I don't know where to start from, I'm not familiar with math. I'm trying to understand this question "how to identify impulse response of a system?".
As you can see as below figure, as I know, the input delta function and output is $h[n]$.
In this case, if I put impulse (function) signal in to above system, then I can get the impulse response. Then I think the output $h[n]$ and impulse response are the same, doesn't it?
- Question 1: What is the meaning of "how to identify impulse response of a system"? Is this asking about convolution or auocorrelation? I can't understand what it does mean.
- Question 2: I want to know how to identify impulse response of a system?
- Question 3: Why do we get the output of $y[n]$ when if we know that input $x[n]$, impulse response $h[n]$. I mean the output $y[n]$ is the same $h[n]$ isn't it? I'm very confused.
If you have any hint, please let me know.
I found a question in my case as below,
1.2.8 Consider a discrete-time LTI system described by the rule $$y(n)=x(n-5)+\frac 12 x(n-7).$$ What is the impulse response $h(n)$ of the system ?
How to identify $h[n]$?
the answer :
$h$ = 1+ 0 = 1
$h$ = 0 + 1/2 = 1/2
. . .