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-]

"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

"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
>
>
>
>

"Jerry Avins" <jya@ieee.org> wrote in message
news:3F3FF81D.7F1F10B9@ieee.org...
> Fred Marshall wrote:
> >
>   ...
> >
> > You are correct about the grammar of course.
> > It should be "impulse response" rather than transfer function.
> >
> Fred,
>
> That's not a error of grammar. "My toe hurts" and "My finger hurts" are
> both grammatically correct. How many people do you know who call nuts
> screws (they go on by turning, don't they?), or screws nails they're
> both cylindrical fasteners, no?)? The right word can be very useful.
>
>                                &#1215;&#4294967295;

Jerry,

Oh!  Yep.  Not grammar.

Fred

Fred Marshall wrote:
> 
  ...
> 
> You are correct about the grammar of course.
> It should be "impulse response" rather than transfer function.
> 
Fred,

That's not a error of grammar. "My toe hurts" and "My finger hurts" are
both grammatically correct. How many people do you know who call nuts
screws (they go on by turning, don't they?), or screws nails they're
both cylindrical fasteners, no?)? The right word can be very useful.

                               ҿ�
Jerry                          ���
-- 
"I view the progress of science as ... the slow erosion of the
 tendency to dichotomize."                    Barbara Smuts, U. Mich.
���������������������������������������������������������������������

"Rick Lyons" <ricklyon@REMOVE.onemain.com> wrote in message
news:3f3fad3b.82047625@news.west.earthlink.net...
> On Fri, 15 Aug 2003 15:50:41 -0400, "Parlous" <parlous@hotmail.com>
> wrote:
>
> >
> >I have a transfer function as follows:
> >
> >h(t) = p(t) - p(t - T)
> >
> >where t is time, T is some real value, and p is the impulse function, p =
> >{1,0,0,0,...}. My question is, because T is a real value and not just an
> >integer, how can i implement a matlab function to evaluate h for some
> >arbitrary length?
> >
> >I can implement h making T an integer and I can get the impluse reponse
of a
> >fractional delay filter, like a lagrange filter. Can I just add the two
> >together? How do I "combine" the two impluse responses, one an integer
> >impluse response the other a fractional delay impluse response?
> >
> >thanks,
> >jeremiah
>
>
> Hi jeremiah,
>
>     your "h(t) = p(t) - p(t - T)" is *not* a
> transfer function.  "Transfer function" in typical DSP
> lingo, is either a z-domain expression or a
> frequency-domain expression.
>
> I'd call your
>         h(t) = p(t) - p(t - T)
>
> a "difference equation" meaning that it relates
> time-domain variables.
>
> 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

On Fri, 15 Aug 2003 15:50:41 -0400, "Parlous" <parlous@hotmail.com>
wrote:

>
>I have a transfer function as follows:
>
>h(t) = p(t) - p(t - T)
>
>where t is time, T is some real value, and p is the impulse function, p =
>{1,0,0,0,...}. My question is, because T is a real value and not just an
>integer, how can i implement a matlab function to evaluate h for some
>arbitrary length?
>
>I can implement h making T an integer and I can get the impluse reponse of a
>fractional delay filter, like a lagrange filter. Can I just add the two
>together? How do I "combine" the two impluse responses, one an integer
>impluse response the other a fractional delay impluse response?
>
>thanks,
>jeremiah


Hi jeremiah,

    your "h(t) = p(t) - p(t - T)" is *not* a 
transfer function.  "Transfer function" in typical DSP 
lingo, is either a z-domain expression or a 
frequency-domain expression.

I'd call your 
        h(t) = p(t) - p(t - T)

a "difference equation" meaning that it relates 
time-domain variables.

Anyway, the impulse response of two cascaded 
filters (connected in series) is the convolution 
of the two individual filters' impulse rsponses.

