88:
256:
247:
214:
794:
47:
150:
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
1158: – for statistical analysis of relations between large quantities of variables (in this context representing many physical signals), to extract previously unknown interesting patterns
1014:
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.
511:
462:
642:
The concept of discrete-time signal processing also refers to a theoretical discipline that establishes a mathematical basis for digital signal processing, without taking
409:
1682:
2048:
777:
properties to perform signal processing tasks. Statistical techniques are widely used in signal processing applications. For example, one can model the
1535:
Sarangi, Susanta; Sahidullah, Md; Saha, Goutam (September 2020). "Optimization of data-driven filterbank for automatic speaker verification".
639:. This technology was a predecessor of digital signal processing (see below), and is still used in advanced processing of gigahertz signals.
17:
360:. The paper laid the groundwork for later development of information communication systems and the processing of signals for transmission.
536:, telephone, and television systems. This involves linear electronic circuits as well as nonlinear ones. The former are, for instance,
1250:
Sengupta, Nandini; Sahidullah, Md; Saha, Goutam (August 2016). "Lung sound classification using cepstral-based statistical features".
2041:
339:
techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital
351:
660:
Digital signal processing is the processing of digitized discrete-time sampled signals. Processing is done by general-purpose
1995:
1973:
1872:
1845:
1818:
1791:
1719:
1692:
1665:
1636:
1475:
1442:
1409:
2086:
617:
is for sampled signals, defined only at discrete points in time, and as such are quantized in time, but not in magnitude.
591:
is for signals that vary with the change of continuous domain (without considering some individual interrupted points).
2034:
60:
684:, real-valued and complex-valued, multiplication and addition. Other typical operations supported by the hardware are
2296:
2076:
1950:
1923:
1744:
1511:
1323:
1294:
200:
131:
109:
74:
102:
2250:
2231:
1068: – analyzing and extracting information from signals and noise based on their stochastic properties
2172:
1835:
1215:
1425:
Slawinska, J.; Ourmazd, A.; Giannakis, D. (2018). "A New
Approach to Signal Processing of Spatiotemporal Data".
758:
systems may be interpreted as conceptually straightforward extensions of linear systems to the non-linear case.
2291:
1911:
636:
1781:
1059: – for determining the spectral content (i.e., the distribution of power over frequency) of a
2117:
1065:
942:
669:
573:
356:
2213:
1080:
1071:
1003:
968:
565:
1808:
2193:
1168:
1007:
265:
727:
involves the analysis and processing of signals produced from nonlinear systems and can be in the time,
2286:
2166:
2143:
1628:
1339:
985:
470:
421:
2160:
2057:
1384:
Berber, S. (2021). Discrete
Communication Systems. United Kingdom: Oxford University Press., page 9,
1230:
1188:
701:
655:
569:
364:
1783:
Statistical Signal
Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals
1368:
Fifty Years of Signal
Processing: The IEEE Signal Processing Society and its Technologies, 1948–1998
2107:
1402:
Nonlinear System
Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains
1183:
1022:
957:
885:
806:
778:
673:
527:
368:
316:
96:
1366:
2102:
1050:
802:
697:
308:
288:
1035:
824:
781:
of noise incurred when photographing an image, and construct techniques based on this model to
693:
677:
380:
278:
113:
66:
35:
1810:
Machine
Learning for Signal Processing: Data Science, Algorithms, and Computational Statistics
532:
Analog signal processing is for signals that have not been digitized, as in most 20th-century
1086:
1385:
2226:
2155:
2138:
1597:
1554:
1125:
614:
234:
171:
844: – a variety of signals are used, including the industry standard 4-20 mA
385:
8:
1116:
1056:
1040:
859:
1601:
1558:
2183:
2178:
2150:
1570:
1544:
1503:
1448:
1210:
964:
863:
855:
770:
736:
643:
465:
336:
300:
1083: – analysis of systems which relate input and output using polynomials
264:
The signal on the left looks like noise, but the signal processing technique known as
2240:
2198:
2188:
2112:
2081:
1991:
1969:
1946:
1929:
1919:
1868:
1841:
1814:
1787:
1740:
1715:
1688:
1661:
1632:
1574:
1517:
1507:
1471:
1438:
1405:
1319:
1290:
1267:
1263:
1205:
1178:
1145:
1135:
997:
893:
889:
878:
874:
732:
632:
603:
588:
577:
553:
332:
328:
31:
1962:: Statistical Signal Processing lecture notes at the University of Waterloo, Canada.
