Improving the frequency response of Savitzky-Golay filters via colored-noise models

Abstract

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' SGfilters is illustrated in a hypothetical pulse/peak-detection application using a test statistic that is shaped by the noise model.

Formation and Evaluation of a Two-Phase Polymer System in Human Plasma as a Method for Extracellular Nanovesicle Isolation

“…A Raman spectrometer was used for measurements: LabRAM HR Evolution (HORIBA France SAS, Longjumeau, France), diffraction grating: 600 lines/mm, objective: Olympus MPlan, 50×, laser wavelength: 633 nm, exposure time: 50 s or 120 s depending on the severity (intensity) of the peaks of Raman scattering. The obtained Raman spectra were processed in MATLAB: the low-frequency component was removed using the BEADS algorithm [ 20 ], the spectra were smoothed using the Savitsky–Golay filter [ 21 ], and normalized to the intensity of the maximum peak to the interval [0; 1]. Before examining samples of different phases of the PTPS, the minimum detectable concentrations of polymers were determined: for DEX: 1.5 × 10 −3 g/dL, for PEG: 7 × 10 −3 g/dL.…”

Fourier transform infrared spectrum pre-processing technique selection for detecting PYLCV-infected chilli plants

“…Moreover, the smoothing curve in the 4000 - SG smoothing is used to smooth the signal by attenuating highfrequency noise, hence the waveform peak shape, amplitude and width of the desired signal will be maintained [62]. Meanwhile, the SG derivative is used as a band-pass filter which can also reduce signals at low frequencies [63,64]. The better classification results from the SG derivative implies that the noise in the spectra occurs not only at high frequencies but also at low frequencies.…”

Optimal Temporal Filtering of the Cosmic-Ray Neutron Signal to Reduce Soil Moisture Uncertainty

“…An SG filter, for instance, smooths sequential data using least-squares polynomial approximation sliding windows. The polynomial is fitted to a set of input samples and then evaluated at a point within the approximation interval, which is similar to discrete convolution [ 36 , 37 ]. While the median filter estimates values based on the median of the sorted values series of values presented by the window size, Kalman filters recursively estimate the current state using previously estimated states and current measurements.…”