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

# combine transfer functions

Started by ●August 15, 2003

Reply by ●August 15, 20032003-08-15

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 ofa> 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 > >

Reply by ●August 15, 20032003-08-15

"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 isthe> 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 reponseof> 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? > >Are you saying that p(t) is the impulse response of a system or an "impulse function" / unit sample? Is the perceived problem that t is sampled and, therefore, defines what an "integer time" is? Maybe just sample at a higher rate to get "fractional" values of t? The equation says that you just add the two together (as in "subtract"). So, yes, you can just add the two together. A block diagram for such a system would look like this: +-----+ | | in >-----+--------------->|p(t) |>---+ | | | | | +-----+ | +-----+ | | | | | +->| sum |-----> out | +-----+ +-----+ | | | | |delay| | | | +-----+ +---->| T |--->|p(t) |>---+ | | | | +-----+ +-----+ So, if you are dealing with discrete arrays / sampled data / then the delay T must be an integer multiple of the sample interval you've chosen. By increasing the sample rate in arbitrary integer increments like x3, x4, x27, etc. then you decrease the increments between values of t / the sample interval / and can set T to whatever degree of accuracy you'd like (using ever-larger arrays of course). This implies that p(t) gets zero-filled between the original samples. Here's an exercise for the student: Note that the block diagram applies in the frequency domain as well (by superposition). So, you might calculate the spectra, from the FFT of p(t) where the delay T in p(t-T) becomes an added linear phase shift term in the FFT of p(t). Then add the resulting spectra and then IFFT the result. This way the value of T comes into the values of frequency samples rather than the spacing of frequency samples. I think that's correct. The resulting temporal samples will be a sampled version of the output for whatever value T might have. [of course the phase shift has to be done correctly or h(t) won't have purely real samples. Really? How can that be when an "analog" version would have p(t) shifted and overlapped so that if p(t) is discrete then there will be pairs of samples separated by T? Fred

Reply by ●August 16, 20032003-08-16

"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).

Reply by ●August 16, 20032003-08-16

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 isthe> 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 reponseof> 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 > > > > > >

Reply by ●August 16, 20032003-08-16

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 integerdelay> and the non-integer delay separately. Then, I take the original signal sand> 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 justan> > > 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 implusereponse> of > > a > > > fractional delay filter, like a lagrange filter. Can I just add thetwo> > > together? How do I "combine" the two impluse responses, one an integer > > > impluse response the other a fractional delay impluse response? > > > > > > thanks, > > > jeremiah > > > > > > > > > > > >

Reply by ●August 17, 20032003-08-17

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, >jeremiahHi 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-]

Reply by ●August 17, 20032003-08-17

"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 reponseof 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

Reply by ●August 17, 20032003-08-17

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. ���������������������������������������������������������������������

Reply by ●August 18, 20032003-08-18

"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. > > ҿ�Jerry, Oh! Yep. Not grammar. Fred