Question

What is the output of the single stage lattice filter if x(n) is the input?

(a) x(n)+Kx(n+1)

(b) x(n)+Kx(n-1)

(c) x(n)+Kx(n-1)+Kx(n+1)

(d) Kx(n-1)

The question was asked during an interview.

This is a very interesting question from Structures for FIR Systems topic in chapter Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Correct choice is (b) x(n)+Kx(n-1)

Explanation: The single stage lattice filter is as shown below.

Here both the inputs are excited and output is selected from the top branch.

Thus the output of the single stage lattice filter is given by y(n)= x(n)+Kx(n-1).