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606:. 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
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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
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Sarangi, Susanta; Sahidullah, Md; Saha, Goutam (September 2020). "Optimization of data-driven filterbank for automatic speaker verification".
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639:. This technology was a predecessor of digital signal processing (see below), and is still used in advanced processing of gigahertz signals.
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360:. The paper laid the groundwork for later development of information communication systems and the processing of signals for transmission.
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536:, 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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1962:: 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
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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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988: – for example analog (passive or active) or digital (
909:, signal processing is used to amplify the signal vs the noise within
805: – for electrical signals representing sound, such as
268:(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
283:
1623:
Telford, William Murray; Geldart, L. P.; Sheriff, Robert E. (1990).
335:, the principles of signal processing can be found in the classical
2011:– free online textbook by Paolo Prandoni and Martin Vetterli (2008)
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311:. Signal processing techniques are used to optimize transmissions,
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838: – for processing signals from arrays of sensors
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subfield that focuses on analyzing, modifying and synthesizing
143:
81:
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237:, received and converted by another transducer to final form.
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which cannot be produced or analyzed using linear methods.
415:
deterministic (then one speaks of a deterministic signal) or
2015:
Scientists and
Engineers Guide to Digital Signal Processing
2008:
1864:
2014:
925:
In communication systems, signal processing may occur at:
1386:
https://books.google.com/books?id=CCs0EAAAQBAJ&pg=PA9
1340:"A Mathematical Theory of Communication – CHM Revolution"
1053: – for processing non-stationary signals
217:
Signal transmission using electronic signal processing.
30:"Signal theory" redirects here. Not to be confused with
1943:
Probability, Random
Variables, and Stochastic Processes
1654:
An Introduction to Applied and Environmental Geophysics
171:
1780:
Peter J. Schreier; Louis L. Scharf (4 February 2010).
1427:
2018 IEEE Statistical Signal Processing Workshop (SSP)
2021:
Julius O. Smith III: Spectral Audio Signal Processing
1588:
Anastassiou, D. (2001). "Genomic signal processing".
676:(DSP chips). Typical arithmetical operations include
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is a technology based on electronic devices such as
233:
waveforms, which then are processed, transmitted as
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2064:
1711:
Digital Signal Processing: An Experimental Approach
1466:V. John Mathews; Giovanni L. Sicuranza (May 2000).
821: – for interpreting moving pictures
505:
456:
403:
315:efficiency, correcting distorted signals, improve
1285:Alan V. Oppenheim and Ronald W. Schafer (1989).
1310:Oppenheim, Alan V.; Schafer, Ronald W. (1975).
735:can produce highly complex behaviors including
1990:, Linear Estimation, Prentice-Hall, NJ, 2000,
1834:Steven B. Damelin; Willard Miller, Jr (2012).
2042:
1908:Fundamentals of Statistical Signal Processing
8:
1861:Daniel P. Palomar; Yonina C. Eldar (2010).
1374:. The IEEE Signal Processing Society. 1998.
75:Learn how and when to remove these messages
2049:
2035:
2027:
1395:
1393:
1714:. Springer Science & Business Media.
1548:
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1487:
594:The methods of signal processing include
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201:Learn how and when to remove this message
132:Learn how and when to remove this message
212:
95:This article includes a list of general
2017:– free online textbook by Stephen Smith
1760:Stoica, Petre; Moses, Randolph (2005).
1361:
1359:
1242:
769:is an approach which treats signals as
621:Analog discrete-time signal processing
352:A Mathematical Theory of Communication
1968:, Adaptive Filters, Wiley, NJ, 2008,
7:
2009:Signal Processing for Communications
1837:The Mathematics of Signal Processing
367:became widely used with specialized
221:convert signals from other physical
1739:(1 ed.). Amsterdam: Elsevier.
1708:Shlomo Engelberg (8 January 2008).
101:it lacks sufficient corresponding
25:
1429:. IEEE Xplore. pp. 338–342.
1252:Computers in Biology and Medicine
692:. Examples of algorithms are the
589:Continuous-time signal processing
56:This article has multiple issues.
2087:Nyquist–Shannon sampling theorem
1807:Max A. Little (13 August 2019).
1264:10.1016/j.compbiomed.2016.05.013
506:{\displaystyle (X_{t})_{t\in T}}
457:{\displaystyle (x_{t})_{t\in T}}
411:, where this function is either
254:
245:
148:
86:
45:
2173:Discrete-time Fourier transform
1945:(third ed.). McGraw-Hill.
