Question

If a three stage lattice filter with coefficients K1=1/4, K2=1/2 K3=1/3, then what are the FIR filter coefficients for the direct form structure?

(a) (1,8/24,5/8,1/3)

(b) (1,5/8,13/24,1/3)

(c) (1/4,13/24,5/8,1/3)

(d) (1,13/24,5/8,1/3)

I got this question during an interview.

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

Answer 1

The correct option is (d) (1,13/24,5/8,1/3)

To elaborate: We get the output from the third stage lattice filter as

A3(z)=1+(13/24)z^-1+(5/8)z^-2+(1/3)z^-3.

Thus the FIR filter coefficients for the direct form structure are (1,13/24,5/8,1/3).