Differential Capacity Voltage Relaxation Analysis for Detecting Low Temperature Plating
Differential capacity voltage relaxation analysis detects sub-zero lithium plating by identifying chemical re-intercalation peaks during post-charge rest.
Savitzky Golay Smoothing
Meaning
Digital signal processing provides a mathematical method for increasing the signal-to-noise ratio in time series data while preserving the underlying shape of peaks. Savitzky golay smoothing accomplishes this through the application of a moving window that fits a low-degree polynomial to subsets of data points by the least squares criterion. Coefficients calculated from the polynomial allow the replacement of each center point with a weighted average of its neighbors.
This approach maintains high frequency components that standard moving averages often attenuate, which makes it suitable for analytical chemistry and spectroscopy where peak height and width accuracy determine quantitative precision.
Polynomial Order
Analysts select a degree for the local polynomial to balance noise reduction against feature distortion. A quadratic fit captures peak curvature, whereas a cubic fit accommodates more complex baseline variations. High orders retain the original data characteristics but provide less reduction in random noise.
The choice hinges on the expected width of the signal features relative to the sampling interval.
Window Size
Large windows produce a flatter output but increase the risk of diminishing the amplitude of narrow peaks. An appropriate span must remain smaller than the full width at half maximum of the smallest feature of interest to prevent artificial broadening. Odd integer values define the count of points included in the calculation of each estimate.
Centering the window ensures that the resulting values remain synchronized with the original temporal or spectral domain.
Mathematical Utility
The implementation of this technique simplifies derivative calculation by applying differentiated coefficients directly to the smoothed output. Standard software packages perform the convolution operation across the entire dataset to generate the filtered result in a single pass. Calculating the first or second derivative through this filter enhances the detection of small spectral shifts or overlapping peaks.
Proper selection of parameters reduces stochastic interference without compromising the integrity of quantitative measurement.