diff --git a/01_fourier.ipynb b/01_fourier.ipynb index 0fa2e13..91a6edd 100644 --- a/01_fourier.ipynb +++ b/01_fourier.ipynb @@ -587,6 +587,59 @@ " axes.flat[1].set_xlim(0, 20);" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## FTs: gaussian with sine" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "f = 1e1 # Hz\n", + "if f > sample_rate/2:\n", + " print(\"Sampling a frequency above the sample_rate/2 gives problems\")\n", + "\n", + "def gaussian(x, mu=0, sigma=1 ):\n", + " return 1/(sigma*np.sqrt(2*np.pi)) * np.exp(- (x-mu)**2 / sigma**2 )\n", + "\n", + "def dgaussian(x, mu=0, sigma=1, dmu=1, dsigma=0):\n", + " return gaussian(x, mu, sigma) + gaussian(x, mu+dmu, sigma+dsigma)\n", + "\n", + "if not True:\n", + " signal = gaussian(t, t[2*len(t)//5], 100/len(t)) - gaussian(t, t[3*len(t)//5], 100/len(t))\n", + "else:\n", + " signal = gaussian(t, t[2*len(t)//5], 100/len(t)) * np.sin(2*np.pi*f*t)\n", + "\n", + "fig, axes = plot_signal_and_spectrum(signal, sample_rate, \"Gaussian pulse\", spectrum_kwargs={'plot_complex':True, 'plot_amplitude':True})\n", + "axes.flat[1].axvline(sample_rate/2, color='r', label='Nyquist Frequency')\n", + "axes.flat[2].axvline(sample_rate/2, color='r')\n", + "axes.flat[1].legend();\n", + "\n", + "if not True:\n", + " axes.flat[1].set_xlim(0, 20);\n", + "else:\n", + " axes.flat[1].set_xlim(max(0, f - max(f/5, 10)), f + max(f/5, 10));\n", + " " + ] + }, { "cell_type": "markdown", "metadata": {},