This thread would've fitted in a lot of categories, but as it's the mathematics I can't quite grasp, I decided to fit it here. I'll be treating the discrete case, so I suppose it's precalculus maths.(adsbygoogle = window.adsbygoogle || []).push({});

Anyways, I know how to compute problems with the impulse response method, but I'm kinda baffled as to why to do it how it's done (as the proof we had in class was rather incomplete).

I looked up wikipedia's article on the matter: http://en.wikipedia.org/wiki/Impulse_response

This is the part I'm having problems understanding:

[tex]T\left[ \sum_{k}x\left[ k\right] \delta \left[ n-k\right] \right] = \sum_{k}x\left[ k\right] T\left[ \delta \left[ n-k\right] \right][/tex]

It's got something to do with linearity, apparently the homogeneity property. I just can't understand why the x[k] is being treated as a constant and the delta isn't.

Then the part of applying the mathematics:

Given a system, eg. y(k) + y(k-1) - y(k-2) = 2^{k}, why am I supposed to write it out as

h(k) + h(k-1) - h(k-2) = delta(k) ?

That is, why does the solution of the latter equation give the impulse response of the system? Could someone show this mathematically?

Am I making any sense?

PS. Could someone recommend any good websites in the matter, I tried googling but found none?

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# Homework Help: Impulse response

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