Question

Determine the nature of the system: y[n] = x[n]x[n – 1] with unit impulse function as an input.

(a) Dynamic, output always zero, non-invertible

(b) Static, output always zero, non-invertible

(c) Dynamic, output always 1, invertible

(d) Dynamic, output always 1, invertible

The question was asked by my college professor while I was bunking the class.

My question is based upon Properties of Systems topic in chapter Signals and Systems Basics of Signals and Systems

Answer 1

The correct option is (a) Dynamic, output always zero, non-invertible

Explanation: Since the system depends on present and past values, therefore, it is not memory less(dynamic).

Now, input is a unit impulse function. Unit impulse function = 1 at n = 0, otherwise it is equal to 0.

For, y[0] = x[0]x[-1] = 1 × 0 = 0

For, y[1] = x[1]x[0] = 0 × 1 = 0

For, y[2] = x[2]x[1] = 0 × 0 = 0

∴ For any time, output is always zero.

Since, the output is always same, the system is non-invertible.