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595:. This technology mainly discusses the modeling of a linear time-invariant continuous system, integral of the system's zero-state response, setting up system function and the continuous time filtering of deterministic signals
1147: – for statistical analysis of relations between large quantities of variables (in this context representing many physical signals), to extract previously unknown interesting patterns
1003:
and reconstruction, which involves measuring a physical signal, storing or transferring it as digital signal, and possibly later rebuilding the original signal or an approximation thereof.
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The concept of discrete-time signal processing also refers to a theoretical discipline that establishes a mathematical basis for digital signal processing, without taking
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properties to perform signal processing tasks. Statistical techniques are widely used in signal processing applications. For example, one can model the
1524:
Sarangi, Susanta; Sahidullah, Md; Saha, Goutam (September 2020). "Optimization of data-driven filterbank for automatic speaker verification".
628:. This technology was a predecessor of digital signal processing (see below), and is still used in advanced processing of gigahertz signals.
349:. The paper laid the groundwork for later development of information communication systems and the processing of signals for transmission.
525:, telephone, and television systems. This involves linear electronic circuits as well as nonlinear ones. The former are, for instance,
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Sengupta, Nandini; Sahidullah, Md; Saha, Goutam (August 2016). "Lung sound classification using cepstral-based statistical features".
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techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital
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Digital signal processing is the processing of digitized discrete-time sampled signals. Processing is done by general-purpose
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is for sampled signals, defined only at discrete points in time, and as such are quantized in time, but not in magnitude.
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is for signals that vary with the change of continuous domain (without considering some individual interrupted points).
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Slawinska, J.; Ourmazd, A.; Giannakis, D. (2018). "A New
Approach to Signal Processing of Spatiotemporal Data".
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systems may be interpreted as conceptually straightforward extensions of linear systems to the non-linear case.
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involves the analysis and processing of signals produced from nonlinear systems and can be in the time,
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Berber, S. (2021). Discrete
Communication Systems. United Kingdom: Oxford University Press., page 9,
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Statistical Signal
Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals
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Fifty Years of Signal
Processing: The IEEE Signal Processing Society and its Technologies, 1948–1998
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Nonlinear System
Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains
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of noise incurred when photographing an image, and construct techniques based on this model to
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Machine
Learning for Signal Processing: Data Science, Algorithms, and Computational Statistics
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Analog signal processing is for signals that have not been digitized, as in most 20th-century
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The signal on the left looks like noise, but the signal processing technique known as
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1951:: Statistical Signal Processing lecture notes at the University of Waterloo, Canada.
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Foundations of
Digital Signal Processing: Theory, Algorithms and Hardware Design
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Statistical signal processing: detection, estimation, and time series analysis
816: – waveform generations, demodulation, filtering, equalization
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Polynomial signal processing is a type of non-linear signal processing, where
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measurements of geophysical data. Processing is conducted within either the
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Time frequency signal analysis and processing a comprehensive reference
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977: – for example analog (passive or active) or digital (
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257:(right) shows that it contains five well-defined frequency components.
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Signal processing matured and flourished in the 1960s and 1970s, and
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Telford, William Murray; Geldart, L. P.; Sheriff, Robert E. (1990).
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324:, the principles of signal processing can be found in the classical
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2000:– free online textbook by Paolo Prandoni and Martin Vetterli (2008)
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650:
300:. Signal processing techniques are used to optimize transmissions,
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827: – for processing signals from arrays of sensors
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subfield that focuses on analyzing, modifying and synthesizing
522:
226:, received and converted by another transducer to final form.
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which cannot be produced or analyzed using linear methods.
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deterministic (then one speaks of a deterministic signal) or
2004:
Scientists and
Engineers Guide to Digital Signal Processing
1997:
1853:
1086:
654:
2003:
914:
In communication systems, signal processing may occur at:
1375:
https://books.google.com/books?id=CCs0EAAAQBAJ&pg=PA9
1329:"A Mathematical Theory of Communication – CHM Revolution"
1042: – for processing non-stationary signals
206:
Signal transmission using electronic signal processing.