1735:Boashash, Boualem, ed. (2003).
1590:IEEE Signal Processing Magazine
1287:Discrete-Time Signal Processing
1216:Least-squares spectral analysis
929:OSI layer 1 in the seven-layer
664:or by digital circuits such as
637:analog feedback shift registers
627:circuits, analog time-division
615:Discrete-time signal processing
64:or discuss these issues on the
27:Field of electrical engineering
1912:Upper Saddle River, New Jersey
1867:. Cambridge University Press.
1840:. Cambridge University Press.
1786:. Cambridge University Press.
670:field-programmable gate arrays
574:voltage-controlled oscillators
488:
474:
439:
425:
398:
392:
163:format but may read better as
1:
2118:Statistical signal processing
1941:Papoulis, Athanasios (1991).
1066:Statistical signal processing
869:Quality improvement, such as
767:Statistical signal processing
731:, or spatiotemporal domains.
566:voltage-controlled amplifiers
556:. Nonlinear circuits include
357:Bell System Technical Journal
354:" which was published in the
350:wrote the influential paper "
1895:Spectral Analysis of Signals
1763:Spectral Analysis of Signals
1468:Polynomial Signal Processing
1289:. Prentice Hall. p. 1.
1081:Polynomial signal processing
1072:Linear time-invariant system
1030:Mathematical methods applied
1008:analog-to-digital converters
969:analog-to-digital conversion
1169:Algebraic signal processing
725:Nonlinear signal processing
266:spectral density estimation
2313:
2167:Discrete Fourier transform
2144:Matched Z-transform method
1892:P Stoica, R Moses (2005).
1652:Reynolds, John M. (2011).
1629:Cambridge University Press
967:(source coding, including
653:
570:voltage-controlled filters
525:
29:
2161:Discrete cosine transform
2058:Digital signal processing
1681:Patrick Gaydecki (2004).
1567:10.1016/j.dsp.2020.102795
1537:Digital Signal Processing
1494:Scharf, Louis L. (1991).
1312:Digital Signal Processing
1231:Sensitivity (electronics)
1189:Dynamic range compression
1023:Digital signal processors
797:Seismic signal processing
702:Infinite impulse response
674:digital signal processors
656:Digital signal processing
365:digital signal processing
2297:Telecommunication theory
2194:Post's inversion formula
2108:Digital image processing
1435:10.1109/SSP.2018.8450704
1400:Billings, S. A. (2013).
1184:Digital image processing
958:forward error correction
884:Source coding including
785:in the resulting image.
779:probability distribution
604:complex frequency domain
528:Analog signal processing
369:digital signal processor
343:of the 1940s and 1950s.
317:subjective video quality
2103:Audio signal processing
1906:Kay, Steven M. (1993).
1051:Time-frequency analysis
803:Audio signal processing
698:finite impulse response
309:scientific measurements
172:converting this article
116:more precise citations.
2023:– free online textbook
1036:Differential equations
996:, frequency domain or
825:Wireless communication
798:
694:fast Fourier transform
507:
458:
405:
375:Definition of a signal
279:electrical engineering
238:
36:Signalling (economics)
2292:Mass media technology
1687:. IET. pp. 40–.
1087:System identification
796:
508:
464:, a realization of a
459:
406:
235:electromagnetic waves
216:
2227:Anti-aliasing filter
2156:Constant-Q transform
2139:Advanced z-transform
1901:. NJ: Prentice Hall.
1769:. NJ: Prentice Hall.
1126:stochastic processes
1041:Recurrence relations
771:stochastic processes
646:into consideration.
471:
422:
404:{\displaystyle x(t)}
386:
371:chips in the 1980s.
305:altimetry processing
1959:Kainam Thomas Wong
1602:2001ISPM...18....8A
1559:2020DSP...10402795S
1117:Functional analysis
1057:Spectral estimation
860:image understanding
2184:Integral transform
2179:Impulse invariance
2151:Bilinear transform
1625:Applied geophysics
1211:Information theory
1089:and classification
1018:Signal compressors
1012:signal acquisition
998:stochastic filters
965:presentation layer
864:speech recognition
856:Feature extraction
799:
789:Application fields
773:, utilizing their
704:(IIR) filter, and
644:quantization error
633:analog delay lines
578:phase-locked loops
503:
466:stochastic process
454:
401:
337:numerical analysis
239:
174:, if appropriate.
