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

I had been asked this question in an interview for job.

Enquiry is from Properties of ROC in portion Laplace Transform and System Design of Signals and Systems

Answer 1

Right option is (c) Non-causal

To elaborate: 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.