Characteristics-Based Design of Generalized-Exponent Bandpass Filters

We develop characteristics-based filter design methods for certain related classes of IIR bandpass filters that have a peak including Generalized-Exponent Filters (GEFs) which are represented as second-order filters raised to non-unitary exponents. Such filters are useful for seismic signal phase-picking, cochlear implants, and equalizers. Instead of requiring specification of a frequency response and tolerance, our characteristics-based methods for filter design accommodates direct specification of a trio of frequency-domain characteristics from amongst the peak frequency, convexity, ndB quality factors, equivalent rectangular bandwidth, maximum group delay, and phase accumulation. We achieve this by deriving filter parameterizations in terms of sets of filter characteristics which involves deriving closed-form expressions mapping sets of filter characteristics to the original filter constants by making sharp-filter approximations. This results in parameterizations for GEFs including ones with simultaneous specification of magnitude-based characteristics and phase-based characteristics (e.g. bandwidths and group delays) which enable designing sharply-tuned filters without significant group delay, and simultaneous control over frequency selectivity and synchronization which is important in designing filterbanks. We demonstrate that the methods directly apply in designing related bandpass and multiband filters. Our methods with direct control over characteristics may also be utilized beyond static filter design for higher-order variable bandpass filter design and may be useful for characteristics-based adaptive filtering. The methods are inherently stable, highly accurate in meeting strict specifications on desired characteristics, simple, and computationally efficient. Furthermore, the general paradigm can guide the development of characteristics-based filter design methods for other classes of filters.