Unformatted text preview: 2005, S. K. Mitra The Frequency Response The Frequency Response H (e jω ) , in general, is a complex function
of ω with a period 2π
• It can be expressed in terms of its real and
imaginary parts
H (e jω ) = H re (e jω ) + j H im (e jω ) • jω • The quantity H (e ) is called the frequency
response of the LTI discretetime system
• H (e jω ) provides a frequencydomain
description of the system
• H (e jω ) is precisely the DTFT of the impulse
response {h[n]} of the system 39 or, in terms of its magnitude and phase,
H (e jω ) = H (e jω ) e jθ(ω)
where
θ(ω) = arg H (e jω )
40 Copyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra The Frequency Response The Frequency Response • The function H (e jω ) is called the
magnitude response and the function θ(ω)
is called the phase response of the LTI
discretetime system
• Design specifications for the LTI discretetime system, in many applications, are
given in terms of the magnitude response or
the phase response or both
41 • In some cases, the magnitude function is
specified in decibels as
G (ω) = 20 log10 H (e jω ) dB
where G(ω) is called the gain function
• The negative of the gain function
A (ω) = − G (ω)
is called the attenuation or loss function
42 C...
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 Fall '13
 Digital Signal Processing, Signal Processing, S. K. Mitra

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