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Simu: 8 moved functions into lib

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Eric Teunis de Boone 2022-08-04 17:22:54 +02:00
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simulations/08_beacon_sync.ipynb
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@ -18,7 +18,13 @@
"import numpy as np\n", "import numpy as np\n",
"import matplotlib.pyplot as plt\n", "import matplotlib.pyplot as plt\n",
"import scipy.signal as signal\n", "import scipy.signal as signal\n",
"import scipy.fft as ft" "\n",
"import os\n",
"import sys\n",
"# Append parent directory to import path so lib can be found\n",
"sys.path.append(os.path.dirname(os.path.abspath(os.getcwd())))\n",
"from lib.util import *\n",
"from lib.plotting import *\n"
] ]
}, },
{ {
@ -120,89 +126,6 @@
"cell_type": "code", "cell_type": "code",
"execution_count": 3, "execution_count": 3,
"metadata": {}, "metadata": {},
"outputs": [],
"source": [
"### signal generation\n",
"def fft_bandpass(signal, band, samplerate):\n",
" \"\"\"\n",
" Simple bandpassing function employing a FFT.\n",
"\n",
" Parameters\n",
" ----------\n",
" signal : arraylike\n",
" band : tuple(low, high)\n",
" Frequencies for bandpassing\n",
" samplerate : float\n",
" \"\"\"\n",
" signal = np.asarray(signal)\n",
"\n",
" fft = ft.rfft(signal)\n",
" freqs = ft.rfftfreq(signal.size, 1/samplerate)\n",
" fft[(freqs < band[0]) | (freqs > band[1])] = 0\n",
" \n",
" return ft.irfft(fft, signal.size), (fft, freqs)\n",
"\n",
"def deltapeak(timelength=1e3, samplerate=1, offset=None, peaklength=1):\n",
" N_samples = int(timelength * samplerate)\n",
" if offset is None:\n",
" offset = (np.random.random(1)*N_samples).astype(int) % N_samples\n",
" elif isinstance(offset, (tuple, list)):\n",
" offset_min = offset[0]\n",
" offset_max = offset[-1]\n",
" \n",
" offset = (np.random.random(1)*(offset_max - offset_min)+offset_min).astype(int) % N_samples\n",
" \n",
" position = (offset + np.arange(0, peaklength)).astype(int) % N_samples\n",
" \n",
" signal = np.zeros(N_samples)\n",
" signal[position] = 1\n",
" \n",
" return signal, position\n",
"\n",
"def sin_delay(f, t, t_delay=0, phase=0):\n",
" return np.sin(2*np.pi*f * (t + t_delay) + phase)\n",
"\n",
"def annotate_width(ax, name, x1, x2, y, text_kw={}, arrow_kw={}):\n",
" default_arrow_kw = dict(\n",
" xy = (x1, y),\n",
" xytext = (x2,y),\n",
" arrowprops = dict(\n",
" arrowstyle=\"<->\",\n",
" shrinkA=False,\n",
" shrinkB=False\n",
" ),\n",
" )\n",
"\n",
" default_text_kw = dict(\n",
" va='bottom',\n",
" ha='center',\n",
" xy=((x1+x2)/2, y)\n",
" )\n",
"\n",
" an1 = ax.annotate(\"\", **{**default_arrow_kw, **arrow_kw})\n",
" an2 = ax.annotate(name, **{**default_text_kw, **text_kw})\n",
"\n",
" return [an1, an2]\n",
"\n",
"def time2phase(time, frequency=1):\n",
" return 2*np.pi*frequency*time\n",
"\n",
"def phase2time(phase, frequency=1):\n",
" return phase/(2*np.pi*frequency)\n",
"\n",
"def time_roll(a, samplerate, time_shift, *roll_args, **roll_kwargs):\n",
" \"\"\"\n",
" Like np.roll, but use samplerate and time_shift to approximate\n",
" the offset to roll.\n",
" \"\"\"\n",
" shift = np.rint(time_shift*samplerate).astype(int)\n",
" return np.roll(a, shift, *roll_args, **roll_kwargs)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [ "outputs": [
{ {
"name": "stdout", "name": "stdout",
@ -278,12 +201,13 @@
"print(\"Beacon difference [ns]:\", phase2time(beacon_phase_offset, f_beacon)/ns)\n", "print(\"Beacon difference [ns]:\", phase2time(beacon_phase_offset, f_beacon)/ns)\n",
"print(\"Beacon difference [phase]:\", beacon_phase_offset)\n", "print(\"Beacon difference [phase]:\", beacon_phase_offset)\n",
"print(\"Impulse offsets [ns]:\", impulses_offsets[:,0]/ns)\n", "print(\"Impulse offsets [ns]:\", impulses_offsets[:,0]/ns)\n",
"print(\"Time difference Impulses [ns]: {}\".format( (impulses_offsets[1,0]-impulses_offsets[0,0])/ns ))" "print(\"Time difference Impulses [ns]: {}\".format( (impulses_offsets[1,0]-impulses_offsets[0,0])/ns ))\n",
"print(\"Time difference Impulses [T]: {}\".format( (impulses_offsets[1,0]-impulses_offsets[0,0])*f_beacon ))"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 5, "execution_count": 4,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -443,18 +367,18 @@
"\\quad = \\Delta A + (kT) + t_\\phi\n", "\\quad = \\Delta A + (kT) + t_\\phi\n",
"$\n", "$\n",
"\n", "\n",
", where $\\Delta A < T$ and $k \\in \\mathbb{Z}$ and $t_\\phi$ is minimisable.\n", ", where $\\Delta A < T$ and $k \\in \\mathbb{Z}$ and $t_\\phi$ is minimisable by synchronising the beacons.\n",
"\n", "\n",
"Then $\\Delta t$ can be determined by iteratively summing the signals, changing $k$, and finding the $k$ belonging to the maximum of the sums." "Then $\\Delta t$ can be determined by iteratively summing the signals, changing $k$, and finding the $k$ belonging to the maximum of the sums."
