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Unformatted text preview: ⎛ ∞ − jω n ∞ − jω n ⎞ − ∑e ⎜ ∑e ⎟ ⎝ n =0 ⎠ n= M ) 1 M = M −1 − jMω 1− e ⎛ ∞ − jω n ⎞ − jMω =1⋅ ⎟ 1− e ⎜ ∑e M 1 − e − jω ⎝ n =0 ⎠ = 1 sin( Mω / 2) − j ( M −1) ω / 2 ⋅ e M sin(ω / 2) − jω n ∑e n=0 46 Copyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra Frequency Response Computation Using MATLAB The Frequency Response • The function freqz(h,1,w) can be used to determine the values of the frequency response vector h at a set of given frequency points w • From h, the real and imaginary parts can be computed using the functions real and imag, and the magnitude and phase functions using the functions abs and angle • Thus, the magnitude response of the M-point moving average filter is given by sin( Mω / 2) H ( e jω ) = 1 ⋅ M sin(ω / 2) and the phase response is given by θ(ω) = − 1 M ( M − 1)ω M/2 2π k + π ∑µ (ω − M ) 2 k =0 47 48 Copyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra 8 Frequency Response Computation Using MATLAB Frequency Response Computation Using MATLAB • Example - Program 3_2.m can be used to generate the mag...
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This document was uploaded on 11/09/2013.

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