Multirate and Multistage Filters

Multirate filters are digital filters that change the sample rate of a digital signal without introducing aliasing or imaging in the rate-converted signal. These filters are categorized as decimators that reduce the sample rate, interpolators that increase the sample rate, and rate converters that do a combination of both. For details on these rate conversion operations and their effect on the signal in time and frequency domains, see Overview of Multirate Filters. DSP System Toolbox™ offers MATLAB^® System objects and Simulink^® blocks that implement decimators, interpolators, and rate converters. Advanced filter technologies such as channelizers, channel synthesizers, two-channel halfband filter banks, and multilevel filter banks use these filters as building components.

You can implement a multirate filter with a large rate conversion factor efficiently in two or more stages rather than in one single stage. When the design is long (contains many coefficients) and costly (requires many multiplications and additions per input sample), the multistage approach is more efficient to implement compared to the single-stage approach. For more details, see Overview of Multistage Filters.

The designMultistageDecimator and designMultistageInterpolator functions in DSP System Toolbox automatically determine the optimal configuration of the filter, which includes determining the number of stages and the rate conversion factor for each stage. An optimal configuration leads to the least computational effort and you can measure the cost of such an implementation using the cost function. For an example, see Multistage Rate Conversion.