An IIR filter having numerator order M and denominator order N is to be realized using direct form II structure. How much total number of multiplications, additions and memory locations are required respectively ?

An IIR filter having numerator order M and denominator order N is to be realized using direct form II structure. How much total number of multiplications, additions and memory locations are required respectively ? Correct Answer M + N + 1, M + N and maximum of {M, N}

IIR Systems are represented in four different ways 

1) Direct Form Structures Form I and Form II

2) Cascade Form Structure

3) Parallel Form Structure

4) Lattice and Lattice-Ladder structure.

Direct Form Structures II:

Additional Information

Direct Form I Structure:

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• Direct form I realization of H(z) can be obtained by cascading the realization of H₁(z) which is all zero system first and then H₂(z) which is all pole system.
• There are M+N-1 unit delay blocks. One unit delay block requires one memory location. Hence direct form structure requires M+N-1 memory locations.
• Direct Form I realization requires M+N+1 number of multiplications and M+N number of additions and M+N+1 number of memory locations.