Say, if the impulse response of a system exists from time t=0. Can I conclude the system has zero delay associated with it? What about the casuality of the system? Explain?
Impulse Response <=> Delay
Started by ●July 6, 2006
Reply by ●July 6, 20062006-07-06
Satish Prabu wrote:> Say, if the impulse response of a system exists from time t=0. Can I > conclude the system has zero delay associated with it? What about the > casuality of the system? Explain?Causality means there is no response (output) prior to the cause (input). This means that the impulse response only exists for positive times (including zero). Your example is causal. The system having no delay means that the response starts (i.e., is nonzero) at t=0, rather than at t=t0, a delay of t0. A delay doesn't have to correspond to a model being unphysical, while lack of causality does imply an unphysical model.
Reply by ●July 6, 20062006-07-06
"Satish Prabu" <satishprabu@gmail.com> writes:> Say, if the impulse response of a system exists from time t=0. Can I > conclude the system has zero delay associated with it? What about the > casuality of the system? Explain?Hi, You cannot conclude that there is no delay just because the impulse response begins at t=0. If the system is a linear phase system, the system has a time delay which is equal for all frequencies. Linear phase systems have an impulse response which is symmetric. So if it is causal (no response before t=0) and linear-phase you will always have a time-delay. For a system with nonlinear phase it is hard to say what the time-delay of the system is, since the delay is frequency dependent in this case. I hope this helps, Anton
Reply by ●July 6, 20062006-07-06
Anton wrote:> "Satish Prabu" <satishprabu@gmail.com> writes: > >> Say, if the impulse response of a system exists from time t=0. Can I >> conclude the system has zero delay associated with it? What about the >> casuality of the system? Explain? > > Hi, > > You cannot conclude that there is no delay just because the > impulse response begins at t=0. > If the system is a linear phase system, the system has a > time delay which is equal for all frequencies. Linear phase > systems have an impulse response which is symmetric. > So if it is causal (no response before t=0) > and linear-phase you will always have a time-delay. > For a system with nonlinear phase it is hard to say what the > time-delay of the system is, since the delay is frequency > dependent in this case. > I hope this helps,Doesn't that depend on what you mean by delay? Assuming that "delay" always means "group delay" can lead to interesting paradoxes. Suppose an FIR filter [1 -4 6 -4 1]. The group delay is three samples, but the output of an impulse is tangible at the first sample. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 6, 20062006-07-06
rtonyreeder@yahoo.com wrote:> Satish Prabu wrote: > >>Say, if the impulse response of a system exists from time t=0. Can I >>conclude the system has zero delay associated with it? What about the >>casuality of the system? Explain? > > > Causality means there is no response (output) prior to the cause > (input). This means that the impulse response only exists for positive > times (including zero). Your example is causal. > > The system having no delay means that the response starts (i.e., is > nonzero) at t=0, rather than at t=t0, a delay of t0. > > A delay doesn't have to correspond to a model being unphysical, while > lack of causality does imply an unphysical model. >Correction: In the context of normal signal processing practice, a signal with an impulse response that is symmetrical around a given time has no delay if and only if the axis of symmetry is at t = 0. Life gets more complicated for non-symmetrical signals, but for any impulse response of finite length (or length greater than 1 for a sampled system) a causal system must have some delay. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●July 6, 20062006-07-06
Tim Wescott wrote:> rtonyreeder@yahoo.com wrote: > >> Satish Prabu wrote: >> >>> Say, if the impulse response of a system exists from time t=0. Can I >>> conclude the system has zero delay associated with it? What about the >>> casuality of the system? Explain? >> >> >> Causality means there is no response (output) prior to the cause >> (input). This means that the impulse response only exists for positive >> times (including zero). Your example is causal. >> >> The system having no delay means that the response starts (i.e., is >> nonzero) at t=0, rather than at t=t0, a delay of t0. >> >> A delay doesn't have to correspond to a model being unphysical, while >> lack of causality does imply an unphysical model. >> > Correction: > > In the context of normal signal processing practice, a signal with an > impulse response that is symmetrical around a given time has no delay if > and only if the axis of symmetry is at t = 0. Life gets more > complicated for non-symmetrical signals, but for any impulse response of > finite length (or length greater than 1 for a sampled system) a causal > system must have some delay.Again, that depends of how delay is defined. There need not be any lag between stimulus and the first indication that a system is responding. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 6, 20062006-07-06
