  Savitzky-Golay (SG) filters are finite impulse response (FIR) realizations of
least-squares polynomial regression and they are widely used for filtering
(e.g. smoothing, interpolating, predicting, differentiating) and processing
(e.g. detecting and classifying) non-stationary signals in non-Gaussian noise.
For such inputs, the Wiener filter is biased and the Kalman filter is
sub-optimal. Sequentially-correlated (i.e. colored) noise models are an
integral part of the Wiener filter and an optional addition to the Kalman
filter; however, their use in SG-filters has been overlooked in recent times.
It is shown here that colored (wide-band and narrow-band) noise models are
readily incorporated into a standard SG-filter and that this also addresses the
well-known deficiency of their poor frequency-selectivity/configurability. A
wide-band noise model sets the main-lobe/side-lobe width/height and provides
physical justification for band-limited design procedures described elsewhere.
The proposed narrow-band noise model, with arbitrarily placed side-lobe nulls,
has the potential to outperform other SG filters when sinusoidal interferers of
known frequency are present. The utility of these whitened SG-filters is
illustrated in a hypothetical pulse/peak-detection application using a test
statistic that is shaped by the noise model.
