#### scdoro

##### Member level 5

The following is the question on finding the behavior of impulse response with some information provided.

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A discrete-time LTI system has frequency response H (ω ) and corresponding

impulse response h[n]. Given that

a. The system is causal.

b. H(ω ) =H∗ (ω )

c. The DTFT of the sequence h[n+1] is real.

Show that the impulse response of the system is of finite duration.

If, in addition to the above, the frequency response has the following properties

d. H (π ) = 0

e. 1 ( ) 2

2

H d π

π

ω ω

π −

∫ =

Is there enough information to identify the system uniquely? If so, determine the

impulse response h[n]. If not, specify as much as you can regarding h[n].

thanks

regards