Question

If R1 is the region of convergence of x (n) and R2 is the region of convergence of y(n), then the region of convergence of x (n) convoluted y (n) is ___________

(a) R1 + R2

(b) R1 – R2

(c) R1 ∩ R2

(d) R1 ∪ R2

I have been asked this question in semester exam.

My doubt is from Discrete Fourier Transform topic in chapter Fourier Transform of Signals and Systems

Answer 1

The correct answer is (c) R1 ∩ R2

To elaborate: The z-transform of x (n) = X (z). Let the region of convergence be R1

The z-transform of y (n) = y (z). Let the region of convergence be R2

The z-transform of x (n) * y (n) is X (z).Y (z) [from property]

So, the region of convergence is R1 ∩ R2.