Here is a question in the textbook that I have no idea how to do:

Consider a causal LTI system with input x[n] and output y[n]

y[n] = 0.25 y[n-1] + x[n]

Determine y[n] if x[n] = UnitImpulse[n-1]

The solution starts off with "Since the system is causal, y[n] = 0 for n < 1".... but I don't understand how they are able to say that...Why do they say this?

 

A causal system will not be able to generate an output before an input is supplied. Since the shifted unit step input is zero for all values before n=1, the output of the causal system is also necessarily zero for all n less than 1.