19:"Signal theory" redirects here. Not to be confused with
1932:
Probability, Random
Variables, and Stochastic Processes
1643:
An Introduction to Applied and Environmental Geophysics
1769:
Peter J. Schreier; Louis L. Scharf (4 February 2010).
1416:
2018 IEEE Statistical Signal Processing Workshop (SSP)
2010:
Julius O. Smith III: Spectral Audio Signal Processing
1611:
1577:
Anastassiou, D. (2001). "Genomic signal processing".
665:(DSP chips). Typical arithmetical operations include
462:
413:
377:
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is a technology based on electronic devices such as
222:
waveforms, which then are processed, transmitted as
1700:
Digital Signal Processing: An Experimental Approach
1455:V. John Mathews; Giovanni L. Sicuranza (May 2000).
810: – for interpreting moving pictures
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304:efficiency, correcting distorted signals, improve
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1274:Alan V. Oppenheim and Ronald W. Schafer (1989).
1299:Oppenheim, Alan V.; Schafer, Ronald W. (1975).
1018:
724:can produce highly complex behaviors including
1979:, Linear Estimation, Prentice-Hall, NJ, 2000,
1823:Steven B. Damelin; Willard Miller, Jr (2012).
2045:
2031:
1897:Fundamentals of Statistical Signal Processing
1816:
1795:
1690:
1663:
1850:Daniel P. Palomar; Yonina C. Eldar (2010).
1748:
1576:
1363:. The IEEE Signal Processing Society. 1998.
64:Learn how and when to remove these messages
2038:
2024:
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1384:
1382:
1703:. Springer Science & Business Media.
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1476:
583:The methods of signal processing include
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190:Learn how and when to remove this message
121:Learn how and when to remove this message
1929:
1880:
1640:
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781:
201:
84:This article includes a list of general
2006:– free online textbook by Stephen Smith
1749:Stoica, Petre; Moses, Randolph (2005).
1379:
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758:is an approach which treats signals as
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1482:
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610:Analog discrete-time signal processing
341:A Mathematical Theory of Communication
2019:
1957:, Adaptive Filters, Wiley, NJ, 2008,
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1998:Signal Processing for Communications
1826:The Mathematics of Signal Processing
1345:
356:became widely used with specialized
210:convert signals from other physical
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29:
1894:
1728:(1 ed.). Amsterdam: Elsevier.
1697:Shlomo Engelberg (8 January 2008).
13:
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90:it lacks sufficient corresponding
14:
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1991:
1418:. IEEE Xplore. pp. 338–342.
1241:Computers in Biology and Medicine
681:. Examples of algorithms are the
578:Continuous-time signal processing
45:This article has multiple issues.
2076:Nyquist–Shannon sampling theorem
1796:Max A. Little (13 August 2019).
1253:10.1016/j.compbiomed.2016.05.013
598:
495:{\displaystyle (X_{t})_{t\in T}}
446:{\displaystyle (x_{t})_{t\in T}}
400:, where this function is either
243:
234:
137:
75:
34:
2162:Discrete-time Fourier transform
1934:(third ed.). McGraw-Hill.
1742:
1724:Boashash, Boualem, ed. (2003).
1717:
1634:
1605:
1579:IEEE Signal Processing Magazine
1570:
1517:
1276:Discrete-Time Signal Processing
1205:Least-squares spectral analysis
918:OSI layer 1 in the seven-layer
653:or by digital circuits such as
626:analog feedback shift registers
616:circuits, analog time-division
604:Discrete-time signal processing
53:or discuss these issues on the
16:Field of electrical engineering
1901:Upper Saddle River, New Jersey
1856:. Cambridge University Press.
1829:. Cambridge University Press.
1775:. Cambridge University Press.
1448:
1367:
1321:
1292:
1267:
1232:
750:
659:field-programmable gate arrays
563:voltage-controlled oscillators
477:
463:
428:
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387:
381:
152:format but may read better as
1:
2107:Statistical signal processing
1930:Papoulis, Athanasios (1991).
