Question

The equation for Heq(s) is \(\frac{\sum_{K=0}^M b_K s^K}{\sum_{K=0}^N a_K s^K}\).

(a) True

(b) False

I have been asked this question during an interview for a job.

This key question is from Backward Difference Method in portion Digital Filters Design of Digital Signal Processing

Answer 1

Right choice is (a) True

Best explanation: The analog filter in the time domain is governed by the following difference equation,

\(\sum_{K=0}^N a_K y^K (t)=\sum_{K=0}^M b_K x^K (t)\)

Taking Laplace transform on both the sides of the above differential equation with all initial conditions set to zero, we get

\(\sum_{K=0}^N a_K s^K Y(s)=\sum_{K=0}^M b_K s^K X(s)\)

=>  Heq(s)=Y(s)/X(s)=\(\frac{\sum_{K=0}^M b_K s^K }{\sum_{K=0}^N a_K s^K}\).