Question

If Y(z) is the z-transform of the output function, X(z) is the z-transform of the input function and H(z) is the z-transform of system function of the LTI system, then H(z)=?

(a) \(\frac{Y(z)}{X(z)}\)

(b) \(\frac{X(z)}{Y(z)}\)

(c) Y(z).X(z)

(d) None of the mentioned

This question was posed to me during an interview for a job.

The query is from Rational Z Transform topic in chapter Z Transform and its Application – Analysis of the LTI Systems of Digital Signal Processing

Answer 1

Right option is (a) \(\frac{Y(z)}{X(z)}\)

To elaborate: We know that for an LTI system, y(n)=h(n)*x(n)

On applying z-transform on both sides we get, Y(z)=H(z).X(z)=>H(z)=\(\frac{Y(z)}{X(z)}\).