  We develop methods to design bandpass filters given desired characteristics
such as peak frequency, bandwidth, and group delay. We develop this filter
design method for filters we refer to as Generalized Auditory Filters (GAFs)
which are represented as second order filters raised to non-unitary exponents
and hence have three degrees of freedom. Our method for filter design
accommodates specification of a trio of frequency-domain characteristics from
amongst the peak frequency, convexity, 3dB, ndB quality factor, equivalent
rectangular bandwidth, maximum group delay, and phase accumulation. To develop
our characteristics-based design methods, we derive expressions for the filter
constants directly in terms of filter characteristics. The parameterization of
GAFs in terms of sets of characteristics allows for specifying magnitude-based
characteristics (e.g. bandwidths) and phase-based characteristics (e.g. group
delays) simultaneously. This enables designing sharply tuned filters without
significant group delay, and is particularly important in filterbanks where
frequency selectivity and synchronization are both important aspects of design.
Using our methods, we directly dictate values for desired filter
characteristics - unlike iterative filter design methods. This allows for more
direct design of GAFs for phase-picking from seismic signals, cochlear
implants, and rainbow sensors. The methods also directly apply to related
bandpass and multi-band filters.
