Question

1.28 Dectermine which of the properties listed in 1.27 hold and which do not hold for each of the following discrite-time systems. Justify your answers. In each example, y[n] denotes the system output and x[n] is the system input.

b) y[n] = x[n-2]-2x[n-8]

c) y[n]=nx[n]

system may or may not be:

1) Memoryless

2) Time invariant

3) Linear

4) causal

Answer 1

b) Since thhe given system follows homogeneity and aditivity so the system is linear.

Since the output of the systems depends on the past inputs so the system is causal

Since the output of the system depends on the past inputs so the system is not memory less.

Since the system doesn't depend on time so the system is time invarient.

c) Since the system output only depends on the present input so the system is causal as well as memoryless.

Since the system depends upon time so the system is time varient.

Since the system follows superposition, so the system is linear