Can someone helps me solve this DSP qn in theory?

[scdoro]

Hi all,

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

************************************************************


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

 

[mro83]

hi
the Info that u are provided is not understandable. but can u determine the pole-zero plot of ur system. if yes it is possible to know thai if that is FIR.
complete ur given data to proceed...

 

[scdoro]

hi all

i have an attachment on the full question.Sorry that my question was not recognisable just now.

I couldnt see how i could determine the impulse response by observing those properties? Can the impulse response be found in this case at all.

thanks

regards

 

[Naresh]

1) Since it is causal n >= 0
2) condition 'b' says that h[n] is real
3) condition 'c' says that h[n+1] is even. So only possible values of n are 0,1,2.
So h[n] is finite.
4) condition 'e' says that h[0] = 2

From here on you can solve the problem.