Design Floating-Point Multirate Filters

The floating-point single-rate filter design process can be followed to design a floating-point multirate filter.

The following figure illustrates the typical magnitude response of a lowpass filter in multirate systems:

In this figure, fs denotes the sampling frequency of the input signal. When designing filter specifications, you must take the filtering mode into consideration. Because decimation and interpolation are special cases of rational resampling, you can use the following filter specifications to design any filter with a rational factor of L/M.

Table 7. Example Filter Specifications
Filter SpecificationValue Range
Passband edge frequency

0   <   f pass   <   min ( Lf s 2 M ,   f s 2 )

Stopband edge frequency

f pass   <   f stop   <   Lf s M − f pass

Typically, fpass is the highest frequency of interest in the input signal. If

f stop   <   min ( Lf s 2 M ,   f s 2 )
the transition band is free of aliases. If you change the constraints of fstop to
min ( Lf s ( 2 M ) ,   f s 2 )   <   f stop   <   ( Lf s 2 M − f pass )
the filter has a wider transition band and a lower order, which can reduce the computational complexity significantly in filtering operations. However, the transition band then contains aliasing in the frequency conversions.