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Talk:Causal system

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I happened to be studying for a Signals & Systems exam, and I noticed this article was a bit hard to understand. So, I went ahead and tried to make the first paragraph a bit clearer, but I don't have the time to make the mathematical notation clearer. I hope there is someone out there that can
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The article lists: y \left( t \right) =x(-t) as an example of an anticausal system...this is only true is t<0. For instance, let t=1. Then the value of the output signal at t=1, y(1), is determined uniquely by the input signal at time t=-1, i.e. x(-1). This is clearly causal.
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y(n)= y(n-1)+ x(n) seems also causal, nevertheless the definition does not include such a case. Can we make a solid statement on that? (My textbook could not clarify it either.)
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the only thing I can think of is a digital filter that because of delays, gets hi-frequency information before the pulse 'hits'. PLEASE talk about this.
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This article could do well with a basic example to illustrate the concept more clearly. A graph and a few equations would go a long way.
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503:"? It seems the current definition is actually giving conditions for when a system is causal at 533: 506: 479: 379: 211: 455:
It should be explained, that in this paragraph two definitions of causality are shown.
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Nutshell: Someone with math notation skills, please clean this article up.
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Should the first mathematical definition include a "for every
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Is there any difference between causal and memory systems?
536: 509: 482: 101:, a collaborative effort to improve the coverage of 549: 522: 495: 580:Start-Class physics articles of Low-importance 557:in order for the system to be causal, right? 8: 530:. The condition given needs to apply at all 206:, which collaborates on articles related to 19: 401:systems do not depend on any future input. 152: 47: 541: 535: 514: 508: 487: 481: 388:systems do not depend on any past input. 154: 49: 7: 262:This article is within the field of 200:This article is within the scope of 95:This article is within the scope of 38:It is of interest to the following 595:Systems articles in systems theory 14: 590:High-importance Systems articles 187: 177: 156: 82: 72: 51: 20: 575:Low-importance physics articles 240:This article has been rated as 135:This article has been rated as 1: 413:08:41, 14 December 2006 (UTC) 363:08:41, 14 December 2006 (UTC) 346:08:41, 14 December 2006 (UTC) 324:19:16, 15 February 2011 (UTC) 220:Knowledge:WikiProject Systems 115:Knowledge:WikiProject Physics 109:and see a list of open tasks. 600:WikiProject Systems articles 585:Start-Class Systems articles 570:Start-Class physics articles 471:18:08, 8 November 2007 (UTC) 445:13:19, 11 October 2007 (UTC) 303:Incorrect example in article 223:Template:WikiProject Systems 118:Template:WikiProject Physics 616: 368:Causal vs. Memory Systems? 295:09:03, 16 April 2017 (UTC) 246:project's importance scale 141:project's importance scale 421:Dependence on the output? 281:Help..what is NON-causal? 261: 239: 172: 134: 67: 46: 451:Mathematical DefinitionS 395:do depend on past input. 551: 524: 497: 378:This information from 258: 195:Systems science portal 28:This article is rated 552: 550:{\displaystyle t_{0}} 525: 523:{\displaystyle t_{0}} 498: 496:{\displaystyle t_{0}} 257: 534: 507: 480: 203:WikiProject Systems 98:WikiProject Physics 547: 520: 493: 382:... hope it helps 351:Example Suggestion 259: 34:content assessment 473: 461:comment added by 447: 431:comment added by 330:Status of Article 314:comment added by 278: 277: 274: 273: 270: 269: 151: 150: 147: 146: 607: 556: 554: 553: 548: 546: 545: 529: 527: 526: 521: 519: 518: 502: 500: 499: 494: 492: 491: 456: 426: 326: 228: 227: 226:Systems articles 224: 221: 218: 197: 192: 191: 190: 181: 174: 173: 168: 160: 153: 123: 122: 121:physics articles 119: 116: 113: 92: 87: 86: 76: 69: 68: 63: 55: 48: 31: 25: 24: 16: 615: 614: 610: 609: 608: 606: 605: 604: 560: 559: 537: 532: 531: 510: 505: 504: 483: 478: 477: 453: 423: 380:System analysis 370: 353: 332: 309: 305: 283: 242:High-importance 225: 222: 219: 216: 215: 212:systems science 193: 188: 186: 167:High‑importance 166: 120: 117: 114: 111: 110: 88: 81: 61: 32:on Knowledge's 29: 12: 11: 5: 613: 611: 603: 602: 597: 592: 587: 582: 577: 572: 562: 561: 544: 540: 517: 513: 490: 486: 463:134.130.44.166 452: 449: 422: 419: 418: 417: 416: 415: 407: 404: 403: 402: 396: 389: 369: 366: 352: 349: 331: 328: 304: 301: 299: 282: 279: 276: 275: 272: 271: 268: 267: 264:Systems theory 260: 250: 249: 238: 232: 231: 229: 199: 198: 182: 170: 169: 161: 149: 148: 145: 144: 137:Low-importance 133: 127: 126: 124: 107:the discussion 94: 93: 90:Physics portal 77: 65: 64: 62:Low‑importance 56: 44: 43: 37: 26: 13: 10: 9: 6: 4: 3: 2: 612: 601: 598: 596: 593: 591: 588: 586: 583: 581: 578: 576: 573: 571: 568: 567: 565: 558: 542: 538: 515: 511: 488: 484: 474: 472: 468: 464: 460: 450: 448: 446: 442: 438: 434: 430: 420: 414: 411: 408: 405: 400: 397: 394: 390: 387: 384: 383: 381: 377: 376: 375: 374: 373: 367: 365: 364: 361: 356: 350: 348: 347: 344: 339: 336: 329: 327: 325: 321: 317: 316:130.15.81.250 313: 302: 300: 297: 296: 292: 288: 280: 265: 256: 252: 251: 247: 243: 237: 234: 233: 230: 213: 209: 205: 204: 196: 185: 183: 180: 176: 175: 171: 165: 162: 159: 155: 142: 138: 132: 129: 128: 125: 108: 104: 100: 99: 91: 85: 80: 78: 75: 71: 70: 66: 60: 57: 54: 50: 45: 41: 35: 27: 23: 18: 17: 475: 454: 433:Fonduesuisse 424: 398: 392: 385: 371: 357: 354: 340: 337: 333: 306: 298: 284: 241: 201: 136: 96: 40:WikiProjects 457:—Preceding 427:—Preceding 393:with memory 358:Good Luck, 341:Good Luck, 310:—Preceding 287:CorvetteZ51 30:Start-class 564:Categories 386:Memoryless 335:do that. 459:unsigned 441:contribs 429:unsigned 391:Systems 312:unsigned 244:on the 217:Systems 208:systems 164:Systems 139:on the 112:Physics 103:Physics 59:Physics 399:Causal 36:scale. 406:Best, 467:talk 437:talk 410:Pg8p 360:Pg8p 343:Pg8p 320:talk 291:talk 236:High 210:and 131:Low 566:: 469:) 443:) 439:• 322:) 293:) 543:0 539:t 516:0 512:t 489:0 485:t 465:( 435:( 318:( 289:( 266:. 248:. 214:. 143:. 42::

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