Consider a discrete-time system that is characterized by the following difference equation:

Y(n) = x(n)cos?₀n,

where ?₀ is constant value, x(n)are the discrete-time input data of the system, y(n)are the discrete-time output data of the system.

 Is the discrete-time system governed by the given difference equation:

(a) static or dynamic?

(b) time-invariant or time-variant?

(c) linear or nonlinear?

(d) causal or noncausal?

(e) stable or unstable?

Explain your answers for all questions and prove your conclusions analytically for questions b,c and d.