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
.

Relevant Pages

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