Question

Question 11 : Signals :

Is \(\color{green}{y[n] = x[\sqrt{n}]}\) a Causal System??

Answer 1

For n = -1, -2, -3, y[n] will be not defined..

For n = 0, y[0] = x[0] implies Causal..

y[1] = x[1]
y[2] = x[??] ??

Answer 2

Non-Causal??

Answer 3

you just scared me @Night-Watcher

Answer 4

@waterineyes Lol, i get that response a lot.

Answer 5

I am your big fan.. You are like Spiderman to me.. :P

Answer 6

@phi

Answer 7

Why thank you! :)

Answer 8

Can we do something about this @phi

Answer 9

And @Night-Watcher there must be no reason why you are like spiderman, that will make me your true fan no?? :P

Answer 10

I think causal... y depends only on past values of x
( I assume this is only integer values , and we ignore non-integer sqr(n) )

Answer 11

And its Counterpart ??

Answer 12

I mean: in continuous time also, y(t) = x(sqrt{t}) is causal??

Answer 13

non-causal: y[n]= x[n^2]

*yes, for continuous t it's causal.

Answer 14

Thank you @phi ..

I will definitely need you as I am doing Signals And Systems, so I will tag you in my posts, if you don't mind.. :)

Answer 15

@phi , I think in continuous time, that will be Non-causal..

For example, for t = 0.05, y(0.05) = x(0.23) something, here output will depend on future input which is yet to apply..

Answer 16

yes, you are correct. for t<1 we are non-causal. Good catch!