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" \n",
" 
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" "
],
"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
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"source": [
"F0=440# need to change backend to make interactive plot\n",
"%matplotlib widget\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# plot zoomed spectrogram\n",
"fig, ax = plt.subplots(figsize=(8, 4))\n",
"spectgram, freqs, bins, image = ax.specgram(y, NFFT=int(FS/2), Fs=FS, mode='magnitude')\n",
"ax.set_ylim(bottom = 2800, top = 3100)\n",
"ax.set_xlim(left = 2, right = 5)\n",
"ax.set_xlabel('time(seconds)')\n",
"ax.set_ylabel('frequency(Hz)')\n",
"ax.set_title('Doppler spectrogram')\n",
"plt.colorbar(image, ax = ax);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Right click to the left of the plot above and then click on \"Create new view for output\". Then the location of your cursor on the plot appears just below the plot in the new window. Check the time and frequencies before and after the passage of the car, for example the one at 3000 Hz: "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# two sample points\n",
"speclocs = [(3.009, 3052),\n",
" (4.506, 2825)]\n",
"\n",
"# calculate mean frequency and frequency difference from mean\n",
"specmean = np.mean(speclocs, axis=0)[-1]\n",
"specdiff = np.diff(speclocs, axis=0)[0][-1]/2\n",
"\n",
"# print values to read\n",
"print('Mean frequency = ' + '{:.0f}'.format(specmean) + ' Hz')\n",
"print('Frequency difference from mean = ' + '{:.0f}'.format(np.absolute(specdiff)) + ' Hz')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That shows that the mean frequency (of that harmonic) was 2938 Hz, and the frequency shift was +-114 Hz. There is an approximate relationship between the Doppler shift Df of a moving sound or radio source of frequency f, and its velocity V, as long as V << C (much smaller): \n",
"\n",
" V = C * Df / f\n",
" \n",
"where C is the propagation speed of the wave (300000 km/s for light/radio, 340 m/s for sound in air, 1500 m/s for sound in water). We can thus infer:\n",
"\n",
" V = 13.2 m/s = 47.5 km/h = 29.5 mph.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The time at which the Doppler shift goes through 0 (about 3.8 s) is called the \"point of closest approach\".\n",
"\n",
"Estimating this point is the base for satellite navigation. A back-of-the-envelope approximate calculations suggested below will help understand the concept, left for students to resolve individually.\n",
"\n",
"A transmitter of 1.572 GHz is installed on a GPS satellite, orbiting at an altitude of about 20,200 km with an orbital period of about 12 hours. Estimate the maximum Doppler shift that will be observed by a ground observer. "
]
}
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