1225:
1055:Statistical signal processing
858:Quality improvement, such as
756:Statistical signal processing
720:, or spatiotemporal domains.
555:voltage-controlled amplifiers
545:. Nonlinear circuits include
505:
346:Bell System Technical Journal
343:" which was published in the
339:wrote the influential paper "
1884:Spectral Analysis of Signals
1752:Spectral Analysis of Signals
1457:Polynomial Signal Processing
1278:. Prentice Hall. p. 1.
1070:Polynomial signal processing
1061:Linear time-invariant system
1019:Mathematical methods applied
997:analog-to-digital converters
958:analog-to-digital conversion
708:
7:
1158:Algebraic signal processing
1151:
714:Nonlinear signal processing
255:spectral density estimation
10:
2302:
2156:Discrete Fourier transform
2133:Matched Z-transform method
1881:P Stoica, R Moses (2005).
1641:Reynolds, John M. (2011).
1618:Cambridge University Press
956:(source coding, including
642:
638:
559:voltage-controlled filters
514:
311:
18:
2201:
2150:Discrete cosine transform
2115:
2084:
2053:
2047:Digital signal processing
1670:Patrick Gaydecki (2004).
1556:10.1016/j.dsp.2020.102795
1526:Digital Signal Processing
1483:Scharf, Louis L. (1991).
1301:Digital Signal Processing
1220:Sensitivity (electronics)
1178:Dynamic range compression
1012:Digital signal processors
786:Seismic signal processing
691:Infinite impulse response
663:digital signal processors
645:Digital signal processing
510:
354:digital signal processing
2286:Telecommunication theory
2183:Post's inversion formula
2097:Digital image processing
1424:10.1109/SSP.2018.8450704
1389:Billings, S. A. (2013).
1173:Digital image processing
947:forward error correction
873:Source coding including
774:in the resulting image.
768:probability distribution
593:complex frequency domain
517:Analog signal processing
358:digital signal processor
332:of the 1940s and 1950s.
306:subjective video quality
2092:Audio signal processing
1895:Kay, Steven M. (1993).
1040:Time-frequency analysis
792:Audio signal processing
687:finite impulse response
298:scientific measurements
161:converting this article
105:more precise citations.
2012:– free online textbook
1025:Differential equations
985:, frequency domain or
814:Wireless communication
787:
683:fast Fourier transform
496:
447:
394:
364:Definition of a signal
268:electrical engineering
227:
25:Signalling (economics)
2281:Mass media technology
1676:. IET. pp. 40–.
1076:System identification
785:
497:
453:, a realization of a
448:
395:
224:electromagnetic waves
205:
2216:Anti-aliasing filter
2145:Constant-Q transform
2128:Advanced z-transform
1890:. NJ: Prentice Hall.
1758:. NJ: Prentice Hall.
1115:stochastic processes
1030:Recurrence relations
760:stochastic processes
635:into consideration.
460:
411:
393:{\displaystyle x(t)}
375:
360:chips in the 1980s.
294:altimetry processing
1948:Kainam Thomas Wong
1591:2001ISPM...18....8A
1548:2020DSP...10402795S
1106:Functional analysis
1046:Spectral estimation
849:image understanding
2173:Integral transform
2168:Impulse invariance
2140:Bilinear transform
1614:Applied geophysics
1200:Information theory
1078:and classification
1007:Signal compressors
1001:signal acquisition
987:stochastic filters
954:presentation layer
853:speech recognition
845:Feature extraction
788:
778:Application fields
762:, utilizing their
693:(IIR) filter, and
633:quantization error
622:analog delay lines
567:phase-locked loops
492:
455:stochastic process
443:
390:
326:numerical analysis
228:
163:, if appropriate.
2276:Signal processing
2263:
2262:
2188:Starred transform
2178:Laplace transform
2102:Speech processing
2071:Estimation theory
1985:978-0-13-022464-4
1963:978-0-470-25388-5
1863:978-0-521-76222-9
1836:978-1-107-01322-3
1809:978-0-19-102431-3
1782:978-1-139-48762-7
1710:978-1-84800-119-0
1683:978-0-85296-431-6
1656:978-0-471-48535-3
1627:978-0-521-33938-4
1599:10.1109/79.939833
1585:(4). IEEE: 8–20.
