The block diagram shown in the figure is of sampling rate conversion by decimation by a factor D technique.

To avoid aliasing, we must reduce the bandwidth of x(n) to Fmax=F/2D. Then we may down-sample by D and thus avoid sampling.

Given the fact that x(n) produces y(m), we note that x(n-n0) does not imply y(n-n0) unless n0 is a multiple of D. Consequently, the overall linear operation, that is linear filtering followed by down sampling on x(n) is not time invariant.

Although the filtering operation on x(n) is linear and time invariant, the down-sampling operation in combination with the filtering results in a time variant system.

Given the fact that x(n) produces y(m), we note that x(n-n0) does not imply y(n-n0) unless n0 is a multiple of D.

\\(\\bar{v}(n)\\) can be viewed as a sequence obtained by multiplying v(n) with a periodic train of impulses p(n) with period D.

We know that if we reduce the sampling rate simply by selecting every Dth value of x(n), the signal will be an aliased version of x(n), with a folding frequency of F/2D.

We know that if we reduce the sampling rate simply by selecting every Dth value of x(n), the signal will be an aliased version of x(n).

The frequency domain characteristic of the output sequence y(m) can be obtained by relating the spectrum of y(m) to the spectrum of the input sequence x(n).

We know that the equation for y(m) is given as