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K mitra the output reduces to yn a h e j1 cos1n 1

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Unformatted text preview: put reaches the steady-state 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 discrete-time 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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