Smoothing

Shipping

smoothing

Low-pass / denoising: moving average, exponential, Gaussian, median, Savitzky-Golay

Signature

Inputs

signalSignalrequired

Outputs

resultSignal

Parameters

Key	Type	Default	Notes
`method`	enum	moving_average	one of: moving_average, exponential, gaussian, median, savitzky_golay
`window_size`	int	5
`alpha`	float	0.2
`sigma`	float	1.0
`order`	int	2

Description

The Smoothing node applies a low-pass / denoising filter to a Signal, attenuating high-frequency content and random fluctuations while preserving the underlying trend. It exposes five distinct algorithms via the method parameter: moving_average, exponential (EWMA), gaussian, median, and savitzky_golay. Each method is a self-contained smoother selected at execution time; the irrelevant parameters for a given method are simply ignored.

Behavior is governed by method-specific controls. window_size sets the number of samples in the moving-average, median, and Savitzky-Golay windows; alpha $\in [0, 1]$ is the forgetting factor of the exponential filter; sigma is the Gaussian kernel standard deviation in samples; and order is the polynomial degree of the Savitzky-Golay fit. The output is a Signal on the same time base as the input — smoothing changes amplitude, not sample count or timestamps.

Units pass through unchanged: smoothing is a weighted linear (or, for median, order-statistic) combination of samples that all share one unit, so the result carries the input unit. For the linear methods the operation is a normalized convolution, so uncertainty ($\pm\sigma$) is reduced: averaging $N$ independent samples of equal variance shrinks the standard deviation toward $σ / N$ . The median method is nonlinear and rejects outliers/impulses rather than averaging them.

Despite the exponential method being conceptually recursive, this node is stateless (stateful: false): it smooths each input block as a complete array and does not retain a running accumulator across graph ticks. For persistent, sample-by-sample continuous filtering use iir_filter.

Mathematics

y_{i} = \frac{1}{W} k = - ⌊ W /2 ⌋ \sum ⌊ W /2 ⌋ x_{i + k} (moving_average)

y_{i} = α x_{i} + (1 - α) y_{i - 1} (exponential)

y_{i} = \frac{\sum _{k} e ^{- k^{2} / (2 σ^{2})} x _{i + k}}{\sum _{k} e ^{- k^{2} / (2 σ^{2})}} (gaussian)

Examples

Denoising a noisy sensor trace

Wire a noisy signal_generator (sine + noise_generator) into Smoothing with method = moving_average and window_size = 11. The output preserves the sine's shape while the broadband noise is cut by roughly $11 \approx 3.3 \times$ in standard deviation. Increase window_size for smoother output at the cost of rounding sharp peaks.

Impulse rejection with median vs. mean

Feed a signal corrupted by sparse spikes into two Smoothing nodes, one median and one moving_average, both window_size = 5:

signal_generator -> smoothing(median,  window_size=5)  -> sink
signal_generator -> smoothing(moving_average, window_size=5) -> sink

The median branch removes the spikes cleanly; the moving_average branch smears each spike across five samples instead of eliminating it.

Applications

Pre-processing noisy measurement data (thermocouples, strain gauges, accelerometers) before derivative or peak-detection stages that amplify noise.
Savitzky-Golay smoothing of spectroscopy and chromatography peaks, preserving peak height and width while denoising.
Exponential (EWMA) trend tracking of slowly drifting process variables in control and monitoring dashboards.
Median filtering to remove salt-and-pepper glitches and dropout spikes from digitized or telemetered signals.

Neat

For a fixed window, **Savitzky-Golay** with polynomial `order` preserves the signal's peak height and higher moments far better than a moving average, because it fits a local polynomial instead of assuming the window is flat.

Because the linear smoothers are normalized convolutions, they reduce measurement uncertainty ($\sigma \to \sigma/\sqrt{N}$ for a length-$N$ average of independent samples) — a rare filter that actively *shrinks* the propagated $\pm\sigma$.

Known issues

Near the signal endpoints, symmetric windows (moving_average, gaussian, median, savitzky_golay) lack neighbors and rely on edge handling; the first and last $\sim W/2$ samples are less reliable than the interior.

The exponential method has an initialization transient: because the node is stateless, $y_0$ seeds from the first sample and small `alpha` values leave a visible warm-up region at the start of each processed block.