Source: https://guthlabs.ai/docs/instruments/filter-designer-higher-order-butterworth-chebyshev-response-plotter/implementation/

instrument implementation / implementation-contract

# Filter Designer — Higher-Order (Butterworth/Chebyshev) Response Plotter implementation

A source-bound implementation contract for Filter Designer — Higher-Order (Butterworth/Chebyshev) Response Plotter; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t8-006

**Effect**: Computation or source lookup only

## Input and validation requirements

A Chebyshev Type I input with zero dB ripple makes ε=0 and the direct pole formula evaluate as asinh(1/0), which is undefined. The instrument must reject the input or explicitly handle the Butterworth limiting case.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "order": 2,
    "filter_type": "Butterworth",
    "topology": "LP",
    "fc_hz": 1000,
    "ripple_db": 0
  },
  "expected_outputs": {
    "canonical_transfer_function": "H(s)=(ωc^2)/(s^2+√2·ωc·s+ωc^2), ωc=2000π rad/s",
    "canonical_poles": [
      "p0=ωc·e^(j3π/4)=−ωc/√2+jωc/√2",
      "p1=ωc·e^(j5π/4)=−ωc/√2−jωc/√2"
    ],
    "magnitude_formula": "|H(j2πf)|=1/sqrt(1+(f/fc)^4)",
    "spot_checks": [
      {
        "at": {
          "f_hz": 0
        },
        "input_side": 1,
        "answer_side": 1
      },
      {
        "at": {
          "f_hz": 1000
        },
        "input_side": 0.7071067811865475,
        "answer_side": 0.7071067811865475
      }
    ]
  },
  "reference_data": {
    "standard_method": "2nd-order Butterworth low-pass prototype",
    "normalization": "H(0)=1"
  },
  "working": "ωc=2πfc=2π(1000)=2000π rad/s. For k=0, angle=π(2·0+2+1)/(2·2)=3π/4, so p0=ωc(cos 3π/4+j sin 3π/4)=−ωc/√2+jωc/√2. For k=1, angle=5π/4, so p1=−ωc/√2−jωc/√2. At f=0: |H|=1/sqrt(1+(0/1000)^4)=1. At f=fc: |H|=1/sqrt(1+1^4)=1/√2=0.7071067811865475."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/filter-designer-higher-order-butterworth-chebyshev-response-plotter/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/filter-designer-higher-order-butterworth-chebyshev-response-plotter/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/filter-designer-higher-order-butterworth-chebyshev-response-plotter/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche8/tranche8-results.json`