1452:
2071:
1605:
1562:
1430:
1259:
1130:
1102:
1075:
1045:
1017:
1011:
972:
918:
835:
818:
812:
724:
599:
545:
296:
292:
226:
1862:
1709:
1657:
1220:
953:
870:
841:
830:
782:
705:
685:
624:
561:
1684:
Foundations of
Digital Signal Processing: Theory, Algorithms and Hardware Design
1979:
1111:
934:
681:
537:
347:
340:
1566:
1496:
Statistical signal processing: detection, estimation, and time series analysis
827: – waveform generations, demodulation, filtering, equalization
754:
Polynomial signal processing is a type of non-linear signal processing, where
2280:
2260:
2255:
2203:
2020:
1987:
1915:
1434:
1315:
1225:
1107:
713:
709:
541:
2026:
1933:
1521:
913:
measurements of geophysical data. Processing is conducted within either the
815: – in digital cameras, computers and various imaging systems
2245:
2236:
1983:
1965:
1271:
1200:
1173:
1140:
946:
845:
748:
740:
689:
312:
213:
175:
793:
2133:
1960:
1893:
1761:
1155:
1150:
1121:
1060:
914:
910:
774:
628:
595:
319:, and to detect or pinpoint components of interest in a measured signal.
2265:
1737:
Time frequency signal analysis and processing a comprehensive reference
1284:
1192:
993:
989:
938:
906:
850:
755:
549:
218:
1609:
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.
1424:
930:
744:
728:
557:
363:
Signal processing matured and flourished in the 1960s and 1970s, and
304:
164:
1623:
Telford, William Murray; Geldart, L. P.; Sheriff, Robert E. (1990).
1465:
1309:
335:, the principles of signal processing can be found in the classical
2221:
2011:– free online textbook by Paolo Prandoni and Martin Vetterli (2008)
1833:
1549:
1196:
1092:
661:
311:. Signal processing techniques are used to optimize transmissions,
222:
160:
1249:
1534:
899:
230:
1860:
1779:
838: – for processing signals from arrays of sensors
1499:
283:
281:
subfield that focuses on analyzing, modifying and synthesizing
533:
237:, received and converted by another transducer to final form.
751:
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:
1097:
665:
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
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
1622:
1588:
Anastassiou, D. (2001). "Genomic signal processing".
676:(DSP chips). Typical arithmetical operations include
473:
424:
388:
623:
is a technology based on electronic devices such as
233:
waveforms, which then are processed, transmitted as
1711:
Digital Signal Processing: An Experimental Approach
1466:V. John Mathews; Giovanni L. Sicuranza (May 2000).
821: – for interpreting moving pictures
1773:
505:
456:
403:
315:efficiency, correcting distorted signals, improve
1734:
2278:
1854:
1707:
1680:
1285:Alan V. Oppenheim and Ronald W. Schafer (1989).
1310:Oppenheim, Alan V.; Schafer, Ronald W. (1975).
1029:
735:can produce highly complex behaviors including
1990:, Linear Estimation, Prentice-Hall, NJ, 2000,
1834:Steven B. Damelin; Willard Miller, Jr (2012).
2056:
2042:
1908:Fundamentals of Statistical Signal Processing
1827:
1806:
1701:
1674:
1861:Daniel P. Palomar; Yonina C. Eldar (2010).
1759:
1587:
1374:. The IEEE Signal Processing Society. 1998.
75:Learn how and when to remove these messages
2049:
2035:
1800:
1395:
1393:
1714:. Springer Science & Business Media.
1548:
1489:
1487:
594:The methods of signal processing include
374:
201:Learn how and when to remove this message
132:Learn how and when to remove this message
1940:
1891:
1651:
1399:
792:
212:
95:This article includes a list of general
2017:– free online textbook by Stephen Smith
1760:Stoica, Petre; Moses, Randolph (2005).
1390:
1361:
1359:
769:is an approach which treats signals as
14:
2279:
1493:
1484:
621:Analog discrete-time signal processing
352:A Mathematical Theory of Communication
2030:
1968:, Adaptive Filters, Wiley, NJ, 2008,
788:
2009:Signal Processing for Communications
1837:The Mathematics of Signal Processing
1356:
367:became widely used with specialized
221:convert signals from other physical
143:
81:
40:
1905:
1739:(1 ed.). Amsterdam: Elsevier.
1708:Shlomo Engelberg (8 January 2008).
24:
1885:
1418:
979:
583:
101:it lacks sufficient corresponding
25:
2308:
2002:
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
609:
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.
1753:
1735:Boashash, Boualem, ed. (2003).
1728:
1645:
1616:
1590:IEEE Signal Processing Magazine
1581:
1528:
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.
