Categorizing Filter Banks (Digital Filter Design Toolkit)

You can categorize filter banks according to the bandwidths of the subbands or the number of subbands.

Uniform and Non-Uniform Filter Banks

You can categorize filter banks into uniform filter banks and non-uniform filter banks according to the bandwidths of the subbands. The following figure shows the magnitude response of a uniform filter bank.

The filter bank separates the signal spectrum into uniformly spaced subbands. Uniform filter banks in the LabVIEW Digital Filter Design Toolkit have the property that the number of subbands is equal to the decimation factor of the subband filters. This is known as a critically sampled uniform filter bank. The subband number of a critically sampled uniform filter bank is equivalent to the decimation factor M, with subband bandwidth 2/M.

A uniform filter bank has uniformly spaced subband bandwidths, which results in a fixed subband resolution in all frequency areas. The following figure illustrates how a non-uniform filter bank can have different subband resolutions in different frequency areas.

In the previous figure, the subband bandwidth in the lower frequency area is narrower than the subband bandwidth in the higher frequency area. Therefore, this non-uniform filter bank can achieve a higher resolution than a uniform filter bank in the low frequency area.

2-band and M-band Filter Banks

You also can categorize filter banks as 2-band and M-band filter banks according to the number of subbands.

Wavelet analysis uses 2-band filter banks, also called quadrature mirror filter (QMF) filter banks. In a QMF filter bank, the magnitude responses of the lowpass band filter and the highpass band filter in the analysis bank are symmetric about /2.

One approach to M-band filter bank design is to apply a cosine modulation to a prototype lowpass filter. The M-band cosine-modulated filter banks used in the LabVIEW Digital Filter Design Toolkit are critically sampled filter banks.

The advantages of cosine-modulated filter bank design are as follows.

• You can reduce the design complexity as you need to design only one prototype lowpass filter. The analysis and synthesis filters are frequency-shifted versions of the prototype filter.
• It is feasible to design perfect reconstruction cosine-modulated filter banks.
• The analysis and synthesis filters have real-valued coefficients.