K mitra copyright 2005 s k mitra the frequency

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Unformatted text preview: opyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra 7 The Frequency Response The Frequency Response • Likewise, for a real impulse response h[n], H re (e jω ) is even and H im (e jω ) is odd • Example - Consider the M-point moving average filter with an impulse response given by h[n] = ⎧1 / M , 0 ≤ n ≤ M − 1 ⎨ 0, otherwise ⎩ • Its frequency response is then given by • Note: Magnitude and phase functions are real functions of ω, whereas the frequency response is a complex function of ω • If the impulse response h[n] is real then it follows from Table 3.2 that the magnitude function is an even function of ω: H (e jω ) = H (e− jω ) 43 and the phase function is an odd function of ω: θ(ω) = −θ(−ω) H ( e jω ) = 44 1 M M −1 − jω n ∑e n=0 Copyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra The Frequency Response The Frequency Response • Likewise, for a real impulse response h[n], H re (e jω ) is even and H im (e jω ) is odd • Example - Consider the M-point moving average filter with an impulse response given by h[n] = ⎧1 / M , 0 ≤ n ≤ M − 1 ⎨ 0, otherwise ⎩ • Its frequency response is then given by H ( e jω ) = 45 1 M • Or, H (e jω ) = (...
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This document was uploaded on 11/09/2013.

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