Impulse response problem

[jagsee1972]

Hello All,
I am stuck on how an impulse response for an input consisting of a sum of sine waves is determined. I cannot seem to make any sense of it. The example I was looking at was from youtube presentations Rose-Hullman.

An input is given as: x[n]=-2+ 3cos((

)n+10cos((3

/4)n-

/5)

The impulse response for this input is just given, dont know its worked out.

h[n]=

+2

[n-1]+3

[n-2].

I was under the impression the impulse response can be determined by applying a delta function to the input for example:

x[n]=

Then the impulse response is
x[n]=

and therefore:

[n]+

[n-1]......

[n-M]

Would appreciate any advice or pointers.

 

[barry]

This is not my field of expertise, but...

The way I remember it, the impulse response of a system is, as you said, the output that results from an impulse input. (Thus, the name, "impulse response" !)

I don't know how you can talk about the "impulse response" of a particular input signal. That's like asking 'what's the frequency response of this signal?'

 

[jagsee1972]

Barry, Thanks for your reply. I dont know how the impulse response was determined for the particular function.

Jag.

 

[barry]

Maybe you've misread (or mis-posted) the question. I could understand if the question was: Here's the impulse response of the circuit, and we apply this input signal; what is the output?

 

[jagsee1972]

Barry,
Thanks for the reply, I think that there is a fundamental problem with my understanding. I thought that the impulse response and the input were intimately linked. That is the impulse response can always be determined from the input as it is the input applied to a delta function.

- - - Updated - - -

Barry,
I think I may have made a crucial error as the impulse response in my example has not been derived from the x[n] shown. The way h[n] has been derived is not shown.

 

[barry]

The impulse response is, by definition, the response of the system to an impulse input. That's it.

So I think the problem is as I stated it in post #4