Question

What is the output from the second stage lattice filter when two single stage lattice filers are cascaded with an input of x(n)?

(a) K1K2x(n-1)+K2x(n-2)

(b) x(n)+K1x(n-1)

(c) x(n)+K1K2x(n-1)+K2x(n-2)

(d) x(n)+K1(1+K2)x(n-1)+K2x(n-2)

The question was posed to me in an internship interview.

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

Answer 1

Right option is (d) x(n)+K1(1+K2)x(n-1)+K2x(n-2)

For explanation: When two single stage lattice filters are cascaded, then the output from the first filter is given by the equation

f1(n)= x(n)+K1x(n-1)

g1(n)=K1x(n)+x(n-1)

The output from the second filter is obtained as

f2(n)=f1(n)+K2g1(n-1)

=x(n)+K2[K1x(n-1)+x(n-2)]+ K1x(n-1)

= x(n)+K1(1+K2)x(n-1)+K2x(n-2).