Savitzky-Golay filter for smoothing and differentiation

Pure R implementation of the Savitzky-Golay filter using local polynomial fitting. Useful for smoothing noisy signals while preserving features like peak height and width better than simple moving averages.

Usage

savgolFilter(x, window_length = 11, poly_order = 3, deriv = 0)

Arguments

x

A numeric vector or matrix (time x channels).

window_length

Window length for the filter. Must be a positive odd integer.

poly_order

Polynomial order for local fitting (must be less than window_length).

deriv

Derivative order. 0 for smoothing, 1 for first derivative, 2 for second derivative, etc.

Value

Filtered/smoothed data with the same dimensions as x.

Details

The Savitzky-Golay filter fits a local polynomial of degree poly_order to a window of window_length points, using least-squares. The filter coefficients are computed analytically and applied via convolution.

For differentiation (deriv > 0), the result is the derivative of the fitted polynomial, which provides a smooth estimate of the derivative.

Edge handling: the first and last floor(window_length/2) points are computed with truncated windows where possible, or set to NA.

References

Savitzky A, Golay MJE (1964). "Smoothing and Differentiation of Data by Simplified Least Squares Procedures." Analytical Chemistry, 36(8), 1627-1639.

See also

butterworthFilter() for frequency-domain Butterworth filtering, movingAverage() for simple moving average smoothing, differentiate() for numerical differentiation.

Examples

# Smooth a noisy sine wave
t <- seq(0, 2 * pi, length.out = 200)
x <- sin(t) + rnorm(200, sd = 0.2)
x_smooth <- savgolFilter(x, window_length = 11, poly_order = 3)

# Compute first derivative
dx <- savgolFilter(x, window_length = 11, poly_order = 3, deriv = 1)