Solution:

In practical applications mostly sampling rate conversion by a rational factor, $L / M$ is required.

The figure represents the general structure of the System where this conversion is used.

Consider a system for decimating a signal by an integer factor M.

Let the input signal sampling frequency be $f_0$, then the decimated signs frequency wi 41 be $f_0 / M$ The decimation factor can be factorized as

$ M=\prod_{i=1}^I M_i $

If the sampling rate alternation system is designed as a cascade system, the computational efficiency is improved significantly.

The reason for using multistage structures are

(1) Multistage systems require reduced computation

(2) Storage space required is less

(3) Filter design problem is simple.

(4) Finite word length effects are less.

The demerits of the systems are that proper control structure is required in implementing the system and proper values of I should be Chosen.