - properties of initial value theorem in Z transform transform of t n e -at u 0 (t) 2-19freqz MATLAB function 11-57 see Z transform - properties of transform of u 0 (t) 2-14full rectification waveform - Laplace initial value theorem in Laplace transform transform of u 1 (t) 2-14transform of - see Laplace transform see Laplace transform - properties of leakage 10-13of common waveforms in-place FFT algorithm 10-20 left shift in discrete-time domainfull-wave rectifier - Fourier series of - see see FFT algorithm see Z transform - properties ofFourier series of common waveforms integration in frequency in Laplace transform Leibnitz’s rule 6Function Block Parameters in Simulink B-10 see Laplace transform - properties of lims= MATLAB command A-27function files in MATLAB A-26 integration in time in Laplace transform line spectra 7-36fundamental frequency 7-1 see Laplace transform - properties of linear difference equation 9-38IN-3