Consider a system S with input x[n] and output y[n] related according to the block diagr...

Consider a system S with input x[n] and output y[n] related according to the block diagram in Figure P2.63-1.

The input x[n] is multiplied by e^−jω0n, and the product is passed through a stable LTI system with impulse response h[n].

(a) Is the system S linear? Justify your answer.

(b) Is the system S time invariant? Justify your answer.

(c) Is the system S stable? Justify your answer.

(d) Specify a system C such that the block diagram in Figure P2.63-2 represents an alternative way of expressing the input–output relationship of the system S. (Note: The system C does not have to be an LTI system.)