{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Fourier transform and power spectra\n", "\n", "First we create a time-varying signal with well-defined frequency content:\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# properties of time series: length, sampling rate...\n", "t_max = 3\n", "dt_bin = 0.0025\n", "n_bins = np.ceil(t_max / dt_bin)\n", "t = dt_bin * np.arange(n_bins)\n", "\n", "# harmonic signal: frequency, offset, amplitude...\n", "f_sin = 42\n", "a_sin = 3.2\n", "a_ofs = 2.1\n", "signal = a_ofs + a_sin * np.sin(2 * np.pi * f_sin * t) # + 50 * np.random.random(int(n_bins))\n", "\n", "# ...just show the signal\n", "plt.figure(1)\n", "plt.plot(t, signal)\n", "plt.xlabel('time t')\n", "plt.ylabel('signal s(t)')\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "### Tasks\n", "\n", "1. Compute the power spectrum of the signal, and confirm that you have a peak at the frequency corresponding to the sine in the signal.\n", "\n", "2. Check if Parseval's theorem is satisfied.\n", "\n", "3. Implement a function which computes the power spectrum by averaging over the power spectra obtained from chunks of the data. Plot it in comparison to the non-averaged spectrum.\n", "\n", "4. Try to add some noise to the signal and watch what happens with the power spectra...\n" ] }, { "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": "3.11.6" } }, "nbformat": 4, "nbformat_minor": 2 }