Re: are these stabability conditions the same?

From: Tim Wescott (tim_at_wescottnospamdesign.com)
Date: 12/28/04 

Date: Tue, 28 Dec 2004 08:29:15 -0800

Ravi Srikantiah wrote:
> Tim and Kiki,
>
>
>>> From this criteria, an ideal low pass filter is not BIBO stable,
>>> since its impulse response is "sinc" function, which can be proved to
>>> have Integrate(|sinc(t)|, t from -inf to inf)=inf...
>
>
> This is NOT true! Integral(-inf +inf) sin (x)/x = pi
> See http://mathworld.wolfram.com/SincFunction.html

The integral of the sinc function is pi. The integral of the _absolute
value_ of the sinc function (which is what the OP is talking about) is
greater than
(some constant) * sum(-inf +inf) 1/n. This sum is infinite, so the the
integral of the _absolute value_ of the sinc function must be as well. 

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