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|
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "57a55a8c",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from numpy_ringbuffer import RingBuffer\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib.image as mpimg"
]
},
{
"cell_type": "markdown",
"id": "dc4b9dfd",
"metadata": {},
"source": [
"# Digital Frame Synchronization\n"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "025c6919",
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Header (N=16): [1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1]\n",
"Stream (N=80): [0 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 1\n",
" 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0\n",
" 0 1 1 1 0 1]\n",
"Correlation peak value: 16 at i=47\n"
]
},
{
"data": {
"text/plain": [
"<StemContainer object of 3 artists>"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1800x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Create test data\n",
"seq = np.unpackbits(np.array([0xbe, 0xef], dtype=np.dtype(\"uint8\")))\n",
"stream = np.concatenate([\n",
" np.random.randint(low=0, high=2, size=32), seq, np.random.randint(low=0, high=2, size=32)\n",
"])\n",
"\n",
"print(f\"Header (N={len(seq)}): {seq}\")\n",
"print(f\"Stream (N={len(stream)}): {stream}\")\n",
"\n",
"# Create buffers for cross correlation\n",
"fifo = RingBuffer(len(seq), dtype=np.dtype(\"uint8\"))\n",
"xcorr = RingBuffer(len(stream) + len(seq), dtype=np.dtype(\"uint8\"))\n",
"\n",
"## fill FIFO with zeros\n",
"fifo.extend(np.zeros(fifo.maxlen))\n",
"\n",
"def correlation(v):\n",
" n = len(seq)\n",
" d = np.logical_xor(v, seq) # or bitwise_xor, no difference in this case\n",
" return n - sum(d)\n",
" \n",
"for i in range(len(stream) + len(seq) + 1):\n",
" xcorr.append(correlation(np.array(fifo)))\n",
" \n",
" # append stream data\n",
" # if the stream is finished use zeros\n",
" fifo.append(stream[i] if i < len(stream) else 0)\n",
"\n",
"# unwrap values\n",
"xc = np.array(xcorr)\n",
"# print(f\"Cross correlation: {xc}\")\n",
"print(f\"Correlation peak value: {np.amax(xc)} at i={np.argmax(xc)}\")\n",
"\n",
"plt.figure(figsize = (25, 5))\n",
"plt.stem(xc)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.9.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
|
