Fit Integral — Control Systems/Curve Fitting

Fit Integral

Control Systems / Curve Fitting

Integrates a polynomial given by its coefficients. With the input in descending powers, c₀·x^L−1 + … + c_L−1, the output is (c₀/L)·x^L + … + (c_L−1/1)·x + K – entry r is c_r/(L−r), and the last entry is the integration constant. This is MATLAB's polyint.

It transforms a curve, not a sample. Wire Curve Fitting / Polynomial Fit into it to integrate a running fit, and Curve Fitting / Evaluate Fit after it to read the area somewhere: the definite integral from a to b is the curve at b minus the curve at a.

Ports

• c – the coefficients, descending powers, as a vector of L entries: a column [L,1] or a row [1,L]. A scalar is a constant polynomial, whose integral is a straight line.
• ic – the antiderivative's coefficients, descending, with L+1 entries and the same orientation as the input.

Parameters

• Integration Constant – K, a single number, written straight into the output's last entry. It is the value the antiderivative takes at x = 0, and it is a parameter rather than a port because it says where the area is measured FROM – a property of the question, not of the signal. Default 0, which is polyint(c)'s own default.
• 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.

Integration Constant is structural and is inlined at export time rather than exposed as a tunable parameter, alongside the divisors. Both follow from settings that also decide the shape of the emitted body, so re-export after changing them.

The three HDL targets are genuine synthesizable Q16.16: the divisors are constants decided by the input's length, so each one is inlined as its reciprocal and multiplied. There is no divider in any generated core.

Simulink bridge

None (Support::None). polyint is a MATLAB function, and the Curve Fitting Toolbox ships no Simulink library at all, so there is no library 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

• Algebraic, with no state: the output depends only on the current input.
• This is not an integrator, and K is not an initial condition. Nothing accumulates: the output at every sample is the antiderivative of the coefficients arriving at that sample, with no memory of the last one. For a running integral of a signal reach for Integrator or Discrete-Time Integrator.
• The units are the fitting axis's. Polynomial Fit writes its curve on x = −i·h, so an area under this curve is in signal units times that h: per sample at h = 1, per second when h is the sampling period.
• Verified against MATLAB. For the coefficients [0.18018728956228861 0.97582972582972149 0.99028980278979795 −0.12171717171717268] this block reproduces polyint(c, 0) entry for entry in R2026a.
• No state space: the map changes the signal's HEIGHT, which a merged feed-through D cannot do, and it is affine rather than linear whenever K is nonzero. Model reduction correctly declines to merge it.