Question

If X(z) is the z-transform of x(n), then what is the z-transform of interpolated signal v(m)?

(a) X(zI)

(b) X(z+I)

(c) X(z/I)

(d) X(zI)

The question was asked in quiz.

I'd like to ask this question from Interpolation by a Factor I topic in section Digital Filters Design of Digital Signal Processing

Answer 1

Correct answer is (d) X(zI)

Explanation: By taking the z-transform of the signal v(m), we get

V(z)=\(\sum_{m=-∞}^∞ v(m)z^{-m}\)

=\(\sum_{m=-∞}^∞ x(m)z^{-mI}\)

= X(z^-I)