295:
42:
2303:
1712:
634:
the difficulty of constructing an antenna to meet a specified absolute bandwidth is easier at a higher frequency than at a lower frequency. For this reason, bandwidth is often quoted relative to the frequency of operation which gives a better indication of the structure and sophistication needed for
1265:
While the geometric mean is more rarely used than the arithmetic mean (and the latter can be assumed if not stated explicitly) the former is considered more mathematically rigorous. It more properly reflects the logarithmic relationship of fractional bandwidth with increasing frequency. For
214:
For other applications, there are other definitions. One definition of bandwidth, for a system, could be the range of frequencies over which the system produces a specified level of performance. A less strict and more practically useful definition will refer to the frequencies beyond which
2061:
1261:
1100:
498:
models of communication systems, the signal spectrum consists of both negative and positive frequencies, can lead to confusion about bandwidth since they are sometimes referred to only by the positive half, and one will occasionally see expressions such as
1635:
1555:
993:
1439:
1368:
1166:
1639:
Percent bandwidth is a less meaningful measure in wideband applications. A percent bandwidth of 100% corresponds to a ratio bandwidth of 3:1. All higher ratios up to infinity are compressed into the range 100â200%.
916:
398:
systems. To say that a system has a certain bandwidth means that the system can process signals with that range of frequencies, or that the system reduces the bandwidth of a white noise input to that bandwidth.
445:
the gain is not specified. In this case, the filter bandwidth corresponds to the passband width, which in this example is the 1 dB-bandwidth. If the filter shows amplitude ripple within the passband, the
1171:
998:
761:
1702:
414:. If the maximum gain is 0 dB, the 3 dB bandwidth is the frequency range where attenuation is less than 3 dB. 3 dB attenuation is also where power is half its maximum. This same
406:
or communication channel is the part of the system's frequency response that lies within 3 dB of the response at its peak, which, in the passband filter case, is typically at or near its
2298:{\displaystyle B_{n}={\frac {\int _{-\infty }^{\infty }|H(f)|^{2}df}{2|H(0)|^{2}}}={\frac {\int _{-\infty }^{\infty }|h(t)|^{2}dt}{2\left|\int _{-\infty }^{\infty }h(t)dt\right|^{2}}}\,.}
377:
1476:
856:
819:
790:
702:
669:
340:
1560:
548:
is the total bandwidth (i.e. the maximum passband bandwidth of the carrier-modulated RF signal and the minimum passband bandwidth of the physical passband channel), and
1481:
927:
1380:
1930:
1891:
1960:
1740:
2338:
2054:
2025:
1989:
1848:
1819:
1769:
1307:
526:
2593:
1302:
1821:
is the bandwidth of an ideal filter with rectangular frequency response centered on the system's central frequency that produces the same average power outgoing
1111:
610:
590:
566:
546:
861:
314:(in W/Hz or V/Hz) is nonzero or above a small threshold value. The threshold value is often defined relative to the maximum value, and is most commonly the
30:
This article is about the concept in signal theory and processing measured in hertz. For use in computing and networking expressed in bits per second, see
1274:
applications they diverge substantially with the arithmetic mean version approaching 2 in the limit and the geometric mean version approaching infinity.
2363:
the bandwidth of the output of some light source, e.g., an ASE source or a laser; the bandwidth of ultrashort optical pulses can be particularly large
379:, is 70.7% of its maximum). This figure, with a lower threshold value, can be used in calculations of the lowest sampling rate that will satisfy the
568:
is the positive bandwidth (the baseband bandwidth of the equivalent channel model). For instance, the baseband model of the signal would require a
268:
of a simple radar pulse is defined as the inverse of its duration. For example, a one-microsecond pulse has a
Rayleigh bandwidth of one megahertz.
707:
2673:
2515:
1654:
1270:
applications, there is only marginal difference between the two definitions. The geometric mean version is inconsequentially larger. For
2668:
2663:
2636:
2577:
2546:
196:
2372:
the width of the range of some other phenomenon, e.g., a reflection, the phase matching of a nonlinear process, or some resonance
1854:
source. The value of the noise equivalent bandwidth depends on the ideal filter reference gain used. Typically, this gain equals
2343:
The noise equivalent bandwidth is widely used to simplify the analysis of telecommunication systems in the presence of noise.
