K mitra phase delay we can rewrite the output

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 11/09/2013.

Ask a homework question - tutors are online