Smoothing Algorithm
Digital signal smoothing algorithms fit successive sub-sets of adjacent data points with low-degree polynomials by linear least squares. Applying a savitzky-golay filter flattens high-frequency noise in spectroscopic and sensor time-series data while preserving higher-order spectral moments. Boundary limits require uniformly spaced data points and suffer edge effects at the start and end of data streams.
Peak Preservation
Convolving raw data streams with pre-calculated polynomial weighting coefficients replaces central data points with evaluated polynomial values. Utilizing a savitzky-golay filter maintains peak height, width and area far better than simple moving average filters. Window length and polynomial degree selection determine the degree of noise reduction and signal distortion balance.
Higher polynomial degrees capture narrow spectral features accurate to underlying physics but pass more high-frequency noise. Lower polynomial degrees increase signal smoothing but broaden sharp spectral absorption lines.
Derivative Calculation
Differentiating the fitted polynomial yields smooth derivative curves directly without amplifying high-frequency measurement noise. Spectroscopic peak detection algorithms employ second-derivative filtering to resolve overlapping spectral bands.
Implementation Limit
Computational implementation uses fixed convolution coefficients calculated prior to processing continuous data streams. Non-uniform sampling intervals require recalculation of weighting matrices, increasing processing overhead. Edge padding strategies prevent artificial endpoint distortions in finite data arrays.