2615:
2491:
1651:) for wideband applications. An octave is a frequency ratio of 2:1 leading to this expression for the number of octaves,
466:
1256:{\displaystyle B_{\mathrm {F} }={\frac {f_{\mathrm {H} }-f_{\mathrm {L} }}{\sqrt {f_{\mathrm {H} }f_{\mathrm {L} }}}}\,.}
630:
The absolute bandwidth is not always the most appropriate or useful measure of bandwidth. For instance, in the field of
2455:
152:
1095:{\displaystyle B_{\mathrm {F} }={\frac {2(f_{\mathrm {H} }-f_{\mathrm {L} })}{f_{\mathrm {H} }+f_{\mathrm {L} }}}\,.}
2056:
is a lowpass system with zero central frequency and the filter reference gain is referred to this frequency, then:
2658:
423:
35:
345:
151:. For example, a 3 kHz band can carry a telephone conversation whether that band is at baseband (as in a
437:, the gain is nominally 0 dB with a small variation, for example within the ±1 dB interval. In the
2459:
2386:
1446:
484:
395:
320:, that is the point where the spectral density is half its maximum value (or the spectral amplitude, in
137:
121:
91:
31:
1992:
223:
below the maximum value or it could mean below a certain absolute value. As with any definition of the
832:
795:
766:
678:
645:
441:(s), the required attenuation in decibels is above a certain level, for example >100 dB. In a
204:
473:
2451:
2426:
2406:
625:
125:
65:
323:
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2394:
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216:
176:
148:
143:
A key characteristic of bandwidth is that any band of a given width can carry the same amount of
117:
83:
2366:
the width of the frequency range that can be transmitted by some element, e.g. an optical fiber
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2611:
2573:
2542:
2511:
2505:
2487:
2378:
the range of frequencies in which some measurement apparatus (e.g., a power meter) can operate
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to stay intact, and the physical passband channel would require a passband filter of at least
430:
403:
391:
200:
160:
129:
2538:
2532:
2375:
the maximum modulation frequency (or range of modulation frequencies) of an optical modulator
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Fractional bandwidth is defined as the absolute bandwidth divided by the center frequency (
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2314:
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2001:
1965:
1824:
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106:
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61:
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communications, for example, bandwidth is the frequency range occupied by a modulated
2652:
1277:
Fractional bandwidth is sometimes expressed as a percentage of the center frequency (
192:
1630:{\displaystyle B_{\mathrm {R} }={\frac {2+B_{\mathrm {F} }}{2-B_{\mathrm {F} }}}\,.}
1377:
Ratio bandwidth is defined as the ratio of the upper and lower limits of the band,
243:
235:
133:
17:
1550:{\displaystyle B_{\mathrm {F} }=2{\frac {B_{\mathrm {R} }-1}{B_{\mathrm {R} }+1}}}
1478:. The relationship between ratio bandwidth and fractional bandwidth is given by,
988:{\displaystyle f_{\mathrm {C} }={\frac {f_{\mathrm {H} }+f_{\mathrm {L} }}{2}}\ }
491:, the bandwidth refers to the frequency range within which the gain is non-zero.
1851:
1434:{\displaystyle B_{\mathrm {R} }={\frac {f_{\mathrm {H} }}{f_{\mathrm {L} }}}\,.}
480:
144:
113:
821:
are the upper and lower frequency limits respectively of the band in question.
1267:
479:, bandwidth refers to the 3 dB-bandwidth. In calculations of the maximum
316:
1363:{\displaystyle \%B_{\mathrm {F} }=100{\frac {\Delta f}{f_{\mathrm {C} }}}\,.}
159:
to some higher frequency. However, wide bandwidths are easier to obtain and
2421:
2411:
2352:
302:
illustrating the concept of â3 dB bandwidth at a gain of approximately 0.707
156:
57:
2307:
The same expression can be applied to bandpass systems by substituting the
1161:{\displaystyle f_{\mathrm {C} }={\sqrt {f_{\mathrm {H} }f_{\mathrm {L} }}}}
2629:
Simulation of
Communication Systems. Modeling, Methodology, and Techniques
2458:. Equal bandwidths can carry equal information only when subject to equal
199:
in the United States) may apportion the regionally available bandwidth to
2382:
2308:
1271:
495:
438:
434:
283:
in the frequency domain which contains most of the energy of the signal.
