Efficient Multirate Filtering

Contents	Abstract	Conclusion	Figures	FREE software
Introduction	Conversion	Narrow-Band	Half-Band	MATLAB Scipts

Filters for Sampling Rate Conversion:

Filters are used in decimation to suppress aliasing, and in interpolation to remove imaging.
The performance of the system for sampling rate conversion is mainly determined by filter characteristics.
Since an ideal frequency response cannot be achieved, the choice of an appropriate specification is the first step in filter design.
In Figure 1, tree types of filter specifications used in practice are sketched.
The first type of specification, shown in Figure 1(a), is used in interpolation when the spectrum of the signal to be interpolated is nonzero in the interval [-p,p].
In the case of decimation, this type of specification minimizes the aliasing in the decimated signal.
The specifications shown in Figure 1(b) are used in interpolation when the highest frequency in the spectrum of the low-rate signal, |w_c|, is band limited to w_c < p, and in decimation when some aliasing from the adjacent band can be accepted.
The specifications shown in Figure 1(c) contain several don't care bands, and are suitable for interpolation for the band limited low-rate signal, |w_c|< p.
In decimation, for a large M this type of specification may bring an excessive aliasing even in applications when some aliasing is accepted. Figure 1.
Three types of filter specifications for sampling rate conversion by factor M.

For the selected type of specifications from Figure 1, we can use an FIR or IIR filter.
Obviously, an FIR filter easily achieves a strictly linear phase response, but requires a larger number of operations per output sample when compared with the equal magnitude response IIR filter.
But in sampling rate conversion systems, the efficiency of FIR filters is significantly improved that makes them very desirable in practice.

Figure 1 Three types of filter specifications for sampling rate conversion by factor M.

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Last updated September 9, 2008