# How to check if h(n) is causal, stable? [closed]

I have $$x(n)$$ = {$$4,-1,-3,1$$} and $$h(n)$$ = {$$2,1,3,5$$}.

I would like to know how can I check whether

$$h(n)$$ is stable filter or not and $$h(n)$$ is causal filter or not?

• hey! Your notation isn't quite right, and that makes it impossible for you to answer this yourself :) $h(n)$ is a single value, the value of the signal (or impulse response) $h$ at time $n$. Now, $\{2,1,3,5\}$ is a set of values, and that's not what you wanted. So, first step, figure out for which $n$ the value of $h$ becomes $2$, for which it becomes $1$ and so on. Then check the definition of "causal"! Apr 19, 2020 at 9:12
• let say h(n = 0) = 2, h(n = 1) = 1, h(n = 2) = 3, h(n = 3) = 5. Apr 19, 2020 at 9:17
• if you say so, congratulations, you've just answered your own causality question. Apr 19, 2020 at 9:23

Firstly, you do not need to specify an input $$x(n)$$ to know whether the system is stable or causal, these are properties of the system itslef, I will interpret $$h(n)$$ you mention as a array describing the system response.
For causality in time domain perspectivefor an LTI system check if $$h(n) =0$$ for all $$n < 0$$, that is the $$h(n)$$ is essentially a right sided sequence.
For stability in time domain perspective, the system response $$h(n)$$ should be absolutely summable, since you have only finite coefficients, this system is stable, any FIR filter is always stable.