1459:
1378:
1332:
1303:
1278:
1243:
761:
670:field-programmable gate arrays
574:voltage-controlled oscillators
488:
474:
439:
425:
398:
392:
163:format but may read better as
13:
1:
2118:Statistical signal processing
1941:Papoulis, Athanasios (1991).
1236:
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
516:
357:Bell System Technical Journal
354:" which was published in the
350:wrote the influential paper "
18:Statistical signal processing
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
719:
7:
1169:Algebraic signal processing
1162:
725:Nonlinear signal processing
266:spectral density estimation
10:
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:
649:
570:voltage-controlled filters
525:
322:
29:
2212:
2161:Discrete cosine transform
2126:
2095:
2064:
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
521:
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
211:
210:
203:
193:
192:
142:
141:
134:
79:
32:Signalling theory
16:(Redirected from
2304:
2072:Detection theory
2051:
2044:
2037:
2028:
2027:
1956:
1937:
1902:
1900:
1879:
1878:
1858:
1852:
1851:
1831:
1825:
1824:
1804:
1798:
1797:
1777:
1771:
1770:
1768:
1757:
1751:
1750:
1732:
1726:
1725:
1705:
1699:
1698:
1678:
1672:
1671:
1649:
1643:
1642:
1620:
1614:
1613:
1585:
1579:
1578:
1552:
1532:
1526:
1525:
1491:
1482:
1481:
1463:
1457:
1456:
1422:
1416:
1415:
1397:
1388:
1382:
1376:
1375:
1373:
1363:
1354:
1353:
1351:
1350:
1344:Computer History
1336:
1330:
1329:
1307:
1301:
1300:
1282:
1276:
1275:
1247:
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
512:
510:
509:
504:
502:
501:
486:
485:
463:
461:
460:
455:
453:
452:
437:
436:
410:
408:
407:
402:
297:potential fields
258:
257:
249:
248:
206:
199:
188:
185:
179:
170:You can help by
152:
151:
144:
137:
130:
126:
123:
117:
112:this article by
103:inline citations
90:
89:
82:
71:
49:
48:
41:
21:
2312:
2311:
2307:
2306:
2305:
2303:
2302:
2301:
2277:
2276:
2275:
2270:
2208:
2122:
2091:
2077:Discrete signal
2060:
2055:
2005:
1953:
1926:
1898:
1888:
1886:Further reading
1883:
1882:
1875:
1859:
1855:
1848:
1832:
1828:
1821:
1805:
1801:
1794:
1778:
1774:
1766:
1758:
1754:
1747:
1733:
1729:
1722:
1706:
1702:
1695:
1679:
1675:
1668:
1658:Wiley-Blackwell
1650:
1646:
1639:
1621:
1617:
1586:
1582:
1533:
1529:
1514:
1492:
1485:
1478:
1464:
1460:
1445:
1423:
1419:
1412:
1398:
1391:
1383:
1379:
1371:
1365:
1364:
1357:
1348:
1346:
1338:
1337:
1333:
1326:
1308:
1304:
1297:
1283:
1279:
1248:
1244:
1239:
1221:Non-local means
1165:
1032:
982:
980:Typical devices
954:data link layer
871:noise reduction
842:Process control
831:Control systems
791:
764:
722:
672:or specialized
658:
652:
625:sample and hold
612:
586:
584:Continuous time
560:, multipliers (
546:additive mixers
538:passive filters
530:
524:
519:
491:
487:
481:
477:
472:
469:
468:
442:
438:
432:
428:
423:
420:
419:
387:
384:
383:
377:
341:control systems
325:
313:digital storage
301:seismic signals
272:
271:
270:
269:
261:
260:
259:
255:
251:
250:
246:
207:
196:
195:
194:
189:
183:
180:
169:
153:
149:
138:
127:
121:
118:
108:Please help to
107:
91:
87:
50:
46:
39:
28:
23:
22:
15:
12:
11:
5:
2310:
2300:
2299:
2294:
2289:
2272:
2271:
2269:
2268:
2263:
2258:
2253:
2248:
2243:
2234:
2229:
2224:
2218:
2216:
2210:
2209:
2207:
2206:
2201:
2196:
2191:
2186:
2181:
2176:
2170:
2164:
2158:
2153:
2148:
2147:
2146:
2141:
2130:
2128:
2124:
2123:
2121:
2120:
2115:
2110:
2105:
2099:
2097:
2093:
2092:
2090:
2089:
2084:
2079:
2074:
2068:
2066:
2062:
2061:
2054:
2053:
2046:
2039:
2031:
2025:
2024:
2018:
2012:
2004:
2003:External links
2001:
2000:
1999:
1980:Thomas Kailath
1977:
1963:
1957:
1951:
1938:
1924:
1903:
1887:
1884:
1881:
1880:
1873:
1853:
1846:
1826:
1819:
1813:. OUP Oxford.