2287:Signal processing
2274:
2273:
2199:Starred transform
2189:Laplace transform
2113:Speech processing
2082:Estimation theory
1996:978-0-13-022464-4
1974:978-0-470-25388-5
1874:978-0-521-76222-9
1847:978-1-107-01322-3
1820:978-0-19-102431-3
1793:978-1-139-48762-7
1721:978-1-84800-119-0
1694:978-0-85296-431-6
1667:978-0-471-48535-3
1638:978-0-521-33938-4
1610:10.1109/79.939833
1596:(4). IEEE: 8–20.
1477:978-0-471-03414-8
1444:978-1-5386-1571-3
1411:978-1-119-94359-4
1206:Fourier transform
1179:Bounded variation
1146:Numerical methods
1136:Estimation theory
963:OSI layer 6, the
952:OSI layer 2, the
902:signal processing
894:video compression
890:image compression
886:audio compression
879:echo cancellation
875:image enhancement
733:Nonlinear systems
333:Ronald W. Schafer
329:Alan V. Oppenheim
275:Signal processing
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32:Signalling theory
18:Signal Processing
16:(Redirected from
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1131:Detection theory
1103:Complex analysis
1076:transform theory
1046:Transform theory
973:data compression
919:frequency domain
836:Array processing
819:Video processing
813:Image processing
783:reduce the noise
706:adaptive filters
686:circular buffers
600:frequency domain
562:frequency mixers
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980:Typical devices
954:data link layer
871:noise reduction
842:Process control
831:Control systems
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672:or specialized
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625:sample and hold
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584:Continuous time
560:, multipliers (
546:additive mixers
538:passive filters
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1026:
1020:
1015:
1001:
981:
978:
977:
976:
961:
950:
935:physical layer
923:
922:
903:
897:
882:
867:
853:
848:
839:
833:
828:
822:
816:
810:
790:
787:
763:
760:
721:
718:
714:Kalman filters
700:(FIR) filter,
682:floating-point
654:Main article:
651:
648:
611:
608:
585:
582:
542:active filters
526:Main article:
523:
520:
518:
515:
514:
513:
500:
497:
494:
490:
484:
480:
476:
451:
448:
445:
441:
435:
431:
427:
416:
400:
397:
394:
391:
379:A signal is a
376:
373:
348:Claude Shannon
324:
321:
263:
262:
253:
252:
244:
243:
242:
241:
240:
209:
208:
191:
190:
156:
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147:
140:
139:
94:
92:
85:
80:
54:
53:
51:
44:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2309:
2298:
2295:
2293:
2290:
2288:
2285:
2284:
2282:
2267:
2264:
2262:
2261:Undersampling
2259:
2257:
2256:Sampling rate
2254:
2252:
2249:
2247:
2244:
2242:
2238:
2235:
2233:
2230:
2228:
2225:
2223:
2220:
2219:
2217:
2215:
2211:
2205:
2204:Zak transform
2202:
2200:
2197:
2195:
2192:
2190:
2187:
2185:
2182:
2180:
2177:
2174:
2171:
2168:
2165:
2162:
2159:
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2154:
2152:
2149:
2145:
2142:
2140:
2137:
2136:
2135:
2132:
2131:
2129:
2125:
2119:
2116:
2114:
2111:
2109:
2106:
2104:
2101:
2100:
2098:
2094:
2088:
2085:
2083:
2080:
2078:
2075:
2073:
2070:
2069:
2067:
2063:
2059:
2052:
2047:
2045:
2040:
2038:
2033:
2032:
2029:
2022:
2019:
2016:
2013:
2010:
2007:
2006:
2002:
1997:
1993:
1989:
1988:Babak Hassibi
1985:
1981:
1978:
1975:
1971:
1967:
1964:
1961:
1958:
1954:
1952:0-07-100870-5
1948:
1944:
1939:
1935:
1931:
1927:
1925:0-13-345711-7
1921:
1917:
1916:Prentice Hall
1913:
1909:
1904:
1897:
1896:
1890:
1889:
1885:
1876:
1870:
1866:
1865:
1857:
1854:
1849:
1843:
1839:
1838:
1830:
1827:
1822:
1816:
1812:
1811:
1803:
1800:
1795:
1789:
1785:
1784:
1776:
1773:
1765:
1764:
1756:
1753:
1748:
1746:0-08-044335-4
1742:
1738:
1731:
1728:
1723:
1717:
1713:
1712:
1704:
1701:
1696:
1690:
1686:
1685:
1677:
1674:
1669:
1663:
1659:
1655:
1648:
1645:
1640:
1634:
1630:
1626:
1619:
1616:
1611:
1607:
1603:
1599:
1595:
1591:
1584:
1581:
1576:
1572:
1568:
1564:
1560:
1556:
1551:
1546:
1542:
1538:
1531:
1528:
1523:
1519:
1515:
1513:0-201-19038-9
1509:
1505:
1501:
1497:
1490:
1488:
1484:
1479:
1473:
1469:
1462:
1459:
1454:
1450:
1446:
1440:
1436:
1432:
1428:
1421:
1418:
1413:
1407:
1403:
1396:
1394:
1390:
1387:
1381:
1378:
1370:
1369:
1362:
1360:
1356:
1345:
1341:
1335:
1332:
1327:
1325:0-13-214635-5
1321:
1318:. p. 5.
