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differentiation in complex frequency transform of common functions notch (band-elimination) 11-8domain property of the Laplace element-by-element operation in MATLAB phase shift 11-1, 11-94transform - see Laplace transform division A-21 RC high-pass 11-4- properties of exponentiation A-21 RC low-pass 11-2differentiation in time domain property multiplication A-20 RLC band-elimination 4-22, 4-31, 11-8of the Laplace transform - see elements of the matrix - see matrix RLC band-pass 4-22, 4-31, 11-7Laplace transform - properties of ellip MATLAB function 11-40 filter design - see also digital filterdifferentiation property of the Fourier elliptic filter - see filter band-elimination 11-41transform 8-12 - see Fourier elliptic filter design - see filter design band-pass 11-41transform - properties of eps in MATLAB A-22 Butterworth analog low-pass 11-14digital filter 11-1, 11-51, 11-70 Euler’s identities C-5 ChebyshevFinite Impulse Response (FIR) 11-52 even functions 6-4, 7-33 Type I 11-25FIR 11-52 even symmetry - see Fourier Type II 11-38IIR 11-51 series - symmetry elliptic 11-39Infinite Impulse Response (IIR) 11-51 Excel's Analysis ToolPak 10-5 high-pass 11-41realization of exit MATLAB command A-2 low-pass 11-14Direct Form I 11-70 expand MATLAB symbolic function 3-10 filter MATLAB function 11-63Direct Form II 11-71 exponential form of complex numbers C-5 final value theorem in Z transformcascade (series) form 11-73 exponential form of the Fourier series - see Z transform - properties ofnon-recursive 11-52 see Fourier series final value theorem in Laplace transformparallel form 11-70 exponential order function - see Laplace transform - properties ofrecursive 11-52 definition of 2-2 find MATLAB function 11-68series (cascade) form 11-73 eye(n) MATLAB function D-7 Finite Impulse Response (FIR) digital filterDigital Filter Design Simulink block 11-78 eye(size(A)) MATLAB function D-7 see digital filterdigital filter design with Simulink 11-70FIR - see digital filterdimpulse MATLAB function 9-29 F first harmonic - see Fourier seriesDirac MATLAB function 1-20 harmonics ofDirect Form I realization - see digital filter factor(s) MATLAB symbolic function 3-4 first-order circuit 5-1realization of Fast Fourier Transform (FFT) 10-1, 10-17 first-order simultaneousDirect Form II realization - see digital filter FDA Tool Digital Filter Design differential equations 5-1realization of Simulink block 11-82 Flip Block command in Simulink B-11direct term in MATLAB 3-4 FFT algorithm format in MATLAB A-31discontinuous function - definition of 1-2 Category I 10-19 fourier MATLAB command 8-33Discrete Fourier Transform (DFT) 10-1 Category II 10-20 Fourier seriesdiscrete impulse response 9-40 decimation in frequency 10-20 exponential form of 7-31discrete-time system transfer function 9-40 decimation in time 10-20 method used in window functions E-17discrete unit step function 9-3 double-memory technique 10-20 trigonometric form of 7-2, 7-10discrete-time exponential sequence 9-16 in-place 10-20 alternate form of 7-25discrete-time systems 9-1 natural input-output 10-20 Fourier series coefficients - evaluation ofdiscrete-time unit ramp function 9-18 FFT definition of 10-1, 10-17 numerical evaluation using Excel 7-46discrete-time unit step function 9-14 fft(x) MATLAB function 10-5, 11-68 numerical evaluation using MATLAB® 7-47Display block in Simulink B-18 Figure Window in MATLAB A-13 Fourier series of common waveformsdisplay formats in MATLAB A-31 filter - see also digital filter full-wave rectifier 7-20, 7-24distinct eigenvalues - see eigenvalues active half-wave rectifier 7-17, 7-20distinct poles - see poles high-pass 4-22, 4-32 square waveformdivision of complex numbers C-4 low-pass 4-22, 4-32, 4-23, 4-35 with even symmetry 7-9, 7-13dot operator in MATLAB all-pass 11-1, 11-94 with odd symmetry 7-8, 7-12division with A-21 all-pole 11-21 sawtooth 7-9, 7-15exponentiation with A-21 band-elimination 11-1, 11-8 triangular 7-9, 7-16multiplication with A-20 band-pass 11-1, 11-7 Fourier series - harmonics ofdouble-memory technique band-stop - see band-elimination first 7-1, 7-10see FFT Algorithm Bessel 11-95 second 7-1, 7-10doublet - see delta function Chebyshev 11-10 third 7-1, 7-10Inverted 11-38Fourier series - symmetryE magnitude-square function 11-26 even 7-7prototype 11-10 half-wave 7-7, 7-34Editor Window in MATLAB A-1 Type I 11-25 odd 7-7Editor/Debugger in MATLAB A-1 Type II 11-38 quarter-wave 7-7 (footnote)eig(x) MATLAB function 5-17 elliptic 11-39 types of 7-7eigenvalues high-pass 4-22, 4-30, 11-1, 11-4 Fourier integral - see Fourier transformdistinct 15-1 low-pass 4-22, 4-30, 11-1, 11-2 Fourier transformmultiple (repeated) 5-15 low-pass analog filter definition of 8-1eigenvector 5-19 prototypes 11-10 inverse of 8-1e -jωt u 0 (t) Fourier transform of - see Fourier maximally flat 11-14 (footnote) special forms of 8-2IN-2