Extracting Operational Gradient From Spatial Tracking Data
Spatial tracking coordinates differentiate into velocity vector fields that reveal operational resistance gradients and physical facility bottlenecks.
Savitzky-Golay filter
Meaning
A mathematical procedure for data smoothing fits a local polynomial function to a subset of adjacent points by way of least squares regression. A savitzky-golay filter operates by sliding a window across a sequence of values to reduce random noise while preserving the shape of the underlying signal. High frequency fluctuations drop away while the amplitude and width of peaks remain intact.
This calculation assumes that the data points possess a regular spacing and that the underlying trend behaves as a low order polynomial within the selected window.
Smoothing Mechanics
This process replaces the central value in the moving window with a new value derived from the polynomial fit. The calculation relies upon fixed coefficients that depend only on the window size and the degree of the polynomial. A smaller window width prioritizes fidelity to the raw data while a larger window creates a stronger attenuation of noise.
These coefficients simplify the computation into a linear convolution that requires little processing power to execute.
Signal Resolution
Analytical software uses the technique to prepare data for derivative calculation or peak identification without the distortion that simple moving averages introduce. The method distinguishes between random fluctuations and actual physical variations in the measurement. Precise separation of these components allows for more accurate baseline correction and area integration.
A filter that employs too broad a window effectively erases narrow features in the signal.
Parameter Selection
Determination of the optimal window width and polynomial order requires an assessment of the signal bandwidth. A choice of order affects how well the function tracks fast changes in the signal. Excessive polynomial degrees allow the filter to pass through noise that the smoothing is intended to remove.
Choice of these two parameters creates the effective cut-off frequency of the signal processing chain.