Question

What is the relation between h(t) and Ha(s)?

(a) Ha(s)=\( \int_{-\infty}^{\infty} h(t)e^{-st} dt\)

(b) Ha(s)=\(\int_0^{\infty} h(t)e^{st} dt\)

(c) Ha(s)=\( \int_{-\infty}^{\infty} h(t)e^{st} dt\)

(d) None of the mentioned

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

The doubt is from Design of IIR Filters from Analog Filters in division Digital Filters Design of Digital Signal Processing

Answer 1

Correct option is (a) Ha(s)=\( \int_{-\infty}^{\infty} h(t)e^{-st} dt\)

Easy explanation: We know that the impulse response h(t) and the Laplace transform Ha(s) are related by the equation.

Ha(s)=\( \int_{-\infty}^{\infty} h(t)e^{-st} dt\).