254:
239:
188:
100:
77:
46:
911:{\displaystyle B_{\mathrm {F} }={\frac {\Delta f}{f_{\mathrm {C} }}}\,.}
294:
195:
spans a limited range of frequencies. A government agency (such as the
220:
207:
do not mutually interfere. In this context, bandwidth is also known as
2484:
Microwave and
Millimeter-wave Remote Sensing for Security Applications
638:
There are two different measures of relative bandwidth in common use:
1644:
227:
of a function, many definitions are suitable for different purposes.
704:). In the following, the absolute bandwidth is defined as follows,
41:
2385:(e.g., in Gbit/s) achieved in an optical communication system; see
1710:
433:
design, a filter specification may require that within the filter
307:
293:
180:
112:
Bandwidth in hertz is a central concept in many fields, including
69:
40:
1893:
at its center frequency, but it can also equal the peak value of
1711:
1715:
Setup for the measurement of the noise equivalent bandwidth
756:{\displaystyle B=\Delta f=f_{\mathrm {H} }-f_{\mathrm {L} }}
1104:
However, the center frequency is sometimes defined as the
136:
and is one of the determinants of the capacity of a given
49:
bandwidth. Here the bandwidth equals the upper frequency.
219:, degradation could, for example, mean more than 3
2627:
Jeruchim, M. C.; Balaban, P.; Shanmugan, K. S. (2000).
1697:{\displaystyle \log _{2}\left(B_{\mathrm {R} }\right).}
2317:
2064:
2033:
2004:
1968:
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534:
505:
454: dB below the nominal passband gain rather than
450: dB point refers to the point where the gain is
348:
326:
109:
or baseband signal, which includes a zero frequency.
75:
It may refer more specifically to two subcategories:
422:, and more generally for the extent of functions as
310:
refers to the frequency range in which the signal's
45:Amplitude (a) vs. frequency (f) graph illustrating
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2297:
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2019:
1983:
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147:, regardless of where that band is located in the
2450:The information capacity of a channel depends on
472:In communication systems, in calculations of the
1962:can be calculated in the frequency domain using
920:The center frequency is usually defined as the
410:, and in the low-pass filter is at or near its
2568:Stutzman, Warren L.; Theiele, Gary A. (1998).
82:is the difference between the upper and lower
56:is the difference between the upper and lower
2608:The Art and Science of Ultrawideband Antennas
8:
924:of the upper and lower frequencies so that,
465:the bandwidth is the frequency at which the
105:is equal to the upper cutoff frequency of a
2507:A Practical Approach to Signals and Systems
2397:of the radiation emitted by excited atoms.
635:the circuit or device under consideration.
2592:: CS1 maint: location missing publisher (
2369:the gain bandwidth of an optical amplifier
306:In some contexts, the signal bandwidth in
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504:
372:{\displaystyle \mathrm {V/{\sqrt {Hz}}} }
358:
353:
349:
347:
327:
325:
164:
2537:(3rd ed.). Prentice-Hall. pp.
1991:or in the time domain by exploiting the
487:, and maximum bit rate according to the
215:performance is degraded. In the case of
2475:
2443:
1777:Spectral leakage § Noise bandwidth
253:for communication systems it refers to
2585:
2510:. John Wiley & Sons. p. 109.
1742:of the system with frequency response
1643:Ratio bandwidth is often expressed in
1850:when both systems are excited with a
386:The bandwidth is also used to denote
7:
1108:of the upper and lower frequencies,
626:Antenna measurement § Bandwidth
230:In the context of, for example, the
175:Bandwidth is a key concept in many
2486:, pp. 268-269, Artech House, 2012
2254:
2249:
2190:
2185:
2094:
2089:
1681:
1614:
1594:
1570:
1532:
1512:
1491:
1471:{\displaystyle B_{\mathrm {R} }:1}
1456:
1443:Ratio bandwidth may be notated as
1419:
1407:
1390:
1348:
1335:
1320:
1311:
1288:
1240:
1228:
1214:
1199:
1181:
1150:
1138:
1121:
1079:
1064:
1047:
1032:
1008:
970:
955:
937:
896:
883:
871:
842:
805:
776:
747:
732:
717:
688:
655:
572:with cutoff frequency of at least
363:
360:
350:
328:
163:at higher frequencies because the
25:
2631:(2nd ed.). Kluwer Academic.
