Question

Assertion (A): The discrete time system described by y[n] =2x[n] +4x[n-1] is unstable

Reason (R): It has an impulse response with a finite number of non-zero samples

(a) Both A and R are true and R is correct explanation of A

(b) Both A and R are true but R is not correct explanation  of A

(c) A is true but R is false

(d) A is false but R is true

The question was asked in class test.

I'd like to ask this question from The Z-Transfer Function in chapter Digital Control Systems of Control Systems

Answer 1

The correct answer is (d) A is false but R is true

The explanation is: For the system to be stable the value of the transfer function in the discrete time domain must be summable and H[n] calculated is summable hence the system is stable.