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THE FEUTEX TOOLKIT

Exponential Smoother Time Response

Calculate exact decay coefficient and residual error after a step.

Signal Processing workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
Formulaα=1−exp(−1/(fsτ)); residual=exp(−t/τ)
Sources and model references

Worked example

Inputs

Desired time constant
0.1 s
Sample rate
1000 Hz
Elapsed duration
0.3 s

Expected results

New-sample weight
0.009950166251 fraction
Step residual fraction
0.04978706837 fraction

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter the labeled inputs in the indicated units.
  2. Calculate and compare every output against the stated model assumptions.

Try this example

{
  "tau": 0.1,
  "fs": 1000,
  "t": 0.3
}

Accuracy and scope

Matched-pole single-pole recursion; duration output uses continuous equivalent. Simplified analytical model; not a design recommendation or safety certification.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.