# 1 should be equal to zero likewise to pass the high

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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 &lt; ω ≤ π 67 The Concept of Filtering • We apply an input x[n] = A cos ω1n + B cos ω2n, 0 &lt; ω1 &lt; ωc &lt; ω2 &lt; 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...
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## This document was uploaded on 11/09/2013.

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