Characteristics-Based Design of Generalized-Exponent Bandpass Filters

We develop characteristics-based design methods for a class of IIR bandpass filters which we refer to as Generalized Exponent Filters (GEFs) and that are represented as second order filters raised to non-unitary exponents. GEFs have a peak, are effectively linear phase, and may be used for phase-picking for seismic signals, cochlear implants, rainbow sensors, and equalizers. The native specifications for GEFs are not on a given frequency response but rather on filter characteristics such as peak frequency, quality factor, and group delay. Our characteristics-based method for design accommodates direct specification of a trio of frequency-domain characteristics from amongst the peak frequency, 3dB quality factor, equivalent rectangular bandwidth, maximum group delay, and phase accumulation. We achieve this by deriving parameterizations for the filters in terms of sets of filter characteristics which involves deriving closed-form analytic expressions mapping sets of filter characteristics to the original filter constants by making sharp-filter approximations. This results in parameterizations for GEFs including mixed parameterizations based on simultaneous specification of magnitude-based characteristics (e.g. bandwidths) and phase-based characteristics (e.g. group delays) which enables designing sharply tuned filters without significant group delay and simultaneous control over frequency selectivity and synchronization which is important in designing filterbanks. Our design methods with direct control over characteristics may also be utilized for higher-order variable bandpass filter design and may be useful for characteristics-based adaptive filtering. Our methods are inherently stable, highly accurate in meeting strict specifications on desired characteristics, and computationally efficient. The methods extend to the design of related bandpass, multiband filters, and filterbanks.