Re: BIBO stability

nisky wrote:
Hi all,

well, i struggled with this one for a while:

is h(t)=2*sin(wt)*cos(Wt)/(pi*t) an impulse responce of a BIBO stable
system? How can I prove it?

I had several directions, but all of them lead me close but not close
enough

One direction is:
h(t)=2(sinc((w+W)t)+sinc((w-W)t)) so I can think of it as a connection
in
parralel of two ideal low-pass filters, which are both not BIBO
stable,
but this does not insure that the whole system is unstable

For the case where w=W it is a simple lawpass filter, which is not
Bibo
stable...

I tryed to prove absolute integrability (or non-integrability), but so
far
without success...

Thanks for the help

Ilana

Whether or not this is homework (and it looks like something I'd assign,

heh heh heh), consider that you should be able to reduce the sin(wt) *
cos(Wt) to a sum -- look in a trig book.

I can see by glancing at this what the answer is, but if you have to
_prove_ it for your homework to be valid you'll have to revisit trig.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google? See http://cfaj.freeshell.org/google/

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it
says.
See details at http://www.wescottdesign.com/actfes/actfes.html


I have broken it into a sum, it is written in the original question:

h(t)=2(sinc((w+W)t)+sinc((w-W)t)) (more or less, pardon me for
disregarding the constant gains, since they are irrelevant here )

But I am stuck at this point...

_____________________________________
Do you know a company who employs DSP engineers?
Is it already listed at http://dsprelated.com/employers.php ?
.

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