Topic: Digital Signal Processing
A digital signal processing system is described by the expression: y(n) = 2x(n) + x(n - 1) + 2y(n - 1). The system is:
- A. A stable FIR filter
- B. A stable IIR filter
- C. An unstable FIR filter
- D. An unstable IIR filter
Answer: D. An unstable IIR filter
Explanation: y(n) = 2x(n) + x(n - 1) + 2y(n - 1) => y(n) - 2y(n - 1) = 2x(n) + x(n - 1). Y(z)/X(z) = (2 + z^-1)/(1 - 2z^-1). As the pole lies at z = 2, which is outside unit circle so it is an unstable system. As the output y(n) consist of y(n - 1) i.e. finite pole, so given system is IIR filter. ∴ System is unstable IIR filter.