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Unformatted text preview: put reaches the steadystate
value ysr [n] = H (e jω )e jωn at n = N 63 and hence, the transient response decays to
zero as n gets very large • One application of an LTI discretetime
system is to pass certain frequency
components in an input sequence without
any distortion (if possible) and to block
other frequency components
• Such systems are called digital filters and
one of the main subjects of discussion in
this course
64 Copyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra The Concept of Filtering The Concept of Filtering • The key to the filtering process is
x[ n] = 1
2π • Thus, by appropriately choosing the values
of the magnitude function H (e jω ) of the
LTI digital filter at frequencies
corresponding to the frequencies of the
sinusoidal components of the input, some of
these components can be selectively heavily
attenuated or filtered with respect to the
others π jω jωn
∫ X (e ) e dω −π • It expresses an arbitrary input as a linear
weighted sum of an infinite number of
exponen...
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This document was uploaded on 11/09/2013.
 Fall '13

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