# Homework Help: Causal system/convolution question

1. Oct 20, 2014

### kidsasd987

1. The problem statement, all variables and given/known data

a) find if the system is causal.
b) find the impulse response

given: y(t)=x(t-1)u(t)

ans:
a) Causal
b) delta(t-1)

2. Relevant equations

3. The attempt at a solution

a)

I thought this is a non-causal system because if our input is delta(t), the resultant output is delta(t-1)
if t=1, input value depends on delta(1), and its output is delta(0). output depends on future value.

b) I don't know where that u(t) comes from...

thanks.

2. Oct 21, 2014

### RUber

Usually this type of problem will the additional condition that x(t) = 0 for t<0, so that it is more clear that this is a weighted ( by u(t) ) shift operation.
I am assuming that x and u are known and y is the output.

3. Oct 21, 2014

### FOIWATER

a) The system is causal because the output is only dependent on past values of input x[t-1] is a time in the past.

b) y[t]=x[t-1]*u[t] --> for the impulse response, we put delta function as input (x) and then solve for output. so, impulse response:
h[t] = delta[t-1]*u[t] = delta[t-1]