Consider three system whose phase response is as shown: (A) (B)
Consider three system whose phase response is as shown:
(A) 
(B) 
(C) 
Consider the following statements and choose the correct option
A. Only system A is distortion less
B. Both system A, and system B are distortion less
C. Both system B and system C are distortion less
D. All A, B, C system are distortion less
Please scroll down to see the correct answer and solution guide.
Right Answer is: D
SOLUTION
For a system to be distortionless, it must satisfy 2 properties:
(a) |H (jω)| = c for all frequencies
(b) arg {H(jω)} = ωt0
Let us consider a system with phase
arg [H(jω)] = ω to + k π
k is an integer
Frequency response can be written as.
H(jω) = (e-j(ω t + kπ))
\({e^{ + jk\pi }}\left\{ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} { - 1}&{k = \pm 1,}&{ \pm 3 \ldots .} \end{array}}\\ {\begin{array}{*{20}{c}} { + 1}&{k = 0,}&{ \pm 2\;, \pm 4} \end{array}} \end{array}} \right.\)
H(jω) = ± ce-jωt
Which satisfy the condition for distortion less except for possible change in the algebraic sign of the scaling factor c.