387:
95:). Some software applications require normalized inputs and produce normalized outputs, which can be re-scaled to physical units when necessary. Mathematical derivations are usually done in normalized units, relevant to a wide range of applications.
648:
1159:
390:
Example of plotting samples of a frequency distribution in the unit "bins", which are integer values. A scale factor of 0.7812 converts a bin number into the corresponding physical unit (hertz).
1109:
979:
1213:
1039:
916:
184:
802:
856:
498:
431:
527:
719:
298:
598:
572:
343:
243:
134:
93:
683:
451:
208:
60:
378:
1348:
454:
1254:
603:
1117:
1061:
931:
1330:
1174:
383:. Therefore, the normalized frequency unit is important when converting normalized results into physical units.
31:
17:
987:
864:
139:
760:
1294:
464:
397:
300:
as the frequency reference, which changes the numeric range that represents frequencies of interest from
1286:
817:
503:
1299:
394:
A common practice is to sample the frequency spectrum of the sampled data at frequency intervals of
1353:
1312:
691:
190:
regardless of whether the original signal is a function of time or distance. For example, when
386:
262:
1329:
Taboga, Marco (2021). "Discrete
Fourier Transform - Frequencies", Lectures on matrix algebra.
1250:
576:
551:
257:
583:
557:
136:) that is used to create the digital signal from a continuous one. The normalized quantity,
1304:
1226:
303:
221:
112:
71:
662:
1290:
436:
193:
45:
351:
1342:
105:
64:
1316:
1272:"On the use of Windows for Harmonic Analysis with the Discrete Fourier Transform"
1271:
1331:
https://www.statlect.com/matrix-algebra/discrete-Fourier-transform-frequencies
1308:
461:) are numbered consecutively, corresponding to a frequency normalization by
39:
725:
256:
toolboxes) that design filters with real-valued coefficients prefer the
253:
211:
659:
The following table shows examples of normalized frequency for
62:) and a constant frequency associated with a system (such as a
1249:. Boston, MA: ©Houghton Mifflin Co. pp. 469, 490.
1133:
1083:
1003:
953:
880:
776:
619:
508:
469:
402:
319:
155:
1177:
1120:
1064:
990:
934:
867:
820:
763:
694:
665:
606:
600:
is normalized with reference to the sampling rate as
586:
560:
506:
467:
439:
400:
354:
306:
265:
224:
196:
142:
115:
74:
48:
103:
A typical choice of characteristic frequency is the
643:{\displaystyle \omega '={\tfrac {\omega }{f_{s}}},}
1207:
1154:{\displaystyle \omega '={\tfrac {\omega }{f_{s}}}}
1153:
1103:
1033:
973:
910:
850:
796:
713:
677:
642:
592:
566:
521:
492:
445:
425:
372:
337:
292:
237:
202:
178:
128:
87:
54:
18:Normalized frequency (digital signal processing)
27:Frequency divided by a characteristic frequency
1104:{\displaystyle f=f'\cdot {\tfrac {f_{s}}{N}}}
974:{\displaystyle f=f'\cdot {\tfrac {f_{s}}{2}}}
8:
650:the normalized Nyquist angular frequency is
457:). The samples (sometimes called frequency
1208:{\displaystyle \omega =\omega '\cdot f_{s}}
1298:
1199:
1176:
1142:
1132:
1119:
1089:
1082:
1063:
1019:
1013:
1002:
989:
959:
952:
933:
896:
890:
879:
866:
842:
819:
785:
775:
762:
699:
693:
664:
628:
618:
605:
585:
559:
507:
505:
475:
468:
466:
438:
408:
401:
399:
353:
318:
305:
279:
273:
264:
229:
223:
195:
164:
154:
141:
120:
114:
79:
73:
47:
1034:{\displaystyle f'={\tfrac {f}{f_{s}/N}}}
911:{\displaystyle f'={\tfrac {f}{f_{s}/2}}}
730:
385:
1237:
179:{\displaystyle f'={\tfrac {f}{f_{s}}},}
797:{\displaystyle f'={\tfrac {f}{f_{s}}}}
7:
728:), and 4 normalization conventions:
580:, can be similarly normalized. When
500:The normalized Nyquist frequency is
493:{\displaystyle {\tfrac {f_{s}}{N}}.}
426:{\displaystyle {\tfrac {f_{s}}{N}},}
25:
1247:Signal and Linear System Analysis
1270:Harris, Fredric J. (Jan 1978).
