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How many memory locations are used for storage of the output point of a sequence of length M in direct form realization?

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How many memory locations are used for storage of the output point of a sequence of length M in direct form realization?

(a) M+1

(b) M

(c) M-1

(d) None of the mentioned

I got this question during an interview.

My doubt is from Structures for FIR Systems in division Discrete Time Systems Implementation of Digital Signal Processing

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The correct option is (c) M-1

The explanation: The direct form realization follows immediately from the non-recursive difference equation given by y(n)=\(\sum_{k=0}^{M-1}b_k x(n-k)\).

We observe that this structure requires M-1 memory locations for storing the M-1 previous inputs.

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