Question

F(t) and G(t) are the one-sided z-transforms of discrete time functions f(nt) and g(nt), the z-transform of ∑f(kt)g(nt-kt) is given by _____________

(a) ∑f(nt)g(nt)z^-n

(b) ∑f(nt)g(nt)z^n

(c) ∑f(kt)g(nt-kt) z^-n

(d) ∑f(nt-kt)g(nt)z^-n

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

I'd like to ask this question from Discrete-Time Fourier Transform topic in division Fourier Transform of Signals and Systems

Answer 1

The correct answer is (a) ∑f(nt)g(nt)z^-n

To elaborate: Given that F (t) and G (t) are the one-sided z-transforms.

Also, f (nt) and g (nt) are discrete time functions, which means that property of Linearity, time shifting and time scaling will be similar to that of continuous Fourier transform. Since, for a continuous Fourier transform, the value of ∑f(kt)g(nt-kt) is given by∑f(nt)g(nt)z^-n.

∴ z-transform of ∑f(kt)g(nt-kt) is given by∑f(nt)g(nt)z^-n.