851:{\displaystyle f=f'\cdot f_{s}}
522:{\displaystyle {\tfrac {N}{2}}}
367:
355:
287:
266:
1:
1169:1000 × 2π / 44100 = 0.14250
1245:Carlson, Gordon E. (1992).
714:{\displaystyle f_{s}=44100}
433:for some arbitrary integer
1370:
1349:Digital signal processing
293:{\displaystyle (f_{s}/2)}
99:Examples of normalization
38:is a ratio of a variable
32:digital signal processing
455:§ Sampling the DTFT
1309:10.1109/PROC.1978.10837
1279:Proceedings of the IEEE
926:1000 / 22050 = 0.04535
812:1000 / 44100 = 0.02268
593:{\displaystyle \omega }
567:{\displaystyle \omega }
252:Some programs (such as
1209:
1155:
1105:
1035:
975:
912:
852:
798:
715:
679:
644:
594:
568:
523:
494:
447:
427:
391:
374:
339:
294:
239:
204:
180:
130:
89:
56:
1210:
1156:
1106:
1036:
976:
913:
853:
799:
716:
680:
645:
595:
569:
524:
495:
448:
428:
389:
375:
340:
338:{\displaystyle \left}
295:
240:
238:{\displaystyle f_{s}}
205:
181:
131:
129:{\displaystyle f_{s}}
90:
88:{\displaystyle f_{s}}
57:
1175:
1118:
1062:
988:
932:
865:
818:
761:
692:
663:
604:
584:
558:
504:
465:
437:
398:
352:
304:
263:
222:
194:
140:
113:
72:
46:
36:normalized frequency
1291:1978IEEEP..66...51H
732:
678:{\displaystyle f=1}
1205:
1163:
1151:
1149:
1101:
1099:
1053:/ 44100 = 0.02268
1043:
1031:
1029:
971:
969:
920:
908:
906:
848:
806:
794:
792:
731:
724:(often denoted by
711:
675:
640:
635:
590:
577:radians per second
574:and with the unit
564:
519:
517:
490:
485:
443:
423:
418:
392:
370:
335:
328:
290:
247:samples per second
235:
200:
176:
171:
126:
85:
52:
1218:
1217:
1148:
1098:
1028:
968:
922:half-cycle/sample
905:
791:
634:
552:Angular frequency
516:
484:
446:{\displaystyle N}
417:
381:half-cycle/sample
327:
258:Nyquist frequency
216:cycles per second
203:{\displaystyle f}
170:
55:{\displaystyle f}
16:(Redirected from
1361:
1334:
1327:
1321:
1320:
1302:
1276:
1267:
1261:
1260:
1242:
1227:Prototype filter
1214:
1212:
1211:
1206:
1204:
1203:
1191:
1160:
1158:
1157:
1152:
1150:
1147:
1146:
1134:
1128:
1110:
1108:
1107:
1102:
1100:
1094:
1093:
1084:
1078:
1056:
1052:
1040:
1038:
1037:
1032:
1030:
1027:
1023:
1018:
1017:
1004:
998:
980:
978:
977:
972:
970:
964:
963:
954:
948:
917:
915:
914:
909:
907:
904:
900:
895:
894:
881:
875:
857:
855:
854:
849:
847:
846:
834:
803:
801:
800:
795:
793:
790:
789:
777:
771:
733:
720:
718:
717:
712:
704:
703:
684:
682:
681:
676:
655:
653:π radians/sample
649:
647:
646:
641:
636:
633:
632:
620:
614:
599:
597:
596:
591:
573:
571:
570:
565:
544:
542:
541:
538:
535:
528:
526:
525:
520:
518:
509:
499:
497:
496:
491:
486:
480:
479:
470:
452:
450:
449:
444:
432:
430:
429:
424:
419:
413:
412:
403:
379:
377:
376:
373:{\displaystyle }
371:
344:
342:
341:
336:
334:
330:
329:
320:
299:
297:
296:
291:
283:
278:
277:
245:is expressed in
244:
242:
241:
236:
234:
233:
210:is expressed in
209:
207:
206:
201:
188:cycle per sample
185:
183:
182:
177:
172:
169:
168:
156:
150:
135:
133:
132:
127:
125:
124:
94:
92:
91:
86:
84:
83:
61:
59:
58:
53:
21:
1369:
1368:
1364:
1363:
1362:
1360:
1359:
1358:
1339:
1338:
1337:
1328:
1324:
1300:10.1.1.649.9880
1274:
1269:
1268:
1264:
1257:
1244:
1243:
1239:
1235:
1223:
1195:
1184:
1173:
1172:
1138:
1121:
1116:
1115:
1085:
1071:
1060:
1059:
1054:
1050:
1009:
1008:
991:
986:
985:
955:
941:
930:
929:
886:
885:
868:
863:
862:
838:
827:
816:
815:
781:
764:
759:
758:
695:
690:
689:
661:
660:
651:
624:
607:
602:
601:
582:
581:
556:
555:
539:
536:
533:
532:
530:
502:
501:
471:
463:
462:
435:
434:
404:
396:
395:
350:
349:
311:
307:
302:
301:
269:
261:
260:
225:
220:
219:
192:
191:
160:
143:
138:
137:
116:
111:
110:
101:
75:
70:
69:
44:
43:
28:
23:
22:
15:
12:
11:
5:
1367:
1365:
1357:
1356:
1351:
1341:
1340:
1336:
1335:
1322:
1262:
1255:
1236:
1234:
1231:
1230:
1229:
1222:
1219:
1216:
1215:
1202:
1198:
1194:
1190:
1187:
1183:
1180:
1170:
1167:
1165:radians/sample
1161:
1145:
1141:
1137:
1131:
1127:
1124:
1112:
1111:
1097:
1092:
1088:
1081:
1077:
1074:
1070:
1067:
1057:
1047:
1041:
1026:
1022:
1016:
1012:
1007:
1001:
997:
994:
982:
981:
967:
962:
958:
951:
947:
944:
940:
937:
927:
924:
918:
903:
899:
893:
889:
884:
878:
874:
871:
859:
858:
845:
841:
837:
833:
830:
826:
823:
813:
810:
804:
788:
784:
780:
774:
770:
767:
755:
754:
749:
744:
739:
722:samples/second
710:
707:
702:
698:
674:
671:
668:
639:
631:
627:
623:
617:
613:
610:
589:
563:
529:with the unit
515:
512:
489:
483:
478:
474:
442:
422:
416:
411:
407:
369:
366:
363:
360:
357:
333:
326:
323:
317:
314:
310:
289:
286:
282:
276:
272:
268:
232:
228:
199:
175:
167:
163:
159:
153:
149:
146:
123:
119:
100:
97:
82:
78:
51:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1366:
1355:
1352:
1350:
1347:
1346:
1344:
1332:
1326:
1323:
1318:
1314:
1310:
1306:
1301:
1296:
1292:
1288:
1284:
1280:
1273:
1266:
1263:
1258:
1252:
1248:
1241:
1238:
1232:
1228:
1225:
1224:
1220:
1200:
1196:
1192:
1188:
1185:
1181:
1178:
1171:
1168:
1166:
1162:
1143:
1139:
1135:
1129:
1125:
1122:
1114:
