Digital Signal Processing, 10th Edition

10Multirate Filtering

Multirate filtering is a technique for reducing the calculation rate needed in digital filters and, in particular, the number of multiplications to be performed per second. As will be shown later, this parameter is generally regarded as a reflection of the complexity of the system.

In a filter, the number of multiplications M_R to be performed per second is given by:

where f_s is the frequency at which the calculations are made. The parameter f_s generally corresponds to the sampling frequency of the signal represented by the numbers to be processed. The factor K depends on the type of filter and on its performance.

In reducing the value of M_R, the factor K can be influenced by choosing the most appropriate type and structure of a filter and by optimizing the order of that filter to suit the constraints and required characteristics. Also, f_s can be influenced by changes in the sampling frequency during processing. In many practical cases, the advantages thus obtained are considerable.

The sampling frequency for a real signal must be more than twice its bandwidth, which can vary during processing. For example, a filtering operation eliminates undesirable components, so the useful bandwidth is reduced. Once the useful bandwidth has been decreased, the sampling frequency of the signal can itself be reduced. As a result, the sampling frequency can be adapted ...