# K mitra phase delay we can rewrite the output

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Unformatted text preview: − jω ⎛ e jω + e − jω ⎞ − jω ⎟e + β e − jω = 2α⎜ ⎜ ⎟ 2 ⎠ ⎝ = (2α cos ω + β)e − jω 72 Copyright © 2005, S. K. Mitra 12 The Concept of Filtering The Concept of Filtering • The magnitude and phase functions are H (e jω ) = 2α cos ω + β θ(ω) = −ω • Thus, the two conditions that must be satisfied are H (e j 0.1 ) = 2α cos(0.1) + β = 0 • In order to block the low-frequency component, the magnitude function at ω = 0.1 should be equal to zero • Likewise, to pass the high-frequency component, the magnitude function at ω = 0.4 should be equal to one 73 H (e j 0.4 ) = 2α cos(0.4) + β = 1 • Solving the above two equations we get α = −6.76195 β = 13.456335 74 Copyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra The Concept of Filtering The Concept of Filtering • Thus the output-input relation of the FIR filter is given by y[n] = −6.76195( x[n] + x[n − 2]) + 13.456335 x[n − 1] where the input is x[n] = {cos(0.1n) + cos(0.4n)}µ[n] • Figure below shows the plots generated by running this program 4 Amplitude 1 • Program 3_3.m can be used to verify the filtering action o...
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## This document was uploaded on 11/09/2013.

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