# Talk:Impulse response

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## questions

(i) The mathematical discussion seems to be based on discrete-time signals. Why? The same discussion could be written using time-continuous functions, resulting in a more general description (in mathematical terms). Or, to put it another way: I get the impression that the article relates to digital signal processing. While the impulse response certainly is important in digital signal processing, it surely is not limited to this discrete-time application. I therefore suggest to rewrite the formulae for the more general case of time-continuous functions. What dou you think?

(ii) Why not use round brackets?

The square brackets are presumably related to the first point you note: the apparent focus on discrete time. It is a bit odd in that context that only the Dirac and never the Kronecker delta function is mentioned. I personally think the huge string of equations is a bit hard to follow and the rest seems disorganized. I'll try to make some edits to the structure of the article in the next few days. Aluvus 08:10, 26 May 2006 (UTC)
I have no idea what the long string of equations is trying to show, in fact it seems the whole content is contained in the last few lines: T[x] = folding(x, L[delta]). E.g. the part about \sum_k x[k] \delta[n-k] lying in the domain of T is redundant, as this sum is identical to the original x[n] by definition. 84.150.103.113 20:00, 4 February 2007 (UTC)

(iii) Impossible?

The article says this: "While this is impossible in any real system, it is a useful concept as an idealization." For an analog system, yes, there is no such thing as an ideal impulse response. However, isn't it possible to have an impulse response from a digital system with discrete samples? (I'm not an expert so I could be wrong about this.) Steveha 04:02, 7 June 2006 (UTC)
Yes, the impulse used is not a Dirac Delta in this case, for the simple reason that you can't go to infinitely short times when discretely sampling. The signal corresponding to the Delta function is the 1 for the zeroth sample, and 0 otherwise. 84.150.103.113 20:00, 4 February 2007 (UTC)
OTOH discrete sampling can be reasonably elegantly analysed in terms of a fixed spaced sequence of dirac delta's, so there is an impulse response when the impulse coincides with one of the sequence.WolfKeeper 20:13, 4 February 2007 (UTC)

Concering (i) I'm saying that " Similar results hold for continuous time systems." I think it is trivial to write down integrals instead of sums.--karatsobanis 20:33, 27 July 2006 (UTC)

This page needs to be split up into sections so its easier to read. Fresheneesz 05:09, 19 April 2006 (UTC)

## Diagram

This needs some pictures. —Ben FrantzDale 20:24, 16 May 2006 (UTC)

## Cleanup

The voice of the article isn't quite encyclopedic. —Ben FrantzDale 04:09, 28 May 2006 (UTC)

## IMAGES

ALL IMAGES ARE SHOWING UP AS EMPTY BOXES. might be temporary.

## Weird section on loudspeakers

I think the section on loudspeakers a little bit to specific for a general article on the impulse response. It appears to claim that the impulse method is a 'silver bullet' which solved problems that other methods (like swept sine or white noise injection) cannot measure. I am not really an expert on acoustics, but for someone with a background in control theory I find this (implied) claim a little bit strange. The loudspeaker could be used as an example, but all the other claims should be removed, unless a proper citation is given.--193.205.74.131 (talk) 12:20, 30 September 2008 (UTC)

The broadband/DSL example cited in the text is misleading. Adaptive equalisation *does* play a role in the DSL technologies in compensating for line conditions, and this does lead to a *partial* improvement in throughput. However, a far more significant factor is that in the pre-DSL era filters were installed on individual phone lines or at the exchange limiting the available bandwidth on a copper line to approx 3kHz (see Loading coil). This is sufficient for a POTS speech service, but the shannon limit for a line with 3kHz bandwidth is approximately 36kbit/sec (see Modem). It wasn't until these filters were removed that sufficient bandwidth was made available for DSL services allowing Mbit levels of service to become available.

I have kept the reference to line equalisation in, but I have reworded this comment so it is less misleading. —Preceding unsigned comment added by Stephenellwood99 (talkcontribs) 23:08, 17 March 2009 (UTC)

## 'Over time'?

Oli-- when you say 'not necessarily over time', do you mean

'as a function of time, or as a function of whatever independent variable parameterizes the dynamics of the system',


or do you mean

'as a function of some independent variable (possibly time), or not as a function of some independent variable'?


I assume you mean the former, but maybe there is a more general interpretation of 'impulse response' that I'm unaware of. Clarification would be appreciated. --Rinconsoleao (talk) 16:44, 18 March 2009 (UTC)

Yes, I mean the former.
I've just re-read the new lead, and I see that without "over time", it's slightly ambiguous (i.e. it could be interpreted as implying a single output). Therefore, if we can find a concise way of saying your first example above, then we should add that. Oli Filth(talk|contribs) 16:50, 18 March 2009 (UTC)

Rinconsoleao, I think the lead was better before, though perhaps a bit too technical in the first paragraph. The odd examples you added are not at all typical or illuminating (neither a television nor a planetary system is something that can be characterized by its impulse response); the removal of the fact that an impulse response characterizes a linear system is a bad idea; and the broader definition "More generally, an impulse response refers to the reaction of any dynamic system in response to some external change" sounds more like a step response than an impulse response. Let's work on getting back to a compromise that represents the traditional technical EE meaning as well as a bit of a generalization if we need it. Dicklyon (talk) 17:05, 18 March 2009 (UTC)

Sorry if I've overstepped. My perspective comes from economics, where an impulse response function refers to the reaction, over time, of any endogenous variable to any change in exogenous parameters. This is nowadays a standard, established term in economics (though it's not a term one encounters in Econ 1). My understanding is that this meaning arrived in economics via time series analysis. As far as I can tell, the meaning in economics only differs from the EE meaning that was originally included on the page insofar as economists will speak of the 'impulse response' to a prolonged change, as well as the 'impulse response' to an instantaneous change. (For example, in a discrete-time macroeconomic model, one might calculate the impulse response of GDP with respect to a one-period balanced-budget increase in government spending, but one might also calculate the impulse response of GDP with respect to a permanent balanced-budget increase in government spending.)
I rewrote the lede assuming that 'impulse response' was a general term from dynamical systems theory. If I'm wrong about that, then I agree that what I wrote is inappropriate. Regardless, the term is now standard in economics, and is clearly closely related to the meaning in EE, so I think mentioning uses of the term outside EE is appropriate, preferably in the most accessible language possible. --Rinconsoleao (talk) 17:25, 18 March 2009 (UTC)
If my examples are too nonstandard for clarity, then I would not object to changing them, but I would still support keeping some examples in the introduction, for the lay reader's sake. --Rinconsoleao (talk) 17:29, 18 March 2009 (UTC)
The most common use of impulse responses is in linear dynamical systems; the term dynamical systems itself usually refers to nonlinear systems, where an impulse response is not generally a very useful concept. I'm not familiar with the economics applications, but I bet they assume a linear or approximately linearizable system, and I surprised that they extend the concept to sustained inputs; what's a source on this besides the dictionary? Dicklyon (talk) 17:57, 18 March 2009 (UTC)

## Laplace transform of Dirac delta is 1?

According to Dirac_delta_function, it is the Fourier transform which is 1. As far as the Laplace transform goes it is stated that

"By analytic continuation of the Fourier transform, the Laplace transform of the delta function is found to be $\int_{0}^{\infty}\delta (t-a)e^{-st} \, dt=e^{-sa}$."

24.85.131.247 (talk) 09:21, 22 October 2012 (UTC)