1466:978-0-471-03414-8
1433:978-1-5386-1571-3
1400:978-1-119-94359-4
1195:Fourier transform
1168:Bounded variation
1135:Numerical methods
1125:Estimation theory
952:OSI layer 6, the
941:OSI layer 2, the
891:signal processing
883:video compression
879:image compression
875:audio compression
868:echo cancellation
864:image enhancement
722:Nonlinear systems
322:Ronald W. Schafer
318:Alan V. Oppenheim
264:Signal processing
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1120:Detection theory
1092:Complex analysis
1065:transform theory
1035:Transform theory
962:data compression
908:frequency domain
825:Array processing
808:Video processing
802:Image processing
772:reduce the noise
695:adaptive filters
675:circular buffers
589:frequency domain
551:frequency mixers
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969:Typical devices
943:data link layer
860:noise reduction
831:Process control
820:Control systems
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661:or specialized
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614:sample and hold
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573:Continuous time
549:, multipliers (
535:additive mixers
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1153:
1150:
1149:
1148:
1142:
1137:
1132:
1127:
1122:
1117:
1108:
1103:
1101:Linear algebra
1094:
1089:
1084:
1079:
1073:
1067:
1058:
1052:
1043:
1037:
1032:
1027:
1020:
1017:
1016:
1015:
1009:
1004:
990:
970:
967:
966:
965:
950:
939:
924:physical layer
912:
911:
892:
886:
871:
856:
842:
837:
828:
822:
817:
811:
805:
799:
779:
776:
752:
749:
710:
707:
703:Kalman filters
689:(FIR) filter,
671:floating-point
643:Main article:
640:
637:
600:
597:
574:
571:
531:active filters
515:Main article:
512:
509:
507:
504:
503:
502:
489:
486:
483:
479:
473:
469:
465:
440:
437:
434:
430:
424:
420:
416:
405:
389:
386:
383:
380:
368:A signal is a
365:
362:
337:Claude Shannon
313:
310:
252:
251:
242:
241:
233:
232:
231:
230:
229:
198:
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145:
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136:
129:
128:
83:
81:
74:
69:
43:
42:
40:
33:
15:
9:
6:
4:
3:
2:
2298:
2287:
2284:
2282:
2279:
2277:
2274:
2273:
2271:
2256:
2253:
2251:
2250:Undersampling
2248:
2246:
2245:Sampling rate
2243:
2241:
2238:
2236:
2233:
2231:
2227:
2224:
2222:
2219:
2217:
2214:
2212:
2209:
2208:
2206:
2204:
2200:
2194:
2193:Zak transform
2191:
2189:
2186:
2184:
2181:
2179:
2176:
2174:
2171:
2169:
2166:
2163:
2160:
2157:
2154:
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2148:
2146:
2143:
2141:
2138:
2134:
2131:
2129:
2126:
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2120:
2118:
2114:
2108:
2105:
2103:
2100:
2098:
2095:
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2090:
2089:
2087:
2083:
2077:
2074:
2072:
2069:
2067:
2064:
2062:
2059:
2058:
2056:
2052:
2048:
2041:
2036:
2034:
2029:
2027:
2022:
2021:
2018:
2011:
2008:
2005:
2002:
1999:
1996:
1995:
1986:
1982:
1978:
1977:Babak Hassibi
1974:
1970:
1967:
1964:
1960:
1956:
1953:
1950:
1947:
1943:
1941:0-07-100870-5
1937:
1933:
1928:
1924:
1920:
1916:
1914:0-13-345711-7
1910:
1906:
1905:Prentice Hall
1902:
1898:
1893:
1886:
1885:
1879:
1878:
1865:
1859:
1855:
1854:
1846:
1838:
1832:
1828:
1827:
1819:
1811:
1805:
1801:
1800:
1792:
1784:
1778:
1774:
1773:
1765:
1754:
1753:
1745:
1737:
1735:0-08-044335-4
1731:
1727:
1720:
1712:
1706:
1702:
1701:
1693:
1685:
1679:
1675:
1674:
1666:
1658:
1652:
1648:
1644:
1637:
1629:
1623:
1619:
1615:
1608:
1600:
1596:
1592:
1588:
1584:
1580:
1573:
1565:
1561:
1557:
1553:
1549:
1545:
1540:
1535:
1531:
1527:
1520:
1512:
1508:
1504:
1502:0-201-19038-9
1498:
1494:
1490:
1486:
1479:
1477:
1468:
1462:
1458:
1451:
1443:
1439:
1435:
1429:
1425:
1421:
1417:
1410:
1402:
1396:
1392:
1385:
1383:
1376:
1370:
1359:
1358:
1351:
1349:
1334:
1330:
1324:
1316:
1314:0-13-214635-5
1310:
1307:. p. 5.