2504:Sundararajan, D. (4 March 2009).
2454:level as well as bandwidth â see
1787:equivalent noise bandwidth (enbw)
458: dB below the maximum gain.
197:Federal Communications Commission
851:{\displaystyle f_{\mathrm {C} }}
814:{\displaystyle f_{\mathrm {L} }}
785:{\displaystyle f_{\mathrm {H} }}
697:{\displaystyle B_{\mathrm {R} }}
664:{\displaystyle B_{\mathrm {F} }}
622:Antenna (radio) § Bandwidth
238:, bandwidth typically refers to
2359:carries a variety of meanings:
1935:The noise equivalent bandwidth
279:is defined as the portion of a
64:. It is typically measured in
2531:Van Valkenburg, M. E. (1974).
2327:
2321:
2268:
2262:
2214:
2209:
2203:
2196:
2158:
2153:
2147:
2140:
2118:
2113:
2107:
2100:
2043:
2037:
2014:
2008:
1978:
1972:
1918:
1914:
1908:
1901:
1879:
1875:
1869:
1862:
1837:
1831:
1808:
1802:
1758:
1752:
1053:
1023:
402:The 3 dB bandwidth of an
1:
242:bandwidth. In the context of
2674:Spectrum (physical sciences)
2610:, p. 75, Artech House, 2015
494:The fact that in equivalent
469:drops 3 dB below peak.
335:{\displaystyle \mathrm {V} }
298:The magnitude response of a
418:convention is also used in
165:§ Fractional bandwidth
27:Range of usable frequencies
2690:
2572:(2nd ed.). New York.
1783:noise equivalent bandwidth
1774:
1707:Noise equivalent bandwidth
619:
424:full width at half maximum
36:Bandwidth (disambiguation)
29:
2669:Filter frequency response
2570:Antenna Theory and Design
2393:A related concept is the
461:In signal processing and
2664:Telecommunication theory
2456:ShannonâHartley theorem
2311:frequency response for
467:closed-loop system gain
2460:signal-to-noise ratios
2334:
2299:
2050:
2021:
1985:
1956:
1926:
1925:{\displaystyle |H(f)|}
1887:
1886:{\displaystyle |H(f)|}
1844:
1815:
1772:
1765:
1736:
1698:
1631:
1551:
1472:
1435:
1364:
1298:
1257:
1162:
1096:
989:
912:
852:
815:
786:
757:
698:
665:
606:
586:
562:
542:
522:
373:
336:
303:
203:holders so that their
122:digital communications
50:
34:. For other uses, see
2387:bandwidth (computing)
2335:
2300:
2051:
2022:
1986:
1957:
1955:{\displaystyle B_{n}}
1927:
1888:
1845:
1816:
1775:Further information:
1766:
1737:
1735:{\displaystyle B_{n}}
1714:
1699:
1632:
1552:
1473:
1436:
1365:
1299:
1258:
1163:
1097:
990:
913:
853:
816:
787:
758:
699:
666:
607:
587:
563:
543:
523:
485:Nyquist sampling rate
396:communication channel
374:
337:
297:
236:Nyquist sampling rate
138:communication channel
92:communication channel
44:
32:Bandwidth (computing)
2333:{\displaystyle H(f)}
2315:
2062:
2049:{\displaystyle H(f)}
2031:
2020:{\displaystyle h(t)}
2002:
1984:{\displaystyle H(f)}
1966:
1939:
1897:
1858:
1843:{\displaystyle H(f)}
1825:
1814:{\displaystyle H(f)}
1796:
1764:{\displaystyle H(f)}
1746:
1719:
1655:
1561:
1482:
1447:
1381:
1308:
1285:
1172:
1112:
999:
928:
862:
833:
825:Fractional bandwidth
796:
767:
708:
679:
646:
640:fractional bandwidth
596:
576:
552:
532:
521:{\displaystyle B=2W}
503:
346:
324:
126:radio communications
