# Ehlers Super Smoother Filter

`D07-F01-A23` · Technical Indicators → Trend Smoothing · archetype `series-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/technical-indicators/trend-smoothing/ehlers-super-smoother-filter/
Agent skill: `npx skills add IslamBaraka90/Fintech-Algorithms-Library` — https://docs.thefintechbuilder.com/guides/agent-skill/

## Install and import

```bash
npm install fintech-algorithms
```

```ts
import { ehlersSuperSmootherFilter } from "fintech-algorithms/technical-indicators/trend-smoothing/ehlers-super-smoother-filter";
```

## Signature

```ts
ehlersSuperSmootherFilter(input)
```

Applies Ehlers' two-pole Butterworth recursion to the two-bar mean of close, with feedback coefficients derived from `period` via `exp(-sqrt(2) * pi / period)`, suppressing high-frequency noise with far less lag than a moving average of the same length.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `TopicInput` | yes | `bars` is a non-empty array of OHLCV records with strictly increasing `timestamp`, finite `open`, `high`, `low`, `close` and non-negative `volume`, all sharing one adjustment basis. From `parameters` this topic reads only `period`, an integer of at least 2, default 14, which sets the filter's cutoff. |

## Returns

`TopicResult`

`series` and `latest` carry a single key, `value`. There is no warm-up: the first two bars pass their close through unchanged before the recursion takes over, so `ready_at` is 0 and no entry is ever null.

## Warm-up

The first `0 bars` positions are `not applicable`. The recursion needs two prior outputs, and the implementation supplies them by seeding indices 0 and 1 with the raw close rather than emitting nulls. `ready_at` is therefore 0, but the first few values are effectively unfiltered and should be treated as transient.

## Errors

- When `parameters.period` is not an integer of at least 2 — throws Error
- When `bars` is empty or a bar violates the OHLCV contract — throws Error

## Complexity

Time `O(n)`, space `O(n)`.

## Worked example

Captured by running this function on the input its own test provides. Real output of real code — but not asserted against a published figure.

### Input

`input`:

```json
{
  "bars": [
    {
      "timestamp": "2024-01-02",
      "basis": "synthetic-unadjusted",
      "open": 100,
      "high": 101.45,
      "low": 98.695,
      "close": 100,
      "volume": 750000,
      "benchmark": 200
    },
    {
      "timestamp": "2024-01-03",
      "basis": "synthetic-unadjusted",
      "open": 101.49111452,
      "high": 103.38381693,
      "low": 100.05480022,
      "close": 101.78791214,
      "volume": 795117,
      "benchmark": 200.56326135
    },
    {
      "timestamp": "2024-01-04",
      "basis": "synthetic-unadjusted",
      "open": 102.45519048,
      "high": 104.6701838,
      "low": 100.91147007,
      "close": 102.9549389,
      "volume": 840234,
      "benchmark": 201.11020913
    }
  ],
  "parameters": {}
}
```

### Call

```ts
ehlersSuperSmootherFilter(input)
```

### Returns

object with 9 fields: topic_id, title, state, ready, ready_at, series, latest, parameters, …

```json
{
  "topic_id": "D07-F01-A23",
  "title": "Ehlers Super Smoother Filter",
  "state": "calculated",
  "ready": true,
  "ready_at": 0,
  "series": {
    "value": [
      100,
      101.78791214,
      102.82125123553132,
      103.40896247631203,
      103.66519218875615,
      103.63747331288454
    ]
  },
  "latest": {
    "value": 103.12560464143179
  },
  "parameters": {},
  "diagnostics": {
    "causal": true,
    "input_count": 96
  }
}
```

## Verification and provenance

Tier: **verified** (via E).

The worked example below is the figure published in this algorithm's article, replayed and asserted by the test suite on every build. The arithmetic cannot drift without the build failing.

Both tiers guarantee the signature. Full explanation: https://docs.thefintechbuilder.com/guides/verification/

Generated from the docs.json payload shipped inside fintech-algorithms@0.13.0.
The signature and parameter list are checked against the compiled implementation at build time,
so a description that contradicts the code fails the build rather than reaching this file.

## Links

- Article (how it works, step by step): https://thefintechbuilder.com/technical-indicators/trend-smoothing/ehlers-super-smoother-filter/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/trend-smoothing/ehlers-super-smoother-filter/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt