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Fixup: always put a ylabel

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Eric Teunis de Boone 2021-11-30 15:35:09 +01:00
parent b01463ddce
commit 0d26b21a27
1 changed files with 8 additions and 5 deletions
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13
01_fourier.ipynb
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@ -59,7 +59,7 @@
" f_\\mathrm{max} = \\frac{1}{2} f_\\mathrm{sampling} = \\frac{1}{2} \\frac{1}{\\Delta t}\n", " f_\\mathrm{max} = \\frac{1}{2} f_\\mathrm{sampling} = \\frac{1}{2} \\frac{1}{\\Delta t}\n",
" .\n", " .\n",
"$$\n", "$$\n",
"Higher frequencies will fall in between two adjacent samples, causing them to go unnoticed in the data. Note that because of folding, such frequencies can actually appear as aliases.\n", "Higher frequencies will fall in between two adjacent samples. This means that these frequencies are then 'measured\\` with differing phases in such a way that they are 'folded' around the Nyquist frequency and appear as aliased frequencies below it.\n",
"\n", "\n",
"Likewise, the lowest frequency depends on the length of the signal $T$, such that over the whole signal one oscillation can be found\n", "Likewise, the lowest frequency depends on the length of the signal $T$, such that over the whole signal one oscillation can be found\n",
"$$\n", "$$\n",
@ -85,7 +85,7 @@
"def ft_spectrum( signal, sample_rate, fft=None, freq=None, mask_bias=False):\n", "def ft_spectrum( signal, sample_rate, fft=None, freq=None, mask_bias=False):\n",
" \"\"\"Return a FT of $signal$, with corresponding frequencies\"\"\"\n", " \"\"\"Return a FT of $signal$, with corresponding frequencies\"\"\"\n",
" n_samples = len(signal)\n", " n_samples = len(signal)\n",
" real_signal = np.all(np.isreal(signal))\n", " real_signal = np.isrealobj(signal)\n",
" \n", " \n",
" if fft is None:\n", " if fft is None:\n",
" if real_signal:\n", " if real_signal:\n",
@ -115,7 +115,7 @@
" ax.set_title(\"Spectrum\")\n", " ax.set_title(\"Spectrum\")\n",
" ax.set_xlabel(\"f (Hz)\")\n", " ax.set_xlabel(\"f (Hz)\")\n",
" ylabel = \"\"\n", " ylabel = \"\"\n",
" if plot_amplitude:\n", " if plot_amplitude or plot_complex:\n",
" ylabel = \"Amplitude\"\n", " ylabel = \"Amplitude\"\n",
" if plot_power:\n", " if plot_power:\n",
" if ylabel:\n", " if ylabel:\n",
@ -127,7 +127,6 @@
" alpha = 0.5\n", " alpha = 0.5\n",
" ax.plot(freqs, np.real(spectrum), '.-', label='Real', alpha=alpha)\n", " ax.plot(freqs, np.real(spectrum), '.-', label='Real', alpha=alpha)\n",
" ax.plot(freqs, np.imag(spectrum), '.-', label='Imag', alpha=alpha)\n", " ax.plot(freqs, np.imag(spectrum), '.-', label='Imag', alpha=alpha)\n",
" ax.legend()\n",
"\n", "\n",
" if plot_power:\n", " if plot_power:\n",
" ax.plot(freqs, np.abs(spectrum)**2, '.-', label='Power', alpha=alpha)\n", " ax.plot(freqs, np.abs(spectrum)**2, '.-', label='Power', alpha=alpha)\n",
@ -135,6 +134,8 @@
" if plot_amplitude:\n", " if plot_amplitude:\n",
" ax.plot(freqs, np.abs(spectrum), '.-', label='Abs', alpha=alpha)\n", " ax.plot(freqs, np.abs(spectrum), '.-', label='Abs', alpha=alpha)\n",
"\n", "\n",
" ax.legend()\n",
"\n",
" return ax\n", " return ax\n",
"\n", "\n",
"\n", "\n",
@ -338,9 +339,11 @@
" print(\"Sampling a frequency above the sample_rate/2 gives problems\")\n", " print(\"Sampling a frequency above the sample_rate/2 gives problems\")\n",
"\n", "\n",
"signal_sine = np.sin( 2*np.pi*f*t )\n", "signal_sine = np.sin( 2*np.pi*f*t )\n",
"\n",
"if False:\n", "if False:\n",
" # aliased peak\n", " # aliased peak\n",
" signal_sine += 1/2*np.sin( 2*np.pi* (1.1* sample_rate/2) *t)\n", " f_alias = (1.1* sample_rate/2)\n",
" signal_sine += 1/2*np.sin( 2*np.pi* f_alias *t)\n",
"\n", "\n",
"fig, axes = plot_signal_and_spectrum(signal_sine, sample_rate, \"Single frequency at $f = {:g}$MHz\".format(f/10**6))\n", "fig, axes = plot_signal_and_spectrum(signal_sine, sample_rate, \"Single frequency at $f = {:g}$MHz\".format(f/10**6))\n",
"axes.flat[1].axvline(sample_rate/2, color='r', label='Nyquist Frequency');\n", "axes.flat[1].axvline(sample_rate/2, color='r', label='Nyquist Frequency');\n",