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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»

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)



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