Number of memory locations used for storage of the output point of a sequence in direct form realization

In direct form realization, a sequence of length M represents a system with M inputs and M outputs. The direct form realization is a basic and commonly used structure for implementing digital filters.

Explanation:

The direct form realization of a system involves a set of delay elements and coefficients. The number of memory locations required for storage of the output point of a sequence depends on the length of the sequence.

Let's consider a direct form realization structure for a sequence of length M:

- The input sequence of length M is denoted as x(n), where n represents the discrete-time index.
- The output sequence of length M is denoted as y(n).
- The direct form realization structure consists of M delay elements, each storing the previous input value.

Memory locations in direct form realization:

- For each input value, it is stored in a separate memory location. Therefore, the number of memory locations required for storing the input sequence of length M is M.
- The delay elements in the direct form realization also require memory locations to store the previous input values. Since there are M delay elements, the number of memory locations required for storing these values is also M.
- The output sequence is obtained by applying the coefficients to the input sequence and the delayed values. In direct form realization, the output point is calculated using the current input value and the delayed input values from the memory locations. Therefore, no additional memory locations are required for storing the output sequence.

Conclusion:

Hence, the total number of memory locations used for storage of the output point of a sequence of length M in direct form realization is M - 1. The correct answer is option C.