K mitra 7 the frequency response note magnitude and

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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 discrete-time system • H (e jω ) provides a frequency-domain 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 discrete-time 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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