1306:
1305:Prentice Hall
1302:
1295:
1287:
1285:0-13-216771-9
1281:
1277:
1270:
1262:
1258:
1254:
1250:
1246:
1242:
1235:
1231:
1221:
1218:
1216:
1215:Reverberation
1213:
1211:
1208:
1206:
1203:
1201:
1198:
1196:
1193:
1191:
1187:
1183:
1179:
1176:
1174:
1171:
1169:
1166:
1164:
1161:
1159:
1156:
1155:
1146:
1143:
1141:
1138:
1136:
1133:
1131:
1128:
1126:
1123:
1121:
1118:
1116:
1112:
1109:
1107:
1104:
1102:
1098:
1097:Vector spaces
1095:
1093:
1090:
1088:
1085:
1083:
1080:
1077:
1074:
1071:
1068:
1066:
1062:
1059:
1056:
1053:
1051:
1047:
1044:
1041:
1038:
1036:
1033:
1031:
1028:
1026:
1023:
1022:
1013:
1010:
1008:
1005:
1002:
998:
994:
991:
988:
984:
980:
976:
973:
972:
963:
959:
955:
951:
948:
944:
940:
937:
933:
929:
925:
921:
917:
916:
915:
909:
905:
901:
897:
893:
890:
887:
884:
880:
876:
872:
869:
865:
861:
857:
854:
850:
846:
843:
841:
838:
836:
832:
829:
826:
823:
821:
818:
815:
812:
809:
806:
803:
800:
797:
793:
790:
789:
784:
775:
773:
769:
765:
761:
757:
748:
746:
741:
739:
735:
731:
727:
723:
719:
715:
706:
704:
700:
696:
692:
688:
684:
680:
679:lookup tables
676:
672:
668:
664:
660:
656:
652:
646:
636:
634:
629:
627:
623:
619:
615:
611:
607:
605:
599:Discrete time
596:
594:
590:
586:
581:
579:
570:
568:
564:
560:
556:
552:
548:
544:
540:
536:
532:
528:
524:
518:
487:
484:
481:
471:
467:
456:
438:
435:
432:
422:
418:
406:
403:
402:
401:
384:
378:
371:
361:
359:
355:
350:
348:
347:
342:
338:
333:
331:
327:
323:
319:
316:According to
309:
307:
303:
299:
295:
291:
287:
283:
279:
275:
274:
269:
265:
256:
225:
221:
217:
213:
209:
204:
194:
191:
176:
167:is available.
