# Quick question about Causal LTI system

by ElijahRockers
Tags: causal
 P: 195 1. The problem statement, all variables and given/known data I am reading a little bit on Causal LTI systems. I know causality means that a system cannot depend on the future, but why does that mean an impulse function, say h(t) = 0, for all t<0 I mean, if t is negative, then it's not really depending on the future, but the past right? Or am I visualizing this wrong?
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P: 25,235
 Quote by ElijahRockers 1. The problem statement, all variables and given/known data I am reading a little bit on Causal LTI systems. I know causality means that a system cannot depend on the future, but why does that mean an impulse function, say h(t) = 0, for all t<0 I mean, if t is negative, then it's not really depending on the future, but the past right? Or am I visualizing this wrong?
h(t)=0 for all t<0 isn't really depending on the past either. It doesn't depend on anything. You just said what it is. There's no evolution equation to specify any time evolution.
P: 195
 Quote by Dick h(t)=0 for all t<0 isn't really depending on the past either. It doesn't depend on anything. You just said what it is. There's no evolution equation to specify any time evolution.
It doesn't depend on anything? But I thought being being a function of t by definition means it depends on t. Sorry if that sounds obtuse, I just can't relate anything you said to anything I've learned..., apparently I am struggling with this.

I just dont see why the system, being causal, means that h(t) has to be 0 for all t<0....

assuming I have some impulse h[n] = h1[n]+h1[n-1] and I know h[n] = 2 for n>0

then at n=0, 2 = h1[0] + h1[-1]. since the system is causal, i could say h1[0] = 2, because h1[-1] = 0. what i don't get is WHY i can say h1[-1]=0...

I hope that makes sense.. it's hard for me to give an example of something I dont really understand in the first place

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P: 25,235
Quick question about Causal LTI system

 Quote by ElijahRockers It doesn't depend on anything? But I thought being being a function of t by definition means it depends on t. Sorry if that sounds obtuse, I just can't relate anything you said to anything I've learned..., apparently I am struggling with this. I just dont see why the system, being causal, means that h(t) has to be 0 for all t<0.... assuming I have some impulse h[n] = h1[n]+h1[n-1] and I know h[n] = 2 for n>0 then at n=0, 2 = h1[0] + h1[-1]. since the system is causal, i could say h1[0] = 2, because h1[-1] = 0. what i don't get is WHY i can say h1[-1]=0... I hope that makes sense.. it's hard for me to give an example of something I dont really understand in the first place
I'm just saying you haven't presented the system you are evolving. You need to look at that. Say,
$$y(t)=\int_{-\infty}^{\infty} x(t-\tau)h(\tau) d\tau$$
where x is the input, y in the output and h is the response function. If you want to calculate ##y(0)## then that doesn't depend, for example, on ##x(1)## because the contribution of ##x(1)## to the integral happens when ##\tau=(-1)## and being causal says ##h(-1)=0##.
 P: 195 It was explained to me like this, earlier today: $y[n] = \sum_{k=-\infty}^{\infty}x[k]h[n-k]$ $y[n] = \sum_{k=-\infty}^{n}x[k]h[n-k] + \sum_{k=n+1}^{\infty}x[k]h[n-k]$ then let h[n] = 0 for n<0 => h[n-k] = 0 for k>n => $\sum_{k=n+1}^{\infty}x[k]h[n-k] = 0$ So now x[k] only depends on values from -infinity to n, which is the past and present.
 Quote by ElijahRockers It was explained to me like this, earlier today: $y[n] = \sum_{k=-\infty}^{\infty}x[k]h[n-k]$ $y[n] = \sum_{k=-\infty}^{n}x[k]h[n-k] + \sum_{k=n+1}^{\infty}x[k]h[n-k]$ then let h[n] = 0 for n<0 => h[n-k] = 0 for k>n => $\sum_{k=n+1}^{\infty}x[k]h[n-k] = 0$ So now x[k] only depends on values from -infinity to n, which is the past and present.