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 8, "execution_count": 7,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"def find_best_integer_periods_sum(samplerate, f_beacon, ref_impulse, impulse, k_step=1):\n", "def find_beacon_integer_period_sum(samplerate, f_beacon, ref_impulse, impulse, k_step=1):\n",
" max_k = int( len(ref_impulse)*f_beacon/samplerate )\n", " max_k = int( len(ref_impulse)*f_beacon/samplerate )\n",
" ks = np.arange(-max_k/2, max_k/2, step=k_step)\n", " ks = np.arange(-max_k/2, max_k/2, step=k_step)\n",
" \n", " \n",
@ -470,12 +394,15 @@
" if maxima[i] > maxima[best_i]:\n", " if maxima[i] > maxima[best_i]:\n",
" best_i = i\n", " best_i = i\n",
" \n", " \n",
" return ks[best_i], (ks, maxima)" " return ks[best_i], (ks, maxima)\n",
"\n",
"def find_beacon_integer_period(samplerate, f_beacon, ref_impulse, impulse, k_step=1):\n",
" return find_beacon_integer_period_sum(samplerate, f_beacon, ref_impulse, impulse, k_step=k_step)"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 9, "execution_count": 8,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
@ -510,9 +437,9 @@
" my_impulse = time_roll(my_impulse, samplerate, -t_phi)\n", " my_impulse = time_roll(my_impulse, samplerate, -t_phi)\n",
"\n", "\n",
" # $\\Delta A$ offset\n", " # $\\Delta A$ offset\n",
" my_impulse = time_roll(my_impulse, samplerate, Delta_A)\n", " my_impulse = time_roll(my_impulse, samplerate, +Delta_A)\n",
"\n", "\n",
"best_k, (ks, maxima) = find_best_integer_periods_sum(samplerate, f_beacon, ref_impulse, my_impulse)\n", "best_k, (ks, maxima) = find_beacon_integer_period(samplerate, f_beacon, ref_impulse, my_impulse)\n",
"print(\"Best k: {:0g}\".format(best_k))\n", "print(\"Best k: {:0g}\".format(best_k))\n",
"print(\"Maximum: {}\".format(maxima[np.where(ks == best_k)][0]))\n", "print(\"Maximum: {}\".format(maxima[np.where(ks == best_k)][0]))\n",
"\n", "\n",
@ -532,7 +459,7 @@
" axes[i].plot(time/ns, my_impulse, label='impulse')\n", " axes[i].plot(time/ns, my_impulse, label='impulse')\n",
" axes[i].legend()\n", " axes[i].legend()\n",
"\n", "\n",
"axes[-1].set_ylabel(\"Sum\")\n", "axes[-1].set_ylabel(\"Coherence Sum\")\n",
"\n", "\n",
"best_maximum = np.max(maxima)\n", "best_maximum = np.max(maxima)\n",
"axes[-1].axhline(best_maximum, alpha=0.7)\n", "axes[-1].axhline(best_maximum, alpha=0.7)\n",
@ -544,7 +471,7 @@
" summed_impulse = ref_impulse + augmented_impulses\n", " summed_impulse = ref_impulse + augmented_impulses\n",
" if True or k%2 == 1:\n", " if True or k%2 == 1:\n",
" axes[-1].plot(time/ns, summed_impulse, label='k={:.0f}'.format(k),\n", " axes[-1].plot(time/ns, summed_impulse, label='k={:.0f}'.format(k),\n",
" alpha=0.1 + 0.9*1/(1+4*abs(best_maximum-maxima[i]))\n", " alpha=0.1 + 0.9*1/(1+2*abs(best_maximum-maxima[i]))\n",
" )\n", " )\n",
" \n", " \n",
"axes[-1].legend()\n", "axes[-1].legend()\n",
@ -558,12 +485,16 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## 1. Solve it" "## 1. Solve it\n",
"\n",
" 1. Find $t_\\phi$\n",
" 2. Find $A_1$, $A_2$\n",
" 3. Find $B_1$, $B_2$"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 10, "execution_count": 9,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
@ -596,7 +527,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 11, "execution_count": 10,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -661,12 +592,12 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"##### 1.1 Beacon Phase Delays" "##### 1.1 Beacon Phase Delay ($t_\\phi$)"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 12, "execution_count": 11,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
@ -679,7 +610,7 @@
], ],
"source": [ "source": [
"beacon_phase_delays = np.array([\n", "beacon_phase_delays = np.array([\n",
" find_beacon_phase_delay(beacon_samplerate, f_beacon, beacons[0], beacon)\n", " find_beacon_phase_delay(beacon_samplerate, f_beacon, ref_beacon, beacon)\n",
" for beacon in beacons\n", " for beacon in beacons\n",
"])\n", "])\n",
"\n", "\n",
@ -690,7 +621,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 13, "execution_count": 12,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
@ -751,7 +682,7 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"##### 1.2 Impulse vs beacon delays\n", "##### 1.2 Impulse vs beacon delays ($A_1, A_2$)\n",
"\n", "\n",
"Find the delay within a single beacon period" "Find the delay within a single beacon period"
] ]