1 should be equal to zero likewise to pass the high

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: tial sequences, or equivalently, as a linear weighted sum of sinusoidal sequences 65 66 Copyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra 11 The Concept of Filtering • To understand the mechanism behind the design of frequency-selective filters, consider a real-coefficient LTI discrete-time system characterized by a magnitude function ω ≤ ωc 1, H ( e jω ) ≅ ⎧ ⎨ ⎩ 0, ωc < ω ≤ π 67 The Concept of Filtering • We apply an input x[n] = A cos ω1n + B cos ω2n, 0 < ω1 < ωc < ω2 < π to this system • Because of linearity, the output of this system is of the form y[n] = A H (e jω1 ) cos(ω1n + θ(ω1 ) ) 68 + B H (e jω2 ) cos(ω2n + θ(ω2 ) ) Copyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra The Concept of Filtering The Concept of Filtering • As H (e jω1 ) ≅ 1, • Example - The input consists of a sum of two sinusoidal sequences of angular frequencies 0.1 rad/sample and 0.4 rad/sample • We need to design a highpass filter that will pass the high-frequency component of the input but block the low-frequency component • For...
View Full Document

This document was uploaded on 11/09/2013.

Ask a homework question - tutors are online