Zero Phase Filter — Control Systems/Signal Smoothing

Zero Phase Filter

Control Systems / Signal Smoothing

Filters the last W samples forwards and then backwards, so the filter's phase response cancels itself and nothing in the output is shifted in time:

y = filtfilt(b, a, u), read at the centre of the window

This is MATLAB's filtfilt. A zero-phase filter is acausal – it needs samples from both sides of the one it answers – so a streaming block has to buy that with delay: the output lags the input by (W−1)/2 samples, and in exchange nothing is phase distorted.

Ports

• u – the signal to filter. Scalar: one channel and its own window – see Notes.
• y – the zero-phase filtered value at the centre of that window. Scalar.

Parameters

• Window Length – W, how many samples the filter sees. An odd whole number from 5 to 101 – odd because the answer is the centre sample and an even window has none. It must also be more than 3·(n−1), where n is the longer of the two coefficient vectors, which is the record length filtfilt itself demands. Bounded above because the dot product is unrolled at export.
• Numerator – b, the filter's numerator coefficients, a vector of up to 12 entries in the usual descending order (b₀ first).
• Denominator – a, the denominator, likewise. Its first entry must be non-zero; everything is normalised by it, exactly as MATLAB does. Use [1] for an FIR filter.
• 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.

No filter runs in any exported core, in either direction. filtfilt is linear in the window – the passes, the reversal, the end extension and the initial conditions are all linear maps – so the centre sample is a fixed linear functional of the W samples, and the block solves for that functional once when the configuration loads. What a core carries is W numbers and one multiply-accumulate over a shift register. The bank is structural: it follows from the window length and both coefficient vectors together, so re-export after changing any of 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.

Simulink bridge

None (Support::None). filtfilt is a Signal Processing Toolbox function and that toolbox ships no Simulink library, 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.

Notes

• Stateful, and discrete by nature (setDiscreteOnlyBlock(true)): the window advances once per sample.
• ⚠ The filter you get is the SQUARE of the filter you designed. The data passes through H twice, so the magnitude response is |H|²: a design with a −3 dB corner has a −6 dB corner here, and its transition band is twice as steep. That is filtfilt's behaviour rather than this block's, and it is the thing most often got wrong – design for half the attenuation you want.
• ⚠ It lags, and it must. A zero-phase filter needs samples on both sides of the one it answers, so the centre of the window is the newest sample it can answer for: the output is (W−1)/2 samples behind the input. Savitzky-Golay Filter makes the same trade for the same reason. If the delay is what matters and the phase is not, an ordinary Discrete Filter is the block to reach for.
• ⚠ The bank is not exactly symmetric, and symmetrising it would be wrong. filtfilt extends the record by 3·(n−1) samples of odd reflection at each end and seeds each pass with steady-state initial conditions, and those two are not mirror images of one another over a finite window. Measured at W = 15 with b = [0.2 0.3 0.2], a = [1 −0.4 0.15], the taps either side of the centre are 0.22051553798359172 and 0.22051735331508093 – equal to six digits and no further.
• Verified against MATLAB. At those settings the bank reproduces R2026a's own filtfilt centre row to 5.6e−17, one unit in the last place, and applied to a fifteen-sample window it answers 0.4657953074281756 against MATLAB's 0.46579530742817565.
• ⚠ Not every (b, a) is a filter this block can build a bank for. A denominator whose steady-state system is singular has no initial conditions to seed with; that is detected when the configuration loads and reported with a reason, rather than emitting the arbitrary answer a pseudo-inverse would produce.
• The window is zero-prefilled, so the first W−1 outputs of a run are a startup transient – the convention Detrend, Savitzky-Golay Filter and Polynomial Fit all follow.
• Scalar only. One channel and its own history; wire one block per channel.
• No state space. Linear in the input, but through a fixed filter bank over W past samples rather than an A/B/C/D pair, so model reduction correctly declines to merge it.