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Lemonergy · Studio block

Discrete derivative

Estimates a rate of change from successive samples and their elapsed time.

Implementation ID
native-discrete-derivative
Reviewed
2026-10-27

Behavior

y[k] = (u[k] − u[k−1])/elapsed_time; startup output = 0. The worked example connects this operation to signals in Lemonergy Studio.

Interface

Discrete derivative interfaceInputs or arguments on the left, observed outputs on the right. Conserving terminals appear below the component. The tables give units and behavior.Discrete derivativeStudio blockin0out0
Original Lemonergy interface view. Lines identify ports; they are not a completed simulation circuit.
Ports and observed outputs
NameDirectionUnitMeaning
in0input1Value; real scalar.
out0output1Derivative; 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

Equations and rules

  • y[k] = (u[k] − u[k−1])/elapsed_time; startup output = 0

Worked example

Discrete derivative — worked example

Value = 2. Derivative at 0 s = 0.

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

Explore the recorded outputs

Discrete derivative recorded example

Discrete derivative
Discrete derivative against timeRecorded synthetic simulation values. Time in seconds; output in —.-0.50-0.250.2500.50.250.750.51—Time (s)
Discrete derivative: 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 derivative — worked example

Estimates a rate of change from successive samples and their elapsed time.

  1. Discrete derivative: y[k] = (u[k] − u[k−1])/elapsed_time; startup output = 0. 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

  • Backward difference at configured ticks; initialization output zero.
  • 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)