K. Martin’s research while affiliated with IBM Research - Thomas J. Watson Research Center and other places

A synthesis procedure for generating orthogonal structures to implement arbitrary transfer functions is described. As compared to earlier techniques associated with orthogonal filter synthesis, which used a cascade of sections or a parallel combination of sections, this method uses feedback to simplify the design process, and results in filter structures that have the low-passband-sensitivity properties associated with orthogonal structures. Additionally, the structure is inherently L2-scaled; thus, the design process is simplified because an additional scaling step is not necessary. One of the other advantages of the new structure is that its stability monitoring is very easy; thus, it is extremely well suited for adaptive applications. The method is motivated by some recently reported resonator-based digital-filter structures

A second-order hyperstable adaptive recursive filter is presented, that does not require the usual post-error filtering that is needed in other hyperstable adaptive schemes to guarantee convergence. The filter is developed for the particular application of frequency estimation of an input sinusoid, rather than as a general infinite impulse response (IIR) adaptive filter. As the adaptive algorithm can be made to converge arbitrarily fast by increasing the μ value, while still retaining stability, it may be used in situations where the input frequency changes have to be tracked very fast, as for instance in frequency hopped spread spectrum M -ary frequency (MFSK) communication systems etc

A design process is described which starts with a prototype resonator-based uniform filter-bank, whose bandpass outputs have poor stopband characteristics, and applies the concept of Lerner grouping of adjacent channels to develop a uniform filter-bank with much better bandpass characteristics. For applications requiring the lower frequencies of the input signal to be resolved more accurately than the higher frequencies, the Lerner based uniform filter-bank may be converted to a nonuniform one by applying an allpass transformation; the merit of using such a transformation is that it retains the good magnitude characteristics of the bandpass channels. The main difference between the present design procedure and that of G. Doblinger (1991) is the manner in which the allpass transformation is applied. Further, unlike previous work, the filter-bank designed here has the property that the sum of the bandpass channels is an allpass function. The implementation of the filter-bank is also considered. The primary additional application of the nonuniform channel-bank examined here is frequency-domain adaptive filtering

Some further results on modulated and extended lapped transforms are reported. Sufficient conditions to ensure perfect reconstruction for extended lapped transforms are derived. These conditions are valid for transforms of length lM and place no restriction on l ; in this respect they apply to a more general case than earlier derivations that constrained l to be even. Also, a new filter structure is reported for implementing the modulated lapped transform. It has a hardware complexity of O ( M ) as compared to O ( M log M ) for other implementations

A frequency-sampling Fourier transform can be efficiently and robustly realized by a resonator-in-a-loop filter bank with uniformity spaced resonators. If the resonator outputs are grouped using a Lerner weighting, where alternating signs are used for each resonator output, then filter banks with greatly reduced sidelobes are obtained at the expense of wider passbands. The filters obtained by grouping the real Fourier transform outputs are linear phase and have exactly 90 degrees phase shift differences compared to those obtained by a Lerner grouping of the imaginary outputs. This allows for the realization of very accurate Hilbert transform bandpass filters.

A generalized filtering structure is developed which is based on the N×N basis matrix of an arbitrary transform. The filtering structure finds application as an efficient sliding transformer of data because it has the low complexity of the associated frequency sampling structure, but has much better sensitivity properties. It can also be used as a filterbank in a multirate filtering system. The analysis filters are seen to require very few multipliers (the synthesis filters are finite impulse response with, at most, as many taps as there are channels in the filterbank) and at the same time provide ≈40 dB attenuation of the nearest sidelobe