1113:
1095:
1090:
1086:
1079:
1075:
1072:
1068:
1065:
1058:
1048:
1046:
1042:
1024:
1020:
1014:
1010:
1005:
999:
995:
992:
984:
983:
965:
960:
956:
949:
945:
942:
938:
935:
928:
925:
923:
919:
901:
897:
891:
887:
882:
876:
872:
869:
861:
860:
843:
839:
835:
831:
828:
824:
821:
814:
811:
809:
805:
786:
782:
778:
772:
768:
765:
757:
756:
753:
750:
748:
745:
743:
742:Numeric range
740:
738:
735:
734:
729:
727:
726:44.1 kHz
723:
708:
705:
700:
696:
687:
672:
669:
666:
657:
654:
637:
629:
625:
621:
615:
611:
608:
587:
579:
578:
561:
554:, denoted by
553:
549:
547:
513:
510:
487:
481:
476:
472:
460:
456:
440:
420:
414:
409:
405:
388:
384:
382:
364:
361:
358:
347:
331:
324:
321:
315:
312:
308:
284:
280:
274:
270:
259:
255:
250:
248:
230:
226:
217:
213:
197:
189:
186:has the unit
173:
165:
161:
157:
151:
147:
144:
121:
117:
108:
107:
106:sampling rate
98:
96:
80:
76:
67:
66:
65:sampling rate
49:
41:
37:
33:
19:
1325:
1285:(1): 51–83.
1282:
1278:
1265:
1246:
1240:
1164:
1044:
921:
808:cycle/sample
807:
751:
746:
741:
736:
721:
685:
658:
652:
575:
550:
546:cycle/sample
545:
458:
393:
380:
346:cycle/sample
345:
251:
246:
215:
187:
104:
102:
63:
35:
29:
747:Calculation
1343:Categories
1256:8170232384
1233:References
1354:Frequency
1295:CiteSeerX
1193:⋅
1186:ω
1179:ω
1136:ω
1123:ω
1080:⋅
950:⋅
836:⋅
622:ω
609:ω
588:ω
562:ω
40:frequency
34:(DSP), a
1221:See also
1189:′
1126:′
1076:′
996:′
946:′
873:′
832:′
769:′
737:Quantity
612:′
148:′
1287:Bibcode
1049:1000 ×
752:Reverse
543:
531:
1317:426548
1315:
1297:
1253:
254:MATLAB
1313:S2CID
1275:(PDF)
709:44100
453:(see
1251:ISBN
1045:bins
459:bins
1305:doi
686:kHz
348:to
218:),
30:In
1345::
1311:.
1303:.
1293:.
1283:66
1281:.
1277:.
688:,
656:.
548:.
249:.
212:Hz
68:,
1333:.
1319:.
1307::
1289::
1259:.
1201:s
1197:f
1182:=
1144:s
1140:f
1130:=
1096:N
1091:s
1087:f
1073:f
1069:=
1066:f
1055:N
1051:N
1025:N
1021:/
1015:s
1011:f
1006:f
1000:=
993:f
966:2
961:s
957:f
943:f
939:=
936:f
902:2
898:/
892:s
888:f
883:f
877:=
870:f
844:s
840:f
829:f
825:=
822:f
787:s
783:f
779:f
773:=
766:f
706:=
701:s
697:f
673:1
670:=
667:f
638:,
630:s
626:f
616:=
540:N
537:/
534:1
514:2
511:N
488:.
482:N
477:s
473:f
441:N
421:,
415:N
410:s
406:f
368:]
365:1
362:,
359:0
356:[
332:]
325:2
322:1
316:,
313:0
309:[
288:)
285:2
281:/
275:s
271:f
267:(
231:s
227:f
214:(
198:f
174:,
166:s
162:f
158:f
152:=
145:f
122:s
118:f
109:(
81:s
77:f
50:f
42:(
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
