596:(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?
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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.
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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
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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
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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
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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
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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
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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
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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;
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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 = folding(x, L). E.g. the part about \sum_k x \delta lying in the domain of T is redundant, as this sum is identical to the original x by definition.
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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.
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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.
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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.--
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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.
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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.
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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. --
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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
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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
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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. --
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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.--
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Sorry if I've overstepped. My perspective comes from economics, where an impulse response function refers to the reaction, over time, of any
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on
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I have kept the reference to line equalisation in, but I have reworded this comment so it is less misleading.
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