In telecommunication systems that transmit and receive different types of signals, there is a requirement to process the various signals at different rates commensurate with the corresponding bandwidths of the signals.

Sampling rate conversion of a digital signal can be accomplished in one of the two general methods. One method is to pass the signal through D/A converter, filter it if necessary, and then to resample the resulting analog signal at the desired rate. The second method is to perform the sampling rate conversion entirely in the digital domain.

The major disadvantage by the given type of conversion is the signal distortion introduced by the D/A converter in the signal reconstruction and by the quantization effects in the A/D conversion.

The process of sampling rate conversion in the digital domain can be viewed as a linear filtering operation as illustrated in the given figure.

There are many applications where quadrature mirror filters can be used. Some of these applications are sub-band coding, trans-multiplexers and many other applications.

There are several applications of sampling rate conversion in multi rate digital signal processing systems, which include the implementation of narrow band filters, quadrature mirror filters and digital filter banks.

The input signal x(n) is characterized by the sampling rate Fx and he output signal y(m) is characterized by the sampling rate Fy, then

Systems that employ multiple sampling rates in the processing of digital signals are called multi rate digital signal processing systems.

One apparent advantage of the given method is that the new sampling rate can be arbitrarily selected and need not have any special relationship with the old sampling rate.

The process of converting a signal from a given rate to a different rate is known as sampling rate conversion.