{
"cells": [
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"cell_type": "markdown",
"id": "79345bf6",
"metadata": {},
"source": [
"# Fourier Processor\n",
"\n",
"The `Fourier` processor performs a sliding-window FFT (Short-Time Fourier Transform) on a time series. It slides a window over the series, computes an FFT per window and aggregates the amplitude spectrum into frequency ranges. The result is a multivariate time series where each column is a frequency range."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "c43db203",
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"execution": {
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"outputs": [],
"source": [
"# Import to be able to import python package from src\n",
"import sys\n",
"sys.path.insert(0, '../../src')"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "0a6f35b1",
"metadata": {
"execution": {
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"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import ontime as on"
]
},
{
"cell_type": "markdown",
"id": "b491e9fc",
"metadata": {},
"source": [
"---\n",
"## Generation of a signal with two frequencies\n",
"\n",
"We build a signal made of a slow sine wave (period of 48 samples) that is present all along, plus a fast sine wave (period of 6 samples) that only appears in the second half of the series."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "44319a61",
"metadata": {
"execution": {
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"shell.execute_reply": "2026-07-22T22:23:05.789629Z"
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"outputs": [],
"source": [
"n = 512\n",
"index = pd.date_range('2022-01-01', periods=n, freq='h')\n",
"t = np.arange(n)\n",
"\n",
"slow = np.sin(2 * np.pi * t / 48)\n",
"fast = np.sin(2 * np.pi * t / 6) * (t >= n // 2)\n",
"\n",
"ts = on.TimeSeries.from_times_and_values(index, slow + fast)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "5bdaee4f",
"metadata": {
"execution": {
"iopub.execute_input": "2026-07-22T22:23:05.791623Z",
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"outputs": [
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"text/html": [
"\n",
"\n",
"\n",
""
],
"text/plain": [
"alt.LayerChart(...)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ts.plot()"
]
},
{
"cell_type": "markdown",
"id": "ad26ba60",
"metadata": {},
"source": [
"---\n",
"## Apply the FFT on sliding windows\n",
"\n",
"The parameters are:\n",
"\n",
"- `window_size`: number of samples per FFT window\n",
"- `step_size`: number of samples the window slides by\n",
"- `n_bins`: number of frequency ranges in the output\n",
"- `frequency_cap`: optional `(min, max)` tuple to restrict the frequency range\n",
"\n",
"Frequencies are expressed in cycles per sample, from 0 to 0.5 (the Nyquist frequency). Here, the slow wave has a frequency of 1/48 ≈ 0.02 and the fast wave 1/6 ≈ 0.17 cycles per sample."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "66fe2beb",
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"execution": {
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