aboutsummaryrefslogtreecommitdiffstats
path: root/notebooks/FIR_mehrere_V2.ipynb
blob: 9fdea2ebb937f88af8e3f244ef9421cc3dc09636 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c377e559",
   "metadata": {},
   "source": [
    "# FIR Filter Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f14e4383",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "from numpy.fft import fft,ifft,fftshift\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e8e2130b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Anfangs werte noch variabel machen \n",
    "delays = [3,5,2]\n",
    "ampl = [0.2,0.5,0.8]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d39d7698",
   "metadata": {},
   "source": [
    "# Dealy Window\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bd005466",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "d =0\n",
    "k = np.linspace(-5,10,1000)\n",
    "h_ideal = np.sinc(k-d)\n",
    "plt.plot(k,h_ideal)\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e48a4dbd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 4.5\n",
    "window_sample= np.arange(np.round(d-(n-1)/2),np.round(d+(n+1)/2))\n",
    "window = []\n",
    "for ws in window_sample:  \n",
    "    idx = (np.abs(k-ws)).argmin()\n",
    "    window.append(idx)\n",
    "    \n",
    "plt.plot(k,h_ideal)\n",
    "plt.plot(window_sample,h_ideal[window],\"-*\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ddadf5d",
   "metadata": {},
   "source": [
    "# FIR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bd6d61b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "delay = 3\n",
    "amplitude = 1\n",
    "\n",
    "d_int = int(np.floor(delay))\n",
    "#d_frac = delay - d_int\n",
    "\n",
    "h_int = np.concatenate([np.zeros(d_int-1), [amplitude], np.zeros(3)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ef41b7d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "#H_int = fft(h_int)\n",
    "#h = ifft(H_int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fea2ae61",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<StemContainer object of 3 artists>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test = np.random.randint(0, 10, size = 20)# Signal\n",
    "\n",
    "y = np.convolve(test.real, h_int)#Faltung\n",
    "\n",
    "plt.stem(test, linefmt=\"C0-\")\n",
    "plt.stem(y, linefmt='C1-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a65b4b37",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 8, 8, 7, 0, 5, 7, 8, 4, 6, 1, 0, 6, 0, 0, 5, 5, 6, 6, 1])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ce9b4835",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 1., 0., 0., 0.])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_int"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "fc67f0a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 3., 8., 8., 7., 0., 5., 7., 8., 4., 6., 1., 0., 6., 0., 0.,\n",
       "       5., 5., 6., 6., 1., 0., 0., 0.])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35e1aaef",
   "metadata": {},
   "source": [
    "# FIR mit Delay \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "d8986bc9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tap with amplitude=1, delay=6\n",
      "Creating filter of order N=13.0\n",
      "[-3.89817183e-17  3.89817183e-17 -3.89817183e-17  3.89817183e-17\n",
      " -3.89817183e-17  3.89817183e-17  1.00000000e+00  3.89817183e-17\n",
      " -3.89817183e-17  3.89817183e-17 -3.89817183e-17  3.89817183e-17\n",
      " -3.89817183e-17  3.89817183e-17]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "delay = 6\n",
    "ampl = 1\n",
    "print(f\"Tap with amplitude={ampl}, delay={delay}\")\n",
    "    \n",
    "order = 2 * np.floor(delay) + 1 #N\n",
    "print(f\"Creating filter of order N={order}\")\n",
    "\n",
    "skip = np.floor(delay) - (order - 1) / 2 #M\n",
    "assert skip >= 0\n",
    "\n",
    "samples = np.arange(0, order+1)\n",
    "\n",
    "h = ampl*(np.sinc(samples-delay)) #sinc\n",
    "\n",
    "#h[0] = 1\n",
    "\n",
    "print(h)\n",
    "t1 =np.arange(0.0,order, 0.01)\n",
    "plt.grid(True)\n",
    "plt.stem(samples, h,linefmt='C0-')\n",
    "plt.plot(t1,np.sinc(t1-delay),'b--')\n",
    "plt.xlabel('Delay')\n",
    "plt.ylabel('Amplitude')\n",
    "plt.show()\n",
    "plt.savefig(\"ganzzahliges_D.png\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "d39528be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1fdac682550>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.arange(200)\n",
    "\n",
    "signal = np.sin(2 * np.pi * t * 0.05)\n",
    "\n",
    "signal_shifted = np.convolve(h, signal, mode='full')\n",
    "\n",
    "plt.plot(t, signal)\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "plt.plot(signal_shifted)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "b6f61760",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tap with amplitude=[4, 1], delay=[5, 6.2]\n",
      "14\n",
      "[ 1.55926873e-16 -1.55926873e-16  1.55926873e-16 -1.55926873e-16\n",
      "  1.55926873e-16  4.00000000e+00  1.55926873e-16 -1.55926873e-16\n",
      "  1.55926873e-16 -1.55926873e-16  1.55926873e-16 -1.55926873e-16\n",
      "  0.00000000e+00  0.00000000e+00]\n",
      "[ 0.03017707 -0.03598036  0.04454711 -0.05846808  0.08504448 -0.15591488\n",
      "  0.93548928  0.23387232 -0.10394325  0.06682066 -0.04923628  0.03897872\n",
      " -0.03225825  0.02751439]\n",
      "[ 1.         -0.03598036  0.04454711 -0.05846808  0.08504448  3.84408512\n",
      "  0.93548928  0.23387232 -0.10394325  0.06682066 -0.04923628  0.03897872\n",
      " -0.03225825  0.02751439]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "delay = [5,6.2]\n",
    "ampl = [4,1]\n",
    "print(f\"Tap with amplitude={ampl}, delay={delay}\")\n",
    "\n",
    "max_order = 2 * np.floor(np.max(delay)) + 1\n",
    "max_samples = np.arange(0, max_order +1) \n",
    "max_len = len(max_samples)\n",
    "print(max_len)\n",
    "\n",
    "sum_x = np.zeros(int(max_len))\n",
    "\n",
    "for (a,d) in zip(ampl,delay):\n",
    "    \n",
    "    order = 2 * np.floor(d) + 1\n",
    "    \n",
    "    skip = np.floor(d) - (order - 1) / 2 #M sollte immer 0 sein \n",
    "    assert skip >= 0\n",
    "\n",
    "    samples = np.arange(0, order+1 ) \n",
    "\n",
    "    h = a*(np.sinc(samples-d)) #sinc\n",
    "    h_len = np.concatenate([h, np.zeros(max_len-len(h))])\n",
    "    print(h_len)\n",
    "    sum_x += h_len\n",
    "    \n",
    "\n",
    "sum_x[0] = 1\n",
    "print(sum_x)\n",
    "\n",
    "\n",
    "\n",
    "plt.stem(max_samples, sum_x)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "52c30c0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delay = [5,6]\n",
    "np.max(delay)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "356ce18c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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
}