Decimation is a process in which the sampling rate is

Decimation:

• Decimation is the process of reducing the sampling rate of the discrete-time signal.
• A low sampling rate reduces storage and computation requirements.

Let us consider a discrete-time signal x[n].

x[n] = \(\begin{Bmatrix} -1 & 6& 9 & -2 & 8\\ & & \uparrow & & \end{Bmatrix}\)

The position of different samples are as follows:

x[0] = 9,  x[1] = -2,  x[2] = 8,  x[-1] = 6,  x[-2] = -1,

Applying the time scaling property by assuming the factor 'a=2' on the x[n], we get:

\(x[n]\overset{scaling}{\rightarrow}x[2n]\)

if a > 1, the process is known as decimation.

if a < 1, the process is known as interpolation.

In the case of decimation, all discrete-time values will be divided by factor 'a' whereas will be multiplied by factor 'a' in interpolation.

The decimated signal x[2n] is:

x[2n] = \(\begin{Bmatrix} -1 & & 9 & & 8\\ & & \uparrow & & \end{Bmatrix}\)

Additional Information In the case of interpolation, the scaling factor 'a' is less than 1.

Lets us assume the scaling factor 'a' = \( {1 \over 2}\)

The interpolated signal x[\( {n \over 2}\)] is:

x[\( {n \over 2}\)] = \(\begin{Bmatrix} -1 & 0& 6 & 0 & 9 & 0 & -2 & 0 & 8\\ & & & &\uparrow & & & & \end{Bmatrix}\)