Discrete Filter — Control Systems/Discrete

Discrete Filter

Control Systems / Discrete

An IIR filter whose coefficients are given in ascending powers of 1/z:

H(z) = (b₀ + b₁z⁻¹ + … + b_Mz^−M) / (a₀ + a₁z⁻¹ + … + a_Nz^−N)

realized as the difference equation y[k] = ( ∑ b_i·u[k−i] − ∑_i≥1 a_i·y[k−i] ) / a₀.

This is the one thing that separates it from Discrete Transfer Function, which takes the same two vectors in descending powers of z. The pair numerator [1], denominator [1 -0.5] means y[k] = u[k] + 0.5·y[k−1] here, but y[k] = u[k−1] + 0.5·y[k−1] there – a whole sample of delay apart, from input that looks identical. Reach for this block when your coefficients came from a filter designer, and for the other when they came from a z-domain transfer function.

Ports

• Input – the signal to filter, of any size [p,m].
• Output – the filtered signal, of the same size.

The filter is SISO, but it is applied independently to every entry of the input signal, each entry carrying its own state.

Parameters

• Numerator – b₀…b_M, a vector in ascending powers of 1/z. A single value makes an all-pole filter.
• Denominator – a₀…a_N, likewise. a₀ must not be zero; it need not be one, and the whole filter is normalized by it. A single value makes the filter FIR, and Discrete FIR Filter is then the more direct block.
• Initial States – the filter's internal state at the start of the run. A scalar seeds every state; a vector of length n = max(M, N) seeds them individually, newest first.
• 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 coefficients are normalized by a₀ and baked into the generated recursion rather than exposed as tunable parameters: they also fix how many state words the core carries, so retuning them on the target is not possible. Change them here and export again.

Simulink bridge

Import and export, mapped to simulink/Discrete/Discrete Filter. "Numerator" to Numerator, "Denominator" to Denominator, "Initial States" to InitialStates, and "Sampling Time (s)" to SampleTime, as on every block.

Three Simulink parameters are always implied rather than offered as a choice: FilterStructure = Direct form II, which is the structure this block realizes and therefore what makes the initial states mean the same thing on both sides, and NumeratorSource / DenominatorSource = Dialog, since the coefficients come from the config here and never from a port.

What does not cross: coefficients or initial states arriving on a port, and external reset, all add input ports in Simulink, and no config value here can add or remove a port. Choosing a different Simulink filter structure does not cross either – the alternatives define their states differently, so the initial states would no longer mean the same thing.

Notes

• Discrete only, and stateful: n = max(M, N) past values per entry.
• Being linear, the block is directly usable by the model reduction and linear-analysis commands.
• Stability is the user's to check: poles outside the unit circle make the output grow without bound, and the block does not stop the run for it.