Hi all, Here's a newbie type question, but one which I haven't seen fully explained elsewhere. Lets say I have a 1000 tap bandpass FIR filter centred on 100kHz and 10kHz wide. We'll assume it's perfect (flat passband). The group delay is 2.5mS. I put a 95kHz continuous sine wave signal at the input, and (after a short delay) it appears as a continuous output at the same level and frequency. Then I suddenly change the frequency of the input signal to 105kHz (as near to instantaneous as possible). My question is : What happens to the output frequency and amplitude, from the filter ? Does it ramp up to 105kHz in a linear fashion, and which parameters govern it's behavior - eg bandwidth of the filter ? group delay ? What is the maximum rate of change of frequency on the input, which can be reproduced, 2.5mS later, on the output ? Any help much appreciated. My background is (non-DSP) electronic engineering rather than mathematical. Regards, Paul
FIR filter response
Started by ●October 27, 2004
Reply by ●October 27, 20042004-10-27
Since FM is a nonlinear thing, I guess this might not be too easy. The exact behaviour will also depend on where in the wave you switch. Why not just try it (using matlab or such)? My guess: the output amplitude will go down during the change, as the side bands do not pass the filter. Settling time should be 100us. Just a thought... Andre Paul Lovell wrote:> Hi all, > > Here's a newbie type question, but one which I haven't seen fully explained > elsewhere. > > Lets say I have a 1000 tap bandpass FIR filter centred on 100kHz and 10kHz > wide. We'll assume it's perfect (flat passband). > The group delay is 2.5mS. > I put a 95kHz continuous sine wave signal at the input, and (after a short > delay) it appears as a continuous output at the same level and frequency. > > Then I suddenly change the frequency of the input signal to 105kHz (as near > to instantaneous as possible). > > My question is : What happens to the output frequency and amplitude, > from the filter ? > > Does it ramp up to 105kHz in a linear fashion, and which parameters govern > it's behavior - eg bandwidth of the filter ? group delay ? > > What is the maximum rate of change of frequency on the input, which can be > reproduced, 2.5mS later, on the output ? > > Any help much appreciated. My background is (non-DSP) electronic > engineering rather than mathematical. > > Regards, Paul > > >-- Please change no_spam to a.lodwig when replying via email!
Reply by ●October 27, 20042004-10-27
Paul Lovell wrote:> Hi all, > > Here's a newbie type question, but one which I haven't seen fully explained > elsewhere. > > Lets say I have a 1000 tap bandpass FIR filter centred on 100kHz and 10kHz > wide. We'll assume it's perfect (flat passband). > The group delay is 2.5mS. > I put a 95kHz continuous sine wave signal at the input, and (after a short > delay) it appears as a continuous output at the same level and frequency. > > Then I suddenly change the frequency of the input signal to 105kHz (as near > to instantaneous as possible). > > My question is : What happens to the output frequency and amplitude, > from the filter ? > > Does it ramp up to 105kHz in a linear fashion, and which parameters govern > it's behavior - eg bandwidth of the filter ? group delay ? > > What is the maximum rate of change of frequency on the input, which can be > reproduced, 2.5mS later, on the output ? > > Any help much appreciated. My background is (non-DSP) electronic > engineering rather than mathematical. > > Regards, Paul1000 taps, 2.5 mS. That's a 200 KHz (to .1%) sample clock: too low to support your numbers. Assuming the numbers were chosen realistically, there are three ways to approach this. The simplest is trying it. The hard way is computing the harmonic content of the signal you describe -- Bessel functions and all that -- and the easy way is superposition. Determine the transient when one signal stops and the transient when the other starts. Add them. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●October 27, 20042004-10-27
As you suggested an instantaneous change in frequency the analysis is mathematically tractable and should require Bessel functions. You can model it as two seperate sinusoidal sources multiplied by two seperate step functions and then summed together. Inverted step for 100kHz and step for 95kHz. You can use duality to your advantage here (i.e. multiplication in one domain is equivalent to convolution in the other). Good luck. Regards, Paavo Jumppanen Author of HarBal Harmonic Balancer http://www.har-bal.com Andre <no_spam@fischer-zoth.de> wrote in message news:<clofl2$9u$02$1@news.t-online.com>...