Question

The system \(x(k) = 7(\frac{1}{3})^k  \,u(-k-1) – 6(\frac{1}{2})^k  \,u(k)\) is ___________

(a) Causal

(b) Anti-causal

(c) Non-causal

(d) Cannot be determined

The question was posed to me in an interview for internship.

This intriguing question originated from Fourier Series and LTI Systems in chapter Fourier Series of Signals and Systems

Answer 1

Correct option is (c) Non-causal

Easy explanation: Taking the z-transform, we get,

\(X (z) = 7\left(\frac{1}{z-\frac{1}{3}}\right) – 6\left(\frac{1}{z-\frac{1}{2}}\right)\)

∴ the ROC for given condition is as derived above.

∴ the bounded signal as a whole is non-causal.