53 lines
1.6 KiB
Plaintext
53 lines
1.6 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Time-Frequency Analysis\n",
|
|
"## Moving window analysis\n",
|
|
"One way to analyse the time-varying frequency content of a signal is to\n",
|
|
"apply windows in the time domain to the signal and to calculate a Fourier spectrum\n",
|
|
"of the windowed part. The window marches along the signal with defined overlap creating\n",
|
|
"a series of Fourier spectra associated with the center times of the windows. The resulting amplitude\n",
|
|
"spectra are then plotted versus window center time. In more detail:\n",
|
|
"\n",
|
|
"1. Choose windowing functions: $w(t,t_m)$ with $t_m$ the center of the window.\n",
|
|
"2. Multiply windowing function with time series: $f_m(t) = f(t)w(t,t_m)$\n",
|
|
"3. Detrend the windowed signal.\n",
|
|
"4. Perform a DFT: $F_{km} = \\Delta t\\sum_{n=0}^N f_m(t)\\exp(-2\\pi i \\frac{kn}{N})$\n",
|
|
" and calculate the absolute value, $|F_{km}|$.\n",
|
|
"5. Plot the resulting matrix: $|F_{km}|$ in the time-frequency plane."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.6.7"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|