> Since FM is a nonlinear thing, I guess this might not be too easy. > The exact behaviour will also depend on where in the wave you switch. > Why not just try it (using matlab or such)? > My guess: the output amplitude will go down during the change, as the > side bands do not pass the filter. Settling time should be 100us. > > Just a thought... > > Andre > > Paul Lovell wrote: > > Hi all, > > > > Here's a newbie type question, but one which I haven't seen fully explained > > elsewhere. > > > > Lets say I have a 1000 tap bandpass FIR filter centred on 100kHz and 10kHz > > wide. We'll assume it's perfect (flat passband). > > The group delay is 2.5mS. > > I put a 95kHz continuous sine wave signal at the input, and (after a short > > delay) it appears as a continuous output at the same level and frequency. > > > > Then I suddenly change the frequency of the input signal to 105kHz (as near > > to instantaneous as possible). > > > > My question is : What happens to the output frequency and amplitude, > > from the filter ? > > > > Does it ramp up to 105kHz in a linear fashion, and which parameters govern > > it's behavior - eg bandwidth of the filter ? group delay ? > > > > What is the maximum rate of change of frequency on the input, which can be > > reproduced, 2.5mS later, on the output ? > > > > Any help much appreciated. My background is (non-DSP) electronic > > engineering rather than mathematical. > > > > Regards, Paul > > > > > >
Reply by ●October 27, 20042004-10-27
Sorry, I mean't to say shouldn't require Bessel functions. Regards, Paavo Jumppanen Author of HarBal Harmonic Balancer http://www.har-bal.com Andre <no_spam@fischer-zoth.de> wrote in message news:<clofl2$9u$02$1@news.t-online.com>...> Since FM is a nonlinear thing, I guess this might not be too easy. > The exact behaviour will also depend on where in the wave you switch. > Why not just try it (using matlab or such)? > My guess: the output amplitude will go down during the change, as the > side bands do not pass the filter. Settling time should be 100us. > > Just a thought... > > Andre > > Paul Lovell wrote: > > Hi all, > > > > Here's a newbie type question, but one which I haven't seen fully explained > > elsewhere. > > > > Lets say I have a 1000 tap bandpass FIR filter centred on 100kHz and 10kHz > > wide. We'll assume it's perfect (flat passband). > > The group delay is 2.5mS. > > I put a 95kHz continuous sine wave signal at the input, and (after a short > > delay) it appears as a continuous output at the same level and frequency. > > > > Then I suddenly change the frequency of the input signal to 105kHz (as near > > to instantaneous as possible). > > > > My question is : What happens to the output frequency and amplitude, > > from the filter ? > > > > Does it ramp up to 105kHz in a linear fashion, and which parameters govern > > it's behavior - eg bandwidth of the filter ? group delay ? > > > > What is the maximum rate of change of frequency on the input, which can be > > reproduced, 2.5mS later, on the output ? > > > > Any help much appreciated. My background is (non-DSP) electronic > > engineering rather than mathematical. > > > > Regards, Paul > > > > > >
Reply by ●October 27, 20042004-10-27
Paavo Jumppanen wrote:> Sorry, I mean't to say shouldn't require Bessel functions.... There's no way for the transition to be instantaneous in discrete time. One sample time is the minimum possible. If it were instantaneous, ti could neither be bandlimited nor all the frequencies finite. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●October 27, 20042004-10-27
Jerry Avins wrote:> There's no way for the transition to be instantaneous in discrete time. > >One sample time is the minimum possible. If it were instantaneous, ti >could neither be bandlimited nor all the frequencies finite. > >Jerry > >You don't believe in infinite gain bandwidth product? Next you'll be telling me you don't believe in perpetual motion. :-) Regards, Steve
Reply by ●October 28, 20042004-10-28
Thanks for your contributions guys, I have always assumed that a 1000 tap filter with 400kHz clock would have 2.5uS sample intervals and therefore a 2.5mS delay. Where am I going wrong here ? Please substitute "one clock cycle" for "instantaneous", in my original request. Anyway, at my level of knowledge, it appears that the best thing to do here is try a simulation. Then I may come back with another question :-) Paul "Paul Lovell" <merit@starnet.freeserve.co.uk> wrote in message news:clof3m$2lg$1@news6.svr.pol.co.uk...> Hi all, > > Here's a newbie type question, but one which I haven't seen fullyexplained> elsewhere. > > Lets say I have a 1000 tap bandpass FIR filter centred on 100kHz and 10kHz > wide. We'll assume it's perfect (flat passband). > The group delay is 2.5mS. > I put a 95kHz continuous sine wave signal at the input, and (after a short > delay) it appears as a continuous output at the same level and frequency. > > Then I suddenly change the frequency of the input signal to 105kHz (asnear> to instantaneous as possible). > > My question is : What happens to the output frequency and amplitude, > from the filter ? > > Does it ramp up to 105kHz in a linear fashion, and which parameters govern > it's behavior - eg bandwidth of the filter ? group delay ? > > What is the maximum rate of change of frequency on the input, which can be > reproduced, 2.5mS later, on the output ? > > Any help much appreciated. My background is (non-DSP) electronic > engineering rather than mathematical. > > Regards, Paul > > >
