Question

What is the output of the system represented by the following direct form?

(a) y(n)=-a1y(n-1)-a2y(n-2)- b0x(n)-b1x(n-1)-b2x(n-2)

(b) y(n)=-a1y(n-1)-a2y(n-2)+b0x(n)

(c) y(n)=-a1y(n-1)-a2y(n-2)+ b0x(n)+b1x(n-1)+b2x(n-2)

(d) y(n)=a1y(n-1)+a2y(n-2)+ b0x(n)+b1x(n-1)+b2x(n-2)

The question was posed to me by my college director while I was bunking the class.

The origin of the question is Implementation of Discrete Time Systems topic in division Discrete Time Signals and Systems of Digital Signal Processing

Answer 1

Right choice is (c) y(n)=-a1y(n-1)-a2y(n-2)+ b0x(n)+b1x(n-1)+b2x(n-2)

The best explanation: The equation of the difference equation of any system is defined as

y(n)=\(-\sum_{k=1}^Na_k y(n-k)+\sum_{k=0}^{M}b_k x(n-k)\)

In the given diagram, N=M=2

So, substitute the values of the N and M in the above equation.

We get, y(n)=-a1y(n-1)-a2y(n-2)+b0x(n)+b1x(n-1)+b2x(n-2)