Good Luck,
[-Rick-]  
   

it seems to be working in matlab. i'll see as time goes on

"Parlous" <parlous@hotmail.com> wrote in message
news:vjt3n8qsgqa521@corp.supernews.com...
>
> well, how about this - i get the impulse response for both the integer
delay
> and the non-integer delay separately. Then, I take the original signal s
and
> convolve it with one of the impluse responses, then take that result and
> convolve it with the other impluse response. This should be the same as
> making one LTI system that incorporates the fractional and integer delay i
> need, correct?
>
>
> "Parlous" <parlous@hotmail.com> wrote in message
> news:vjqeafbg14mm32@corp.supernews.com...
> > i mentioned i had the transfer function h(t) - that is incorrect! it is
> the
> > impluse response function i have!
> >
> > sorry
> >
> >
> > "Parlous" <parlous@hotmail.com> wrote in message
> > news:vjqe7kbjicm07@corp.supernews.com...
> > >
> > > I have a transfer function as follows:
> > >
> > > h(t) = p(t) - p(t - T)
> > >
> > > where t is time, T is some real value, and p is the impulse function,
p
> =
> > > {1,0,0,0,...}. My question is, because T is a real value and not just
an
> > > integer, how can i implement a matlab function to evaluate h for some
> > > arbitrary length?
> > >
> > > I can implement h making T an integer and I can get the impluse
reponse
> of
> > a
> > > fractional delay filter, like a lagrange filter. Can I just add the
two
> > > together? How do I "combine" the two impluse responses, one an integer
> > > impluse response the other a fractional delay impluse response?
> > >
> > > thanks,
> > > jeremiah
> > >
> > >
> >
> >
>
>

well, how about this - i get the impulse response for both the integer delay
and the non-integer delay separately. Then, I take the original signal s and
convolve it with one of the impluse responses, then take that result and
convolve it with the other impluse response. This should be the same as
making one LTI system that incorporates the fractional and integer delay i
need, correct?


"Parlous" <parlous@hotmail.com> wrote in message
news:vjqeafbg14mm32@corp.supernews.com...
> i mentioned i had the transfer function h(t) - that is incorrect! it is
the
> impluse response function i have!
>
> sorry
>
>
> "Parlous" <parlous@hotmail.com> wrote in message
> news:vjqe7kbjicm07@corp.supernews.com...
> >
> > I have a transfer function as follows:
> >
> > h(t) = p(t) - p(t - T)
> >
> > where t is time, T is some real value, and p is the impulse function, p
=
> > {1,0,0,0,...}. My question is, because T is a real value and not just an
> > integer, how can i implement a matlab function to evaluate h for some
> > arbitrary length?
> >
> > I can implement h making T an integer and I can get the impluse reponse
of
> a
> > fractional delay filter, like a lagrange filter. Can I just add the two
> > together? How do I "combine" the two impluse responses, one an integer
> > impluse response the other a fractional delay impluse response?
> >
> > thanks,
> > jeremiah
> >
> >
>
>

"Parlous" <parlous@hotmail.com> wrote in message news:<vjqeafbg14mm32@corp.supernews.com>...
> i mentioned i had the transfer function h(t) - that is incorrect! it is the
> impluse response function i have!
> 
> sorry
> 
> 
> "Parlous" <parlous@hotmail.com> wrote in message
> news:vjqe7kbjicm07@corp.supernews.com...
> >
> > I have a transfer function as follows:
> >
> > h(t) = p(t) - p(t - T)
> >
> > where t is time, T is some real value, and p is the impulse function, p =
> > {1,0,0,0,...}. My question is, because T is a real value and not just an
> > integer, how can i implement a matlab function to evaluate h for some
> > arbitrary length?
> >
> > I can implement h making T an integer and I can get the impluse reponse of
>  a
> > fractional delay filter, like a lagrange filter. Can I just add the two
> > together? How do I "combine" the two impluse responses, one an integer
> > impluse response the other a fractional delay impluse response?
> >
> > thanks,
> > jeremiah
> >
> >

Let me understand this correctly. You want to implement 
h'(t) = p(t) - p(t - T') 
where T' is the non-integer.

Let T'' = T' - T where T is the integer part. You have the lagrangian
interpolation filter to get you a delay of T''. That is, you have
h(t) = p(t) - p(t - T) (the integer part)
and
h''(t) = a p(t) + b p (t - 1) (the fractional part) 

This is just an example as I don't know exactly what a lagrangian
filter looks like. But any interpolation filter interpolates a
fractional sample from the adjacent integer samples. Basically, I have
considered an interpolation filter that creates s(T') from s(T) and
s(T+1) as
s(T') = a S(T) + b s(T+1). 

Then your h'(t) becomes:
h'(t) = p(t) - a p(t - T) - b p(t - T - 1) 

So, the answer is: You can't just add the fractional delay impulse
response
h''(t) = a p(t) + b p(t - 1) to the integer delay impulse response
h(t) = p(t) - p(t - T).