Question

To implement the linear time invariant recursive system described by the difference equation y(n)=\(-\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^M b_k x(n-k)\) in Direct form-I, how many number of delay elements and multipliers are required respectively?

(a) M+N+1, M+N

(b) M+N-1, M+N

(c) M+N, M+N+1

(d) None of the mentioned

I had been asked this question in an interview for job.

My question is from Implementation of Discrete Time Systems in portion Discrete Time Signals and Systems of Digital Signal Processing

Answer 1

Right answer is (c) M+N, M+N+1

The explanation is: From the given equation, there are M+N delays, so it requires M+N number of delay elements and it has to perform M+N+1 multiplications, so it require that many number of multipliers.