Jerry Avins <jya@ieee.org> writes:> Anton wrote: >> "Satish Prabu" <satishprabu@gmail.com> writes: >> >>> Say, if the impulse response of a system exists from time t=0. Can I >>> conclude the system has zero delay associated with it? What about the >>> casuality of the system? Explain? >> Hi, >> You cannot conclude that there is no delay just because the >> impulse response begins at t=0. >> If the system is a linear phase system, the system has a >> time delay which is equal for all frequencies. Linear phase >> systems have an impulse response which is symmetric. >> So if it is causal (no response before t=0) and linear-phase you >> will always have a time-delay. >> For a system with nonlinear phase it is hard to say what the >> time-delay of the system is, since the delay is frequency >> dependent in this case. >> I hope this helps, > > Doesn't that depend on what you mean by delay? Assuming that "delay" > always means "group delay" can lead to interesting paradoxes. Suppose > an FIR filter [1 -4 6 -4 1]. The group delay is three samples, but the > output of an impulse is tangible at the first sample.Hi Jerry, It does depend on what we mean be delay. But how would you define it? If it is really just about the first non-zero output from the system, it would not make a lot of sense to talk about the delay caused by filters, since all causal filters that I have used would have a delay of 0. By the way, isn't the group delay for your example 2 samples? gr. Anton
Reply by ●July 6, 20062006-07-06
Anton wrote:> Jerry Avins <jya@ieee.org> writes: > >> Anton wrote: >>> "Satish Prabu" <satishprabu@gmail.com> writes: >>> >>>> Say, if the impulse response of a system exists from time t=0. Can I >>>> conclude the system has zero delay associated with it? What about the >>>> casuality of the system? Explain? >>> Hi, >>> You cannot conclude that there is no delay just because the >>> impulse response begins at t=0. >>> If the system is a linear phase system, the system has a >>> time delay which is equal for all frequencies. Linear phase >>> systems have an impulse response which is symmetric. >>> So if it is causal (no response before t=0) and linear-phase you >>> will always have a time-delay. >>> For a system with nonlinear phase it is hard to say what the >>> time-delay of the system is, since the delay is frequency >>> dependent in this case. >>> I hope this helps, >> Doesn't that depend on what you mean by delay? Assuming that "delay" >> always means "group delay" can lead to interesting paradoxes. Suppose >> an FIR filter [1 -4 6 -4 1]. The group delay is three samples, but the >> output of an impulse is tangible at the first sample. > > Hi Jerry, > > It does depend on what we mean be delay. But how would you > define it? If it is really just about the first non-zero output > from the system, it would not make a lot of sense to talk about > the delay caused by filters, since all causal filters that I have used > would have a delay of 0. By the way, isn't the group delay for > your example 2 samples?Two samples it is. As to how I would define it, that's easy. I would most of the time use "delay" to mean "group delay". The exceptions would be when defining something (The group delay of a 5-tap FIR is two samples") and when answering a question when the questioner might easily be misled by an invalid assumption. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 6, 20062006-07-06
On Thu, 06 Jul 2006 13:24:05 -0400, Jerry Avins <jya@ieee.org> wrote:>Tim Wescott wrote: >> rtonyreeder@yahoo.com wrote: >>(snipped)>>> >> Correction: >> >> In the context of normal signal processing practice, a signal with an >> impulse response that is symmetrical around a given time has no delay if >> and only if the axis of symmetry is at t = 0. Life gets more >> complicated for non-symmetrical signals, but for any impulse response of >> finite length (or length greater than 1 for a sampled system) a causal >> system must have some delay. > >Again, that depends of how delay is defined. There need not be any lag >between stimulus and the first indication that a system is responding. > >JerryHi Jer, when I read the original post, I was going to suggest that the original poster ask his professor for some clear definitions of the terminology used in the questions, and then figure out the answer for himself. [-Rick-]
Reply by ●July 7, 20062006-07-07
Tim Wescott wrote:> In the context of normal signal processing practice, a signal with an > impulse response that is symmetrical around a given time has no delay if > and only if the axis of symmetry is at t = 0. Life gets more > complicated for non-symmetrical signals, but for any impulse response of > finite length (or length greater than 1 for a sampled system) a causal > system must have some delay.I am not sure what you mean Tim. First, an impulse response is not dependent on the input signal. It is a "parameter" of the system being modeled. Second, I don't see how a symmetric impulse response, with axis of symmetry at t=0, can be causal. If it isn't causal, it generates output before the input, and thus, has negative delay. Third, most impulse responses are not symmetric, since they must be causal to model a real physical system. Such doesn't appear to add complication. Fourth, physical systems are causal (a subset of possible causal impulse responses, i.e., causality doesn't imply a physical system), and can be as prompt as you can make them. The response time can be faster than you can make your time step, no matter how fine you make the temporal grid. A low pass filter, for example, integrates during an impulse, no matter how short the impulse. At least, that is how it seems to me.
