# Hilbert Transform Trend/Cycle Mode

`D09-F06-A05` · Statistical Time Series → Hilbert and Ehlers Cycle Analytics · archetype `record-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/statistical-time-series/hilbert-and-ehlers-cycle-analytics/hilbert-transform-trend-cycle-mode/
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 { hilbertTransformTrendCycleMode } from "fintech-algorithms/statistical-time-series/hilbert-and-ehlers-cycle-analytics/hilbert-transform-trend-cycle-mode";
```

## Signature

```ts
hilbertTransformTrendCycleMode(input)
```

Labels each bar `trend` or `cycle` by asking whether the distance from `close` to its exponential trend exceeds 1.5 times the current Hilbert phasor amplitude. Any contract failure is rethrown as an `Error` whose message begins `topic calculation failed: `.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `TopicInput` | yes | `bars` is a non-empty array of rows with `timestamp`, `open`, `high`, `low`, `close` and `volume`, strictly ordered by timestamp. This topic genuinely uses `parameters.period`, which defaults to 20 and must be an integer of at least 4; it is the span of the `close` EMA that supplies the `trend` series. |

## Returns

`TopicResult`

Three series, each mirrored in `latest`: `mode` is the text `trend` or `cycle`, `trend` is the EMA of `close` over `period`, and `amplitude` is the Hilbert phasor magnitude. `parameters` echoes the supplied parameters and `diagnostics` reports `causal` and `input_count`. The series have different warm-ups and `ready_at` follows the earliest of them, 6.

## Warm-up

The first `6 nulls for `amplitude`, and `period - 1` nulls for `trend` and `mode` (19 at the default period of 20)` positions are `null`. `amplitude` needs the 4-bar EMA of `close` plus three bars of the quadrature filter, so it starts at index 6 and sets `ready_at` to 6. `trend` is an EMA seeded from the first full window of `period` closes, so it starts at index `period - 1`, and `mode` needs both, so it starts with `trend`.

## Errors

- When `parameters.period` is present but is not an integer of at least 4 — throws Error
- When `bars` is empty, a `timestamp` is missing or not strictly increasing, an OHLCV field is not finite, `volume` is negative, or `high` and `low` do not bracket `open` and `close` — 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
hilbertTransformTrendCycleMode(input)
```

### Returns

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

```json
{
  "topic_id": "D09-F06-A05",
  "title": "Hilbert Transform Trend/Cycle Mode",
  "state": "calculated",
  "ready": true,
  "ready_at": 6,
  "series": {
    "mode": [null, null, null, null, null, null],
    "trend": [null, null, null, null, null, null],
    "amplitude": [null, null, null, null, null, null]
  },
  "latest": {
    "mode": "trend",
    "trend": 103.9546773984291,
    "amplitude": 0.8769323358697945
  },
  "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/statistical-time-series/hilbert-and-ehlers-cycle-analytics/hilbert-transform-trend-cycle-mode/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/statistical-time-series/hilbert-and-ehlers-cycle-analytics/hilbert-transform-trend-cycle-mode/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/statistical-time-series/llms.txt