2482:Jeffrey A. Nanzer,
2427:Spectral efficiency
2407:Bandwidth extension
2309:equivalent baseband
2258:
2194:
2098:
1297:{\displaystyle \%B}
275:essential bandwidth
244:Nyquist symbol rate
155:telephone line) or
86:of, for example, a
62:band of frequencies
18:Frequency bandwidth
2395:spectral linewidth
2330:
2295:
2241:
2177:
2081:
2046:
2017:
1993:Parseval's theorem
1981:
1952:
1922:
1883:
1840:
1811:
1791:frequency response
1773:
1761:
1732:
1694:
1627:
1547:
1468:
1431:
1360:
1294:
1253:
1158:
1092:
985:
908:
848:
811:
782:
753:
694:
661:
616:Relative bandwidth
602:
582:
558:
538:
518:
369:
332:
304:
264:Rayleigh bandwidth
217:frequency response
177:telecommunications
149:frequency spectrum
118:information theory
84:cutoff frequencies
51:
2659:Signal processing
2606:Hans G. Schantz,
2517:978-0-470-82354-5
2289:
2169:
1789:) of a system of
1621:
1545:
1425:
1354:
1279:percent bandwidth
1247:
1246:
1156:
1086:
984:
980:
902:
605:{\displaystyle B}
585:{\displaystyle W}
561:{\displaystyle W}
541:{\displaystyle B}
431:electronic filter
404:electronic filter
390:, for example in
366:
201:broadcast license
179:applications. In
130:signal processing
16:(Redirected from
2681:
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2624:
2618:
2604:
2598:
2597:
2591:
2583:
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2555:
2534:Network Analysis
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2055:
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2023:
2018:
1997:impulse response
1995:with the system
1990:
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1341:
1333:
1325:
1324:
1323:
1303:
1301:
1300:
1295:
1262:
1260:
1259:
1254:
1248:
1245:
1244:
1243:
1233:
1232:
1231:
1221:
1220:
1219:
1218:
1217:
1204:
1203:
1202:
1191:
1186:
1185:
1184:
1167:
1165:
1164:
1159:
1157:
1155:
1154:
1153:
1143:
1142:
1141:
1131:
1126:
1125:
1124:
1101:
1099:
1098:
1093:
1087:
1085:
1084:
1083:
1082:
1069:
1068:
1067:
1056:
1052:
1051:
1050:
1037:
1036:
1035:
1018:
1013:
1012:
1011:
994:
992:
991:
986:
982:
981:
976:
975:
974:
973:
960:
959:
958:
947:
942:
941:
940:
917:
915:
914:
909:
903:
901:
900:
899:
889:
881:
876:
875:
874:
857:
855:
854:
849:
847:
846:
845:
820:
818:
817:
812:
810:
809:
808:
791:
789:
788:
783:
781:
780:
779:
762:
760:
759:
754:
752:
751:
750:
737:
736:
735:
703:
701:
700:
695:
693:
692:
691:
670:
668:
667:
662:
660:
659:
658:
612:to stay intact.
611:
609:
608:
603:
591:
589:
588:
583:
567:
565:
564:
559:
547:
545:
544:
539:
527:
525:
524:
519:
477:channel capacity
412:cutoff frequency
408:center frequency
388:system bandwidth
381:sampling theorem
378:
376:
375:
370:
368:
367:
359:
357:
341:
339:
338:
333:
331:
319:
312:spectral density
300:band-pass filter
277:
276:
266:
265:
251:channel capacity
232:sampling theorem
88:band-pass filter
60:in a continuous
21:
2689:
2688:
2684:
2683:
2682:
2680:
2679:
2678:
2649:
2648:
2647:
2646:
2639:
2626:
2625:
2621:
2605:
2601:
2584:
2580:
2567:
2566:
2562:
2553:
2551:
2549:
2530:
2529:
2525:
2518:
2503:
2502:
2498:
2481:
2477:
2472:
2467:
2466:
2449:
2445:
2440:
2417:Noise bandwidth
2403:
2349:
2313:
2312:
2240:
2236:
2235:
2231:
2212:
2176:
2156:
2135:
2116:
2080:
2065:
2060:
2059:
2029:
2028:
2000:
1999:
1964:
1963:
1942:
1937:
1936:
1895:
1894:
1856:
1855:
1823:
1822:
1794:
1793:
1779:
1744:
1743:
1722:
1717:
1716:
1709:
1675:
1671:
1658:
1653:
1652:
1649:frequency level
1608:
1601:
1588:
1581:
1564:
1559:
1558:
1526:
1525:
1506:
1505:
1485:
1480:
1479:
1450:
1445:
1444:
1413:
1401:
1384:
1379:
1378:
1375:
1373:Ratio bandwidth
1342:
1334:
1314:
1306:
1305:
1283:
1282:
1234:
1222:
1208:
1193:
1192:
1175:
1170:
1169:
1144:
1132:
1115:
1110:
1109:
1073:
1058:
1057:
1041:
1026:
1019:
1002:
997:
996:
964:
949:
948:
931:
926:
925:
922:arithmetic mean
890:
882:
865:
860:
859:
836:
831:
830:
827:
799:
794:
793:
770:
765:
764:
741:
726:
706:
705:
682:
677:
676:
673:ratio bandwidth
649:
644:
643:
628:
618:
594:
593:
574:
573:
570:low-pass filter
550:
549:
530:
529:
501:
500:
474:ShannonâHartley
443:transition band
416:half-power gain
344:
343:
322:
321:
315:
292:
281:signal spectrum
274:
273:
263:
262:
248:Shannon-Hartley
209:channel spacing
173:
107:low-pass filter
96:signal spectrum
39:
28:
23:
22:
15:
12:
11:
5:
2687:
2685:
2677:
2676:
2671:
2666:
2661:
2651:
2650:
2645:
2644:
2637:
2619:
2599:
2578:
2560:
2547:
2523:
2516:
2496:
2474:
2473:
2471:
2468:
2465:
2464:
2442:
2441:
2439:
2436:
2435:
2434:
2432:Spectral width
2429:
2424:
2419:
2414:
2409:
2402:
2399:
2391:
2390:
2379:
2376:
2373:
2370:
2367:
2364:
2348:
2345:
2329:
2326:
2323:
2320:
2294:
2285:
2280:
2276:
2273:
2270:
2267:
2264:
2261:
2256:
2251:
2248:
2244:
2239:
2234:
2229:
2226:
2221:
2216:
2211:
2208:
2205:
2202:
2198:
2192:
2187:
2184:
2180:
2173:
2165:
2160:
2155:
2152:
2149:
2146:
2142:
2138:
2133:
2130:
2125:
2120:
2115:
2112:
2109:
2106:
2102:
2096:
2091:
2088:
2084:
2077:
2072:
2068:
2045:
2042:
2039:
2036:
2016:
2013:
2010:
2007:
1980:
1977:
1974:
1971:
1949:
1945:
1920:
1916:
1913:
1910:
1907:
1903:
1881:
1877:
1874:
1871:
1868:
1864:
1839:
1836:
1833:
1830:
1810:
1807:
1804:
1801:
1760:
1757:
1754:
1751:
1729:
1725:
1708:
1705:
1693:
1689:
1683:
1678:
1674:
1670:
1665:
1661:
1626:
1616:
1611:
1607:
1604:
1596:
1591:
1587:
1584:
1578:
1572:
1567:
1543:
1540:
1534:
1529:
1523:
1520:
1514:
1509:
1502:
1499:
1493:
1488:
1467:
1464:
1458:
1453:
1430:
1421:
1416:
1409:
1404:
1398:
1392:
1387:
1374:
1371:
1359:
1350:
1345:
1340:
1337:
1331:
1328:
1322:
1317:
1313:
1293:
1290:
1252:
1242:
1237:
1230:
1225:
1216:
1211:
1207:
1201:
1196:
1189:
1183:
1178:
1152:
1147:
1140:
1135:
1129:
1123:
1118:
1106:geometric mean
1091:
1081:
1076:
1072:
1066:
1061:
1055:
1049:
1044:
1040:
1034:
1029:
1025:
1022:
1016:
1010:
1005:
979:
972:
967:
963:
957:
952:
945:
939:
934:
907:
898:
893:
888:
885:
879:
873:
868:
844:
839:
826:
823:
807:
802:
778:
773:
749:
744:
740:
734:
729:
725:
722:
719:
716:
713:
690:
685:
657:
652:
617:
614:
601:
581:
557:
537:
517:
514:
511:
508:
463:control theory
420:spectral width
365:
362:
356:
352:
330:
291:
285:
185:carrier signal
172:
169:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2686:
2675:
2672:
2670:
2667:
2665:
2662:
2660:
2657:
2656:
2654:
2640:
2638:0-306-46267-2
2634:
2630:
2623:
2620:
2617:
2613:
2609:
2603:
2600:
2595:
2589:
2581:
2579:0-471-02590-9
2575:
2571:
2564:
2561:
2550:
2548:0-13-611095-9
2544:
2540:
2536:
2535:
2527:
2524:
2519:
2513:
2509:
2508:
2500:
2497:
2493:
2489:
2485:
2479:
2476:
2469:
2461:
2457:
2453:
2447:
2444:
2437:
2433:
2430:
2428:
2425:
2423:
2420:
2418:
2415:
2413:
2410:
2408:
2405:
2404:
2400:
2398:
2396:
2388:
2384:
2380:
2377:
2374:
2371:
2368:
2365:
2362:
2361:
2360:
2358:
2354:
2346:
2344:
2341:
2324:
2318:
2310:
2305:
2292:
2283:
2278:
2274:
2271:
2265:
2259:
2246:
2242:
2237:
2232:
2227:
2224:
2219:
2206:
2200:
2182:
2178:
2171:
2163:
2150:
2144:
2136:
2131:
2128:
2123:
2110:
2104:
2086:
2082:
2075:
2070:
2066:
2057:
2040:
2034:
2011:
2005:
1998:
1994:
1975:
1969:
1947:
1943:
1933:
1911:
1905:
1872:
1866:
1853:
1834:
1828:
1805:
1799:
1792:
1788:
1784:
1778:
1755:
1749:
1727:
1723:
1713:
1706:
1704:
1691:
1687:
1676:
1672:
1668:
1663:
1659:
1650:
1646:
1641:
1637:
1624:
1609:
1605:
1602:
1589:
1585:
1582:
1576:
1565:
1541:
1538:
1527:
1521:
1518:
1507:
1500:
1497:
1486:
1465:
1462:
1451:
1441:
1428:
1414:
1402:
1396:
1385:
1372:
1370:
1357:
1343:
1338:
1329:
1326:
1315:
1291:
1280:
1275:
1273:
1269:
1263:
1250:
1235:
1223:
1209:
1205:
1194:
1187:
1176:
1145:
1133:
1127:
1116:
1107:
1102:
1089:
1074:
1070:
1059:
1042:
1038:
1027:
1020:
1014:
1003:
977:
965:
961:
950:
943:
932:
923:
918:
905:
891:
886:
877:
866:
837:
824:
822:
800:
771:
742:
738:
727:
723:
720:
714:
711:
683:
674:
650:
641:
636:
633:
627:
623:
615:
613:
599:
579:
571:
555:
535:
515:
512:
509:
506:
497:
492:
490:
489:Hartley's law
486:
482:
478:
475:
470:
468:
464:
459:
457:
453:
449:
444:
440:
436:
432:
427:
425:
421:
417:
413:
409:
405:
400:
397:
393:
389:
384:
382:
354:
318:
313:
309:
301:
296:
289:
286:
284:
282:
278:
269:
267:
258:
256:
252:
249:
245:
241:
237:
233:
228:
226:
222:
218:
212:
210:
206:
202:
198:
194:
190:
186:
182:
178:
170:
168:
166:
162:
158:
154:
150:
146:
141:
139:
135:
131:
127:
123:
119:
115:
110:
108:
104:
102:
97:
93:
89:
85:
81:
79:
73:
72:(symbol Hz).
71:
67:
63:
59:
55:
48:
43:
37:
33:
19:
2628:
2622:
2607:
2602:
2569:
2563:
2552:. Retrieved
2533:
2526:
2506:
2499:
2483:
2478:
2446:
2392:
2356:
2350:
2342:
2306:
2058:
1934:
1786:
1782:
1780:
1647:(i.e., as a
1642:
1638:
1442:
1376:
1278:
1276:
1264:
1103:
919:
828:
672:
639:
637:
629:
493:
471:
460:
455:
451:
447:
428:
415:
401:
387:
385:
305:
290:dB bandwidth
287:
272:
270:
261:
259:
229:
224:
213:
174:
167:is smaller.
142:
134:spectroscopy
111:
99:
76:
74:
53:
52:
2355:, the term
1852:white noise
481:symbol rate
257:bandwidth.
