  The increased temporal and spectral resolution of oversampled systems allows
many sensor-signal analysis tasks to be performed (e.g. detection,
classification and tracking) using a filterbank of low-pass digital
differentiators. Such filters are readily designed via flatness constraints on
the derivatives of the complex frequency response at dc, pi and at the centre
frequencies of narrowband interferers, i.e. using maximally-flat (MaxFlat)
designs. Infinite-impulse-response (IIR) filters are ideal in embedded online
systems with high data-rates because computational complexity is independent of
their (fading) memory. A novel procedure for the design of MaxFlat IIR
filterbanks with improved passband phase linearity is presented in this paper,
as a possible alternative to Kalman and Wiener filters in a class of
derivative-state estimation problems with uncertain signal models. Butterworth
poles are used for configurable bandwidth and guaranteed stability. Flatness
constraints of arbitrary order are derived for temporal derivatives of
arbitrary order and a prescribed group delay. As longer lags (in samples) are
readily accommodated in oversampled systems, an expression for the optimal
group delay that minimizes the white-noise gain (i.e. the error variance of the
derivative estimate at steady state) is derived. Filter zeros are optimally
placed for the required passband phase response and the cancellation of
narrowband interferers in the stopband, by solving a linear system of
equations. Low complexity filterbank realizations are discussed then their
behaviour is analysed in a Teager-Kaiser operator to detect pulsed signals and
in a state observer to track manoeuvring targets in simulated scenarios.