Reply by ●October 28, 20042004-10-28
Jerry Avins <jya@ieee.org> wrote in message news:<2ub2baF27kps1U1@uni-berlin.de>...> Paavo Jumppanen wrote: > > > Sorry, I mean't to say shouldn't require Bessel functions. > > ... > > There's no way for the transition to be instantaneous in discrete time. > One sample time is the minimum possible. If it were instantaneous, ti > could neither be bandlimited nor all the frequencies finite. > > JerryYou're nit picking Jerry. Look at the original post. He states that "I suddenly change the frequency of the input signal to 105kHz (as near to instantaneous as possible)." I don't know about you but that lends itself nicely to analyzing the situation as an instantaneous change in frequency as a first approximation. He also states that "I put a 95kHz continuous sine wave signal at the input". This implies continuous time to me which means the change in frequency is occuring in the analog domain and can be approximated by an instantaneous change. Take the resulting continuous spectrum of the continuous time signal and apply the effects of sampling to it to translate it into the digital domain if you will, but as I see it the "modulation" occurs in the continuous time domain. Finally, he mentions the system is a 1000 tap bandpass FIR with a 2.5mS group delay. Nowhere does he mention digital so I am free to interpret this as a continuous time domain device if I wish. Continous time analog FIRs are possible. SAWs are a commonly used example, though don't fit that frequency range. So what exactly is wrong with the suggestion I gave to Paul Lovell? Paavo Jumppanen Author of HarBal Harmonic Balancer http://www.har-bal.com
Reply by ●October 28, 20042004-10-28
Paavo Jumppanen wrote:> Jerry Avins <jya@ieee.org> wrote in message news:<2ub2baF27kps1U1@uni-berlin.de>... > >>Paavo Jumppanen wrote: >> >> >>>Sorry, I mean't to say shouldn't require Bessel functions. >> >> ... >> >>There's no way for the transition to be instantaneous in discrete time. >>One sample time is the minimum possible. If it were instantaneous, ti >>could neither be bandlimited nor all the frequencies finite. >> >>Jerry > > > You're nit picking Jerry. > > Look at the original post. He states that "I suddenly change the > frequency of the input signal to 105kHz (as near to instantaneous as > possible)." I don't know about you but that lends itself nicely to > analyzing the situation as an instantaneous change in frequency as a > first approximation."Sudden" isn't "instantaneous". Usually, it is unimportant to distinguish those cases, but forgetting that there is a distinction sometimes leads to apparent paradox and frustrating puzzlement. We agree that it is easily calculated without Bessel functions using superposition. You call it nitpicking, I call it sweeping up lint.> He also states that "I put a 95kHz continuous sine wave signal at the > input". This implies continuous time to me which means the change in > frequency is occuring in the analog domain and can be approximated by > an instantaneous change. Take the resulting continuous spectrum of the > continuous time signal and apply the effects of sampling to it to > translate it into the digital domain if you will, but as I see it the > "modulation" occurs in the continuous time domain.The question is "what does the sampler see", presumably after the anti-alias filter. I don't want to touch that!> Finally, he mentions the system is a 1000 tap bandpass FIR with a > 2.5mS group delay. Nowhere does he mention digital so I am free to > interpret this as a continuous time domain device if I wish. Continous > time analog FIRs are possible. SAWs are a commonly used example, > though don't fit that frequency range.I suspect that the art of building an analog 1000 tap bandpass FIR with a 2.5 mS group delay has, sadly, been lost.> So what exactly is wrong with the suggestion I gave to Paul Lovell?It was fine. Of the three approaches I had earlier outlined, it is the one I suggested is practical (albeit fancied up with step functions). I assume you didn't see that post Where was the use Bessel functions mentioned if not in it? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