191:receiver's
145:information
114:electronics
58:frequencies
2653:Categories
2616:1608079562
2554:2008-06-22
2492:1608071723
2470:References
1268:narrowband
620:See also:
317:3 dB point
2588:cite book
2422:Rise time
2412:Broadband
2383:data rate
2357:bandwidth
2353:photonics
2347:Photonics
2255:∞
2250:∞
2247:−
2243:∫
2191:∞
2186:∞
2183:−
2179:∫
2095:∞
2090:∞
2087:−
2083:∫
1669:
1606:−
1519:−
1336:Δ
1312:%
1289:%
1206:−
1039:−
884:Δ
739:−
718:Δ
157:modulated
103:bandwidth
80:bandwidth
54:Bandwidth
2401:See also
1272:wideband
632:antennas
528:, where
496:baseband
439:stopband
435:passband
426:(FWHM).
255:passband
240:baseband
189:FM radio
171:Overview
101:Baseband
78:Passband
47:baseband
2539:383â384
1645:octaves
205:signals
161:process
94:, or a
2635:
2614:
2576:
2545:
2514:
2490:
2027:. If
983:
763:where
671:) and
624:, and
483:, the
392:filter
132:, and
2452:noise
2438:Notes
308:hertz
225:width
193:tuner
187:. An
181:radio
70:hertz
2633:ISBN
2612:ISBN
2594:link
2574:ISBN
2543:ISBN
2512:ISBN
2488:ISBN
2381:the
1785:(or
1781:The
1557:and
1168:and
995:and
792:and
383:.
271:The
260:The
234:and
153:POTS
90:, a
66:unit
2351:In
2340:.
1932:.
1660:log
1330:100
1304:),
858:),
429:In
394:or
342:or
246:or
68:of
2655::
2590:}}
2586:{{
2541:.
1281:,
221:dB
211:.
140:.
128:,
124:,
120:,
116:,
98:.
2641:.
2596:)
2582:.
2557:.
2520:.
2494:.
2462:.
2389:.
2328:)
2325:f
2322:(
2319:H
2293:.
2284:2
2279:|
2275:t
2272:d
2269:)
2266:t
2263:(
2260:h
2238:|
2233:2
2228:t
2225:d
2220:2
2215:|
2210:)
2207:t
2204:(
2201:h
2197:|
2172:=
2164:2
2159:|
2154:)
2151:0
2148:(
2145:H
2141:|
2137:2
2132:f
2129:d
2124:2
2119:|
2114:)
2111:f
2108:(
2105:H
2101:|
2076:=
2071:n
2067:B
2044:)
2041:f
2038:(
2035:H
2015:)
2012:t
2009:(
2006:h
1979:)
1976:f
1973:(
1970:H
1948:n
1944:B
1919:|
1915:)
1912:f
1909:(
1906:H
1902:|
1880:|
1876:)
1873:f
1870:(
1867:H
1863:|
1838:)
1835:f
1832:(
1829:H
1809:)
1806:f
1803:(
1800:H
1771:.
1759:)
1756:f
1753:(
1750:H
1728:n
1724:B
1692:.
1688:)
1682:R
1677:B
1673:(
1664:2
1625:.
1615:F
1610:B
1603:2
1595:F
1590:B
1586:+
1583:2
1577:=
1571:R
1566:B
1542:1
1539:+
1533:R
1528:B
1522:1
1513:R
1508:B
1501:2
1498:=
1492:F
1487:B
1466:1
1463::
1457:R
1452:B
1429:.
1420:L
1415:f
1408:H
1403:f
1397:=
1391:R
1386:B
1358:.
1349:C
1344:f
1339:f
1327:=
1321:F
1316:B
1292:B
1251:.
1241:L
1236:f
1229:H
1224:f
1215:L
1210:f
1200:H
1195:f
1188:=
1182:F
1177:B
1151:L
1146:f
1139:H
1134:f
1128:=
1122:C
1117:f
1090:.
1080:L
1075:f
1071:+
1065:H
1060:f
1054:)
1048:L
1043:f
1033:H
1028:f
1024:(
1021:2
1015:=
1009:F
1004:B
978:2
971:L
966:f
962:+
956:H
951:f
944:=
938:C
933:f
906:.
897:C
892:f
887:f
878:=
872:F
867:B
843:C
838:f
806:L
801:f
777:H
772:f
748:L
743:f
733:H
728:f
724:=
721:f
715:=
712:B
689:R
684:B
675:(
656:F
651:B
642:(
600:B
580:W
556:W
536:B
516:W
513:2
510:=
507:B
456:x
452:x
448:x
364:z
361:H
355:/
351:V
329:V
288:x
38:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
