Smooth — Control Systems/Signal Smoothing

Smooth

Control Systems / Signal Smoothing

Smooths a stream by fitting a local regression to the last Span samples and emitting its value at the centre of that window. This is MATLAB's smooth on a stream, and it carries the same three uniformly-spaced methods: a centred moving average, lowess (a local straight line) and loess (a local parabola), the last two weighted so that samples near the centre count for more than samples near the edge.

Writing t for a sample's offset from the centre and h = (Span−1)/2, the weighted pair solve w = row 0 of (V′WV)⁻¹V′W with tri-cube weights W(t) = (1 − (|t|/h)³)³ and a local basis V = [1, t] or [1, t, t²]. Row 0 is the whole answer because the basis at t = 0 is [1, 0, 0]: the fitted value at the centre is the constant term of the local fit.

Ports

• u – the sampled signal being smoothed. Scalar: one channel and its own window – see Notes.
• y – the smoothed value, scalar, lagging the input by (Span−1)/2 samples. Its size is the input's and does not depend on any setting.

Parameters

• Smoothing Method – which local fit is made. Three values, named as MATLAB names them:
  • moving – the unweighted average of all Span samples. The same numbers as Machine Learning / Feature Engineering / Rolling Statistics in its Mean mode, shifted by (Span−1)/2 samples; reach for that block when a trailing mean with no lag is what is wanted, and for this one when the answer has to line up with smooth.
  • lowess – a tri-cube-weighted straight line. The default, as it is MATLAB's. It follows a ramp exactly where a moving average of the same length lags it.
  • loess – a tri-cube-weighted parabola. It preserves a peak's height where lowess flattens it, at the price of rejecting less noise.
• Span – how many samples the fit sees. A whole number from 1 to 101. An even value is silently rounded up to the next odd one, exactly as smooth does, because a centred window has to have a centre. Bounded above because the dot product is unrolled at export.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text.

The weight row is structural and is inlined into the arithmetic at export time rather than exposed as a tunable parameter: it follows from both settings, and changing either changes how many multiplies the core contains, which no runtime parameter can do. Re-export after changing them.

The three HDL targets are genuine synthesizable Q16.16: a shift register and one fixed multiply-accumulate, with the products accumulated at full width and shifted back once at the end rather than per term. No fit is solved in hardware – it happened at export time.

Simulink bridge

None (Support::None). smooth is a Curve Fitting Toolbox function, and that toolbox ships no Simulink library at all, so there is no path a diagram could name. The bridge reports this block rather than dropping it silently, and it therefore has no parity testbench; code export verification still covers it across all ten languages. No configuration of it crosses either, including "Sampling Time (s)", which has no counterpart to be written to.

Notes

• Stateful, and discrete by nature (setDiscreteOnlyBlock(true)): the window advances once per sample.
• One solve, then arithmetic. A fit evaluated at one point is a linear function of the window, so the small weighted system is solved once when the configuration loads and every sample afterwards is a single dot product. Nothing inverts a matrix per sample, here or in any exported core.
• The output lags (Span−1)/2 samples, because the centre of the last Span samples is that far in the past and a stream cannot see the future half of a centred window. Savitzky-Golay Filter offers an endpoint evaluation that avoids the lag; smooth has no such option, so neither does this block.
• The two extreme samples of the span carry weight exactly zero under lowess and loess, because the tri-cube weight is normalised by h and vanishes at ±h. A span of 7 therefore fits five points. This is MATLAB's behaviour, not an approximation of it, and it is why an effective smoothing length is two shorter than the span looks. Under moving all Span samples count.
• Verified against MATLAB. Over spans 5, 7, 9 and 11 and all three methods, the row derived here reproduces smooth's interior impulse response to 4.4e−16 and its interior output on a 20-sample record to 1.3e−15, in R2026a.
• The window is zero-prefilled, and the zeros count. The first Span−1 outputs of a run are a startup transient in which the fit sees samples that were never measured. MATLAB has no such phase because it is handed the whole vector at once and shrinks its window at the ends; a stream cannot. The convention matches Moving Median, Detrend, Hampel Filter and Savitzky-Golay Filter.
• Three of MATLAB's six methods are deliberately absent. sgolay is the same local polynomial with the weights left at 1, and is Savitzky-Golay Filter in this family. rlowess and rloess add a bisquare reweighting computed from the fit's own residuals, so their weights are a function of the data rather than of the configuration – there is no row to inline, and every generated core would have to carry five iterations of a weighted solve per sample.
• Scalar only. One channel and its own history; wire one block per channel. A shared window would mix them.
• Smoothing is not filtering the noise away. A short span follows the input closely and rejects little; a long one rejects more and lags more, and under lowess it also flattens any feature narrower than the span.
• No state space. The block is linear in its input, but its output depends on Span past samples through a fixed row rather than through an A/B/C/D pair, so it carries none and model reduction correctly declines to merge it.