1317:
1316:Prentice Hall
1313:
1306:
1303:
1298:
1296:0-13-216771-9
1292:
1288:
1281:
1278:
1273:
1269:
1265:
1261:
1257:
1253:
1246:
1243:
1236:
1232:
1229:
1227:
1226:Reverberation
1224:
1222:
1219:
1217:
1214:
1212:
1209:
1207:
1204:
1202:
1198:
1194:
1190:
1187:
1185:
1182:
1180:
1177:
1175:
1172:
1170:
1167:
1166:
1162:
1157:
1154:
1152:
1149:
1147:
1144:
1142:
1139:
1137:
1134:
1132:
1129:
1127:
1123:
1120:
1118:
1115:
1113:
1109:
1108:Vector spaces
1106:
1104:
1101:
1099:
1096:
1094:
1091:
1088:
1085:
1082:
1079:
1077:
1073:
1070:
1067:
1064:
1062:
1058:
1055:
1052:
1049:
1047:
1044:
1042:
1039:
1037:
1034:
1033:
1029:
1024:
1021:
1019:
1016:
1013:
1009:
1005:
1002:
999:
995:
991:
987:
984:
983:
979:
974:
970:
966:
962:
959:
955:
951:
948:
944:
940:
936:
932:
928:
927:
926:
920:
916:
912:
908:
904:
901:
898:
895:
891:
887:
883:
880:
876:
872:
868:
865:
861:
857:
854:
852:
849:
847:
843:
840:
837:
834:
832:
829:
826:
823:
820:
817:
814:
811:
808:
804:
801:
800:
795:
788:
786:
784:
780:
776:
772:
768:
761:
759:
757:
752:
750:
746:
742:
738:
734:
730:
726:
719:
717:
715:
711:
707:
703:
699:
695:
691:
690:lookup tables
687:
683:
679:
675:
671:
667:
663:
657:
649:
647:
645:
640:
638:
634:
630:
626:
622:
618:
616:
610:Discrete time
609:
607:
605:
601:
597:
592:
590:
583:
581:
579:
575:
571:
567:
563:
559:
555:
551:
547:
543:
539:
535:
529:
521:
516:
498:
495:
492:
482:
478:
467:
449:
446:
443:
433:
429:
417:
414:
413:
412:
395:
389:
382:
374:
372:
370:
366:
361:
359:
358:
353:
349:
344:
342:
338:
334:
330:
327:According to
322:
320:
318:
314:
310:
306:
302:
298:
294:
290:
286:
285:
280:
276:
267:
236:
232:
228:
224:
220:
215:
205:
202:
187:
178:is available.
