Generating proportional, or constant Q filters, from discrete Fourier transform constant resolution filters
Abstract
Discrete Fourier transforms, such as the FFT, yield filters of constant resolution or bandwidth. For some applications, filters having constant Q or proportional bandwidth are preferred. Such filters may be made from a weighted sum of a set of the FFT filters. A formal procedure for obtaining the weighting coefficients is described which is based on expanding the desired filter function in a truncated set of orthogonal basis functions, the FFT filters. Only solution of a small set of simultaneous equations is required along with some iteration to adjust for minor deviations from specifications. Examples of actual composite filters produced by the procedure are given. These trials show the procedures to be fast and effective.
 Publication:

National Telecommunications Conference, Volume 2
 Pub Date:
 1975
 Bibcode:
 1975ntc.....2...31K
 Keywords:

 Digital Filters;
 Fast Fourier Transformations;
 Orthogonal Functions;
 Q Factors;
 Signal Processing;
 Spectral Resolution;
 Algorithms;
 Bandwidth;
 Computer Techniques;
 Proportional Control;
 Signal Distortion;
 Weighting Functions;
 Electronics and Electrical Engineering