combine transfer functions

"Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message
news:cDP%a.4090$Jk5.3891444@feed2.centurytel.net...
>
>
> Given the impulse response as stated, the p(t) filters aren't in cascade
but
> in parallel with a differential delay of T.  At least I don't see how to
get
> a cascaded structure immediately out of this expression.


Hello Fred,

It seems that you have your output written as the sum of two fractions, so
just find a common denominator to put it all into one fraction, and then see
if the numerator has a part that will factor out. It is likely that this
will be ugly, but that is how I'd approach it.

Clay





>
> Fred
>
>
>
>

"Clay S. Turner" <physicsNOOOOSPPPPAMMMM@bellsouth.net> wrote in message
news:zN50b.1339$a9.1020@fe03.atl2.webusenet.com...
>
> "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message
> news:cDP%a.4090$Jk5.3891444@feed2.centurytel.net...
> >
> >
> > Given the impulse response as stated, the p(t) filters aren't in cascade
> but
> > in parallel with a differential delay of T.  At least I don't see how to
> get
> > a cascaded structure immediately out of this expression.
>
>
> Hello Fred,
>
> It seems that you have your output written as the sum of two fractions, so
> just find a common denominator to put it all into one fraction, and then
see
> if the numerator has a part that will factor out. It is likely that this
> will be ugly, but that is how I'd approach it.
>
> Clay

Clay,

Well, if we're talking about rational transfer functions, OK.  But I was
talking about the sum of two impulse responses p(t) and p(t-T).  That's
conceptually pretty easy - particularly if p(t) is a FIR and if we aren't
concerned about T being an integral of a sample interval.

Hey!  Nobody has mentioned my "exercise for the student".  I haven't taken
the time to figure it out.  It must be some simple obvious thing because it
tries to get around T not being an integer multiple of the sampling
interval.

Fred

On Sun, 17 Aug 2003 11:26:05 -0700, "Fred Marshall"
<fmarshallx@remove_the_x.acm.org> wrote:

>

>>
>> Anyway, the impulse response of two cascaded
>> filters (connected in series) is the convolution
>> of the two individual filters' impulse rsponses.
>
>Rick,
>
>You are correct about the grammar of course.
>It should be "impulse response" rather than transfer function.
>
>Given the impulse response as stated, the p(t) filters aren't in cascade but
>in parallel with a differential delay of T.  At least I don't see how to get
>a cascaded structure immediately out of this expression.
>
>Fred

Hi Fred,
   Oops, ... I think you're right.   For some reason 
I thought cascade.  Anyway, yep, the impulse response of two 
filters in parallel is the sum of the imp responses.

[-Rick-]