177:
173:
167:
166:
162:
157:This article
155:
146:
145:
136:
133:
125:
115:
111:
105:
104:
98:
93:
84:
83:
78:
76:
69:
68:
63:
62:
57:
52:
43:
42:
37:
33:
19:
2251:Quantization
2246:Oversampling
2237:Nyquist rate
2232:Downsampling
1984:Ali H. Sayed
1966:Ali H. Sayed
1942:
1907:
1894:
1863:
1856:
1836:
1829:
1809:
1802:
1782:
1775:
1762:
1755:
1736:
1730:
1710:
1703:
1683:
1676:
1653:
1647:
1624:
1618:
1593:
1589:
1583:
1540:
1536:
1530:
1495:
1467:
1461:
1426:
1420:
1401:
1380:
1367:
1347:. Retrieved
1343:
1334:
1311:
1305:
1286:
1280:
1255:
1251:
1245:
1201:noise gating
1174:Audio filter
1141:Optimization
1074:theory, and
947:multiplexing
943:equalization
924:
846:current loop
766:
765:
753:
749:subharmonics
737:bifurcations
723:
708:such as the
659:
641:
629:multiplexers
620:
619:
613:
593:
587:
531:
378:
362:
355:
345:
326:
282:
274:
273:
225:to electric
197:
181:
176:Editing help
158:
128:
122:January 2017
119:
100:
72:
65:
59:
58:Please help
55:
2134:Z-transform
1156:Data mining
1151:Time series
1122:Probability
1061:time series
915:time domain
911:time-series
775:statistical
762:Statistical
678:fixed-point
596:time domain
554:delay lines
550:integrators
219:Transducers
114:introducing
2281:Categories
2266:Upsampling
2127:Techniques
2096:Sub-fields
1550:2007.10729
1543:: 102795.
1349:2019-05-13
1237:References
1193:companding
939:modulation
921:, or both.
907:geophysics
858:, such as
851:Seismology
756:polynomial
558:compandors
517:Categories
287:, such as
97:references
61:improve it
2241:frequency
1575:220665533
1470:. Wiley.
1404:. Wiley.
931:OSI model
745:harmonics
729:frequency
720:Nonlinear
662:computers
496:∈
447:∈
346:In 1948,
223:waveforms
184:June 2017
67:talk page
2222:Aliasing
2214:Sampling
1934:26504848
1522:61160161
1453:52153144
1272:27286184
1197:limiting
1163:See also
1093:Calculus
1004:Samplers
949:, etc.);
809:or music
381:function
1598:Bibcode
1555:Bibcode
1000:, etc.)
986:Filters
900:Genomic
696:(FFT),
650:Digital
418:a path
323:History
284:signals
231:voltage
227:current
110:improve
2175:(DTFT)
2065:Theory
1994:
1986:, and
1972:
1949:
1932:
1922:
1871:
1844:
1817:
1790:
1743:
1718:
1691:
1664:
1635:
1573:
1520:
1510:
1500:Boston
1474:
1451:
1441:
1408:
1322:
1293:
1270:
1199:, and
1025:(DSPs)
933:, the
892:, and
877:, and
807:speech
747:, and
710:Wiener
602:, and
576:, and
552:, and
522:Analog
307:, and
293:images
277:is an
159:is in
99:, but
2169:(DFT)
2163:(DCT)
1899:(PDF)
1767:(PDF)
1571:S2CID
1545:arXiv
1449:S2CID
1372:(PDF)
741:chaos
666:ASICs
534:radio
289:sound
165:prose
1992:ISBN
1970:ISBN
1947:ISBN
1930:OCLC
1920:ISBN
1869:ISBN
1842:ISBN
1815:ISBN
1788:ISBN
1741:ISBN
1716:ISBN
1689:ISBN
1662:ISBN
1633:ISBN
1518:OCLC
1508:ISBN
1472:ISBN
1439:ISBN
1406:ISBN
1320:ISBN
1291:ISBN
1268:PMID
1124:and
1110:and
1098:Code
1010:for
1006:and
971:and
862:and
712:and
688:and
680:and
635:and
331:and
161:list
1606:doi
1563:doi
1541:104
1431:doi
1260:doi
994:IIR
990:FIR
917:or
905:In
568:),
229:or
34:or
2283::
2239:/
1982:,
1928:.
1918:.
1914::
1910:.
1660:.
1656:.
1631:.
1627:.
1604:.
1594:18
1592:.
1569:.
1561:.
1553:.
1539:.
1516:.
1506:.
1502::
1498:.
1486:^
1447:.
1437:.
1392:^
1358:^
1342:.
1314:.
1266:.
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668:,
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572:,
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299:,
295:,
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70:.
2050:e
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1998:.
1976:.
1955:.
1936:.
1877:.
1850:.
1823:.
1796:.
1749:.
1724:.
1697:.
1670:.
1641:.
1612:.
1608::
1600::
1577:.
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1299:.
1274:.
1262::
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426:(
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129:(
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20:)
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