Computation of frequency response
Let the system function be given by the following equation
The frequency response is H (e jw ) or H(ω) = H (z)z = e jw . Therefore
where
The magnitude and phase of H (ejw ) are given, by
Theorem The frequency response H (e jw ) for the BIBO-stable system will always converge.
Accordingly every BIBO-stable system will have the frequency response and the describable steady- state response to sinusoidal inputs. But, converse of this statement is not true, which means that the fact that H (e jw ) exists does not imply that the system is stable.
Example The ideal low pass filter
For the H(ω) given in the figure drawn below find out h(n), the unit sample response.
Solution The unit sample response is inverse DTFT of H(ω)
It is seen that h(n) ≠ 0 for negative n so that the ideal low pass filter is noncausal. Furthermore, 
h(n) tails off as n goes from 0 to ∞ and from 0 to -∞, it can be shown that 
not finite. This shows that ideal low pass filter is not BIBO-stable either.
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