Ch3Handouts_2

# K mitra d d d 0 if the above constraint is not

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (e jω ) − X im (e jω ) re dω Copyright © 2005, S. K. Mitra 5 The Unwrapped Phase Function The Unwrapped Phase Function • The phase function can thus be defined unequivocally by its derivative dθ(ω) / dω: ω θ(ω) = ∫[ 0 dθ( η) dη • The phase function defined by ω θ(ω) = ∫[ dη, 0 dθ( η) dη dη is called the unwrapped phase function of X (e jω ) and it is a continuous function of ω • ⇒ ln X (e jω ) exists with the constraint θ(0) = 0 31 32 Copyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra The Unwrapped Phase Function The Frequency Response • Moreover, the phase function will be an odd function of ω if 1 π 2π ∫[ 0 dθ( η) dη dη = 0 • If the above constraint is not satisfied, then the computed phase function will exhibit absolute jumps greater than π 33 34 • Most discrete-time signals encountered in practice can be represented as a linear combination of a very large, maybe infinite, number of sinusoidal discrete-time signals of different angular frequencies • Thus, knowing the response of the LTI system to a single sinusoidal signal, we can determine its response to more complicated signals by making use of the superposition property Copyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra The Frequency Response...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online