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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 Mpoint 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 Mpoint 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.
 Fall '13

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