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Lemonergy · Studio block

Discrete pole-zero model

Builds a causal discrete filter from real-coefficient poles, zeros and gain.

Implementation ID
native-discrete-zero-pole
Reviewed
2026-10-27

Behavior

H(z) = gain × ∏(z − zeroᵢ) / ∏(z − poleⱼ). The worked example connects this operation to signals in Lemonergy Studio.

Interface

Discrete pole-zero model interfaceInputs or arguments on the left, observed outputs on the right. Conserving terminals appear below the component. The tables give units and behavior.Discrete pole-zero modelStudio blockin0out0
Original Lemonergy interface view. Lines identify ports; they are not a completed simulation circuit.
Ports and observed outputs
NameDirectionUnitMeaning
in0input1Input; real scalar.
out0output1Output; real scalar.

Parameters

Defaults are initial model values. Select values for your own model and operating conditions.

Configuration fields
ParameterUnitDefaultMeaning and limits
Sample period
sampleTimeS		s0.1Exact sample grid period. Elapsed-time integration begins after initialization.
Minimum 1e-06
Gain
params[0]		11Configured finite numerical parameter.
Zeros
tables[0]		1[]Complex roots as real, imaginary pairs. Conjugate pairs required.
Poles
tables[1]		1[0.5, 0]Real, imaginary pairs.
Initial histories
tables[2]		1[]Leave empty; initial histories are zero.

Equations and rules

  • H(z) = gain × ∏(z − zeroᵢ) / ∏(z − poleⱼ)

Worked example

Discrete pole-zero model — worked example

Input = 1. Output at 0 s = 0.

Open Studio example after release →
Numerical checks for the bundled synthetic example
OutputTime (s)Expected valueUnitAbsolute tolerance
Output
out0		0011e-08

Explore the recorded outputs

Discrete pole-zero model recorded example

Discrete pole-zero model
Discrete pole-zero model against timeRecorded synthetic simulation values. Time in seconds; output in —.-0.159843800.41958980.250.99902340.51.5784570.752.1578911—Time (s)
Discrete pole-zero model: 0 — at 0 s

11 actual recorded samples. Lines are visual guides between samples. Synthetic example, not measured cell data.

Download the recorded samples (JSON) · Open this Studio example after release

Use in a workflow

Discrete pole-zero model — worked example

Builds a causal discrete filter from real-coefficient poles, zeros and gain.

  1. Discrete pole-zero model: H(z) = gain × ∏(z − zeroᵢ) / ∏(z − poleⱼ). The worked example connects this operation to signals in Lemonergy Studio.
    • Use the block reference for settings and connections.
    • Implementation tested locally; public release pending.
Open Studio example after release

Connected concepts

Limits and interpretation

  • Proper real-coefficient transfer in z, conjugate-compatible roots, zero input/output histories.
  • Shapes and element types are explicit. Values must be finite; automatic reshaping and unit conversion are not performed.

Scientific and mathematical references

These sources explain the scientific and mathematical background. The behavior, interface and limits above define the Lemonergy implementation; a citation does not imply every model option in the source is implemented.

  1. Introduction to Digital Filters with Audio Applications — Difference Equation

    Julius O. Smith III · Author text, Stanford CCRMA; online edition hosted by DSPRelated · 2007

    Technical reference · Causal FIR/IIR difference equations and coefficient/history conventions.

Implementation sources

This reference follows the public interface and locally verified numerical checks for an upcoming release.

Contract: Lemonergy Studio public contract · Verification record: verification-2026-10-27

  • docs/glossary/native-block-verification.json

This implementation and its workflow uses (JSON) · Knowledge graph (JSON-LD)