1799:
1792:
1772:
1752:
1745:
1727:
1720:
1700:
1693:
1673:
1666:
1644:
1637:
1615:
1580:
1527:
1512:
1504:Addison–Wesley
1483:
1476:
1458:
1443:
1417:
1410:
1389:
1377:
1355:
1331:
1324:
1302:
1295:
1277:
1258:(1): 118–129.
1241:
1240:
1238:
1235:
1234:
1233:
1228:
1223:
1218:
1213:
1208:
1203:
1186:
1181:
1176:
1171:
1164:
1161:
1160:
1159:
1153:
1148:
1143:
1138:
1133:
1128:
1119:
1114:
1112:Linear algebra
1105:
1100:
1095:
1090:
1084:
1078:
1069:
1063:
1054:
1048:
1043:
1038:
1031:
1028:
1027:
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:
154:
147:
140:
139:
94:
92:
85:
80:
54:
53:
51:
44:
26:
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:
2157:
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:
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:
1876:
1870:
1866:
1865:
1857:
1849:
1843:
1839:
1838:
1830:
1822:
1816:
1812:
1811:
1803:
1795:
1789:
1785:
1784:
1776:
1765:
1764:
1756:
1748:
1746:0-08-044335-4
1742:
1738:
1731:
1723:
1717:
1713:
1712:
1704:
1696:
1690:
1686:
1685:
1677:
1669:
1663:
1659:
1655:
1648:
1640:
1634:
1630:
1626:
1619:
1611:
1607:
1603:
1599:
1595:
1591:
1584:
1576:
1572:
1568:
1564:
1560:
1556:
1551:
1546:
1542:
1538:
1531:
1523:
1519:
1515:
1513:0-201-19038-9
1509:
1505:
1501:
1497:
1490:
1488:
1479:
1473:
1469:
1462:
1454:
1450:
1446:
1440:
1436:
1432:
1428:
1421:
1413:
1407:
1403:
1396:
1394:
1387:
1381:
1370:
1369:
1362:
1360:
1345:
1341:
1335:
1327:
1325:0-13-214635-5
1321:
1318:. p. 5.
1317:
1316:Prentice Hall
1313:
1306:
1298:
1296:0-13-216771-9
1292:
1288:
1281:
1273:
1269:
1265:
1261:
1257:
1253:
1246:
1242:
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:
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:
1024:
1021:
1019:
1016:
1013:
1009:
1005:
1002:
999:
995:
991:
987:
984:
983:
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:
786:
784:
780:
776:
772:
768:
759:
757:
752:
750:
746:
742:
738:
734:
730:
726:
717:
715:
711:
707:
703:
699:
695:
691:
690:lookup tables
687:
683:
679:
675:
671:
667:
663:
657:
647:
645:
640:
638:
634:
630:
626:
622:
618:
616:
610:Discrete time
607:
605:
601:
597:
592:
590:
581:
579:
575:
571:
567:
563:
559:
555:
551:
547:
543:
539:
535:
529:
498:
495:
492:
482:
478:
467:
449:
446:
443:
433:
429:
417:
414:
413:
412:
395:
389:
382:
372:
370:
366:
361:
359:
358:
353:
349:
344:
342:
338:
334:
330:
327:According to
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:.
1256:75
1254:.
1195:,
1191:,
992:,
975:).
960:);
945:,
941:,
888:,
873:,
743:,
739:,
716:.
668:,
631:,
598:,
580:.
572:,
564:,
548:,
544:,
540:,
303:,
299:,
295:,
291:,
70:.
2050:e
2043:t
2036:v
1998:.
1976:.
1955:.
1936:.
1877:.
1850:.
1823:.
1796:.
1749:.
1724:.
1697:.
1670:.
1641:.
1612:.
1608::
1600::
1577:.
1565::
1557::
1547::
1524:.
1480:.
1455:.
1433::
1414:.
1352:.
1328:.
1299:.
1274:.
1262::
956:(
937:(
896:.
881:.
866:.
499:T
493:t
489:)
483:t
479:X
475:(
450:T
444:t
440:)
434:t
430:x
426:(
399:)
396:t
393:(
390:x
204:)
198:(
186:)
182:(
168:.
135:)
129:(
124:)
120:(
106:.
77:)
73:(
38:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.