166:
162:
156:
155:
151:
146:This article
144:
135:
134:
125:
122:
114:
104:
100:
94:
93:
87:
82:
73:
72:
67:
65:
58:
57:
52:
51:
46:
41:
32:
31:
26:
22:
2240:Quantization
2235:Oversampling
2226:Nyquist rate
2221:Downsampling
1973:Ali H. Sayed
1955:Ali H. Sayed
1931:
1896:
1883:
1852:
1845:
1825:
1818:
1798:
1791:
1771:
1764:
1751:
1744:
1725:
1719:
1699:
1692:
1672:
1665:
1642:
1636:
1613:
1607:
1582:
1578:
1572:
1529:
1525:
1519:
1484:
1456:
1450:
1415:
1409:
1390:
1369:
1356:
1336:. Retrieved
1332:
1323:
1300:
1294:
1275:
1269:
1244:
1240:
1234:
1190:noise gating
1163:Audio filter
1130:Optimization
1063:theory, and
936:multiplexing
932:equalization
913:
835:current loop
755:
754:
742:
738:subharmonics
726:bifurcations
712:
697:such as the
648:
630:
618:multiplexers
609:
608:
602:
582:
576:
520:
367:
351:
344:
334:
315:
271:
263:
262:
214:to electric
186:
170:
165:Editing help
147:
117:
111:January 2017
108:
89:
61:
54:
48:
47:Please help
44:
2123:Z-transform
1145:Data mining
1140:Time series
1111:Probability
1050:time series
904:time domain
900:time-series
764:statistical
751:Statistical
667:fixed-point
585:time domain
543:delay lines
539:integrators
208:Transducers
103:introducing
2270:Categories
2255:Upsampling
2116:Techniques
2085:Sub-fields
1539:2007.10729
1532:: 102795.
1338:2019-05-13
1226:References
1182:companding
928:modulation
910:, or both.
896:geophysics
847:, such as
840:Seismology
745:polynomial
547:compandors
506:Categories
276:, such as
86:references
50:improve it
2230:frequency
1564:220665533
1459:. Wiley.
1393:. Wiley.
920:OSI model
734:harmonics
718:frequency
709:Nonlinear
651:computers
485:∈
436:∈
335:In 1948,
212:waveforms
173:June 2017
56:talk page
2211:Aliasing
2203:Sampling
1923:26504848
1511:61160161
1442:52153144
1261:27286184
1186:limiting
1152:See also
1082:Calculus
993:Samplers
938:, etc.);
798:or music
370:function
1587:Bibcode
1544:Bibcode
989:, etc.)
975:Filters
889:Genomic
685:(FFT),
639:Digital
407:a path
312:History
273:signals
220:voltage
216:current
99:improve
2164:(DTFT)
2054:Theory
1983:
1975:, and
1961:
1938:
1921:
1911:
1860:
1833:
1806:
1779:
1732:
1707:
1680:
1653:
1624:
1562:
1509:
1499:
1489:Boston
1463:
1440:
1430:
1397:
1311:
1282:
1259:
1188:, and
1014:(DSPs)
922:, the
881:, and
866:, and
796:speech
736:, and
699:Wiener
591:, and
565:, and
541:, and
511:Analog
296:, and
282:images
266:is an
148:is in
88:, but
2158:(DFT)
2152:(DCT)
1888:(PDF)
1756:(PDF)
1560:S2CID
1534:arXiv
1438:S2CID
1361:(PDF)
730:chaos
655:ASICs
523:radio
278:sound
154:prose
1981:ISBN
1959:ISBN
1936:ISBN
1919:OCLC
1909:ISBN
1858:ISBN
1831:ISBN
1804:ISBN
1777:ISBN
1730:ISBN
1705:ISBN
1678:ISBN
1651:ISBN
1622:ISBN
1507:OCLC
1497:ISBN
1461:ISBN
1428:ISBN
1395:ISBN
1309:ISBN
1280:ISBN
1257:PMID
1113:and
1099:and
1087:Code
999:for
995:and
960:and
851:and
701:and
677:and
669:and
624:and
320:and
150:list
1595:doi
1552:doi
1530:104
1420:doi
1249:doi
983:IIR
979:FIR
906:or
894:In
557:),
218:or
23:or
2272::
2228:/
1971:,
1917:.
1907:.
1903::
1899:.
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1645:.
1620:.
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1593:.
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1581:.
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1550:.
1542:.
1528:.
1505:.
1495:.
1491::
1487:.
1475:^
1436:.
1426:.
1381:^
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1925:.
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