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| -rw-r--r-- | notebooks/FrameSynchronization.ipynb | 130 |
1 files changed, 130 insertions, 0 deletions
diff --git a/notebooks/FrameSynchronization.ipynb b/notebooks/FrameSynchronization.ipynb new file mode 100644 index 0000000..9a7719f --- /dev/null +++ b/notebooks/FrameSynchronization.ipynb @@ -0,0 +1,130 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "5d5acf43", + "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": "4b294887", + "metadata": {}, + "source": [ + "# Digital Frame Synchronization\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "5bec50ff", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Header sequence (N=16): [1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1]\n", + "Cross correlation: [ 3. 3. 4. 4. 4. 4. 3. 6. 7. 7. 3. 6. 6. 8. 7. 6. 7. 11.\n", + " 8. 7. 7. 10. 8. 8. 10. 8. 10. 7. 8. 8. 8. 10. 8. 11. 12. 9.\n", + " 8. 10. 8. 11. 9. 10. 9. 16. 10. 10. 10. 12. 10. 14. 9. 10. 9. 13.\n", + " 11. 9. 11. 8. 9. 11. 9. 9. 8. 8. 7. 9. 12. 5. 7. 9. 7. 10.\n", + " 12. 6. 6. 9. 8. 6. 8. 5. 5. 8. 7. 5. 5. 4. 3. 4. 3. 3.\n", + " 3. 3.]\n", + "Corrlation peak value: 16.0\n" + ] + }, + { + "data": { + "text/plain": [ + "<StemContainer object of 3 artists>" + ] + }, + "execution_count": 14, + "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.array([(0xbeef >> i) & 0x1 for i in range(4 * 4)])\n", + "# seq = np.array([1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1])\n", + "\n", + "stream = np.concatenate([\n", + " np.random.randint(low=0, high=2, size=30), seq, np.random.randint(low=0, high=2, size=30)\n", + "])\n", + "\n", + "print(f\"Header sequence (N={len(seq)}): {seq}\")\n", + "# print(f\"Data stream: {stream}\")\n", + "\n", + "# compute cross correlation\n", + "def distance(v):\n", + " return len(seq) - sum(np.logical_xor(v, seq))\n", + "\n", + "fifo = RingBuffer(len(seq))\n", + "xcorr = RingBuffer(len(stream) + len(seq))\n", + "\n", + "## fill FIFO with zeros\n", + "fifo.extend(np.zeros(fifo.maxlen))\n", + "\n", + "for i in range(len(stream) + len(seq)):\n", + " #print(np.array(fifo))\n", + " xcorr.append(distance(np.array(fifo)))\n", + " \n", + " # if the stream is finished use zeros\n", + " fifo.pop()\n", + " if i < len(stream):\n", + " fifo.appendleft(stream[i])\n", + " else:\n", + " fifo.appendleft(0)\n", + "\n", + "print(f\"Cross correlation: {np.array(xcorr)}\")\n", + "print(f\"Correlation peak value: {max(np.array(xcorr))}\")\n", + "\n", + "plt.figure(figsize = (25, 5))\n", + "plt.stem(np.array(xcorr))" + ] + } + ], + "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 +} |