17:
75:. A high spectral flatness (approaching 1.0 for white noise) indicates that the spectrum has a similar amount of power in all spectral bands — this would sound similar to white noise, and the graph of the spectrum would appear relatively flat and smooth. A low spectral flatness (approaching 0.0 for a pure tone) indicates that the spectral power is concentrated in a relatively small number of bands — this would typically sound like a mixture of
382:
112:
377:{\displaystyle \mathrm {Flatness} ={\frac {\sqrt{\prod _{n=0}^{N-1}x(n)}}{\frac {\sum _{n=0}^{N-1}x(n)}{N}}}={\frac {\exp \left({\frac {1}{N}}\sum _{n=0}^{N-1}\ln x(n)\right)}{{\frac {1}{N}}\sum _{n=0}^{N-1}x(n)}}}
427:
research, it has been used as one of the features measured on birdsong audio, when testing similarity between two excerpts. Spectral flatness has also been used in the analysis of
582:
Tchernichovski, O., Nottebohm, F., Ho, C. E., Pesaran, B., Mitra, P. P., 2000. A procedure for an automated measurement of song similarity. Animal
Behaviour 59 (6), 1167–1176,
557:"Wiener entropy is an alternative measure of the noisiness of a signal. It is defined as the ratio of the geometric mean to the arithmetic mean of the power spectrum."
602:"Burns & Rajan (2015) Combining complexity measures of EEG data: multiplying measures reveal previously hidden information. F1000Research. 4:137"
653:"A Mathematical Approach to Correlating Objective Spectro-Temporal Features of Non-linguistic Sounds With Their Subjective Perceptions in Humans"
566:
398:. Note that a single (or more) empty bin yields a flatness of 0, so this measure is most useful when bins are generally not empty.
713:
542:
708:
428:
408:
The spectral flatness can also be measured within a specified sub-band, rather than across the whole band.
492:
Shlomo Dubnov (2004). "Generalization of
Spectral Flatness Measure for Non-Gaussian Linear Processes".
36:
554:
452:
J. D. Johnston (1988). "Transform coding of audio signals using perceptual noise criteria".
501:
82:
Dubnov has shown that spectral flatness is equivalent to information theoretic concept of
8:
505:
679:
652:
628:
601:
525:
469:
83:
684:
633:
517:
424:
529:
674:
664:
623:
613:
583:
509:
473:
461:
618:
67:
in this context is in the sense of the amount of peaks or resonant structure in a
432:
103:
99:
68:
702:
669:
521:
513:
688:
637:
587:
545:"defined as the ratio of geometric mean to arithmetic mean of the spectrum"
405:
scale for reporting, with a maximum of 0 dB and a minimum of −∞ dB.
72:
16:
392:
76:
48:
20:
Maximum spectral flatness (approaching 1) is achieved by white noise.
465:
44:
40:
416:
This measurement is one of the many audio descriptors used in the
402:
417:
401:
The ratio produced by this calculation is often converted to a
47:, and provides a way to quantify how much a sound resembles a
570:
52:
487:
485:
483:
420:
standard, in which it is labelled "AudioSpectralFlatness".
480:
115:
98:
The spectral flatness is calculated by dividing the
567:
A Large Set of Audio
Features for Sound Description
376:
700:
454:IEEE Journal on Selected Areas in Communications
451:
491:
43:. Spectral flatness is typically measured in
650:
599:
678:
668:
627:
617:
445:
79:, and the spectrum would appear "spiky".
15:
543:The Song Features › Wiener entropy
701:
71:, as opposed to the flat spectrum of
13:
138:
135:
132:
129:
126:
123:
120:
117:
14:
725:
58:
569:- technical report published by
411:
644:
593:
576:
560:
548:
536:
431:diagnostics and research, and
368:
362:
312:
306:
233:
227:
185:
179:
93:
1:
651:Burns, T.; Rajan, R. (2019).
619:10.12688/f1000research.6590.1
600:Burns, T.; Rajan, R. (2015).
438:
106:of the power spectrum, i.e.:
102:of the power spectrum by the
714:Spectrum (physical sciences)
429:electroencephalography (EEG)
391:represents the magnitude of
7:
10:
730:
709:Digital signal processing
657:Frontiers in Neuroscience
494:Signal Processing Letters
39:to characterize an audio
37:digital signal processing
670:10.3389/fnins.2019.00794
514:10.1109/LSP.2004.831663
35:, is a measure used in
588:10.1006/anbe.1999.1416
378:
358:
296:
223:
175:
88:dual total correlation
51:, as opposed to being
21:
379:
332:
270:
197:
149:
19:
573:in 2003. Section 9.1
113:
29:tonality coefficient
555:Luscinia parameters
506:2004ISPL...11..698D
374:
84:mutual information
22:
372:
330:
268:
241:
240:
194:
86:that is known as
25:Spectral flatness
721:
693:
692:
682:
672:
648:
642:
641:
631:
621:
597:
591:
580:
574:
564:
558:
552:
546:
540:
534:
533:
489:
478:
477:
449:
383:
381:
380:
375:
373:
371:
357:
346:
331:
323:
320:
319:
315:
295:
284:
269:
261:
247:
242:
236:
222:
211:
195:
193:
188:
174:
163:
147:
146:
141:
31:, also known as
729:
728:
724:
723:
722:
720:
719:
718:
699:
698:
697:
696:
649:
645:
598:
594:
581:
577:
565:
561:
553:
549:
541:
537:
490:
481:
450:
446:
441:
433:psychoacoustics
414:
347:
336:
322:
321:
285:
274:
260:
259:
255:
248:
246:
212:
201:
196:
189:
164:
153:
148:
145:
116:
114:
111:
110:
104:arithmetic mean
96:
63:The meaning of
61:
12:
11:
5:
727:
717:
716:
711:
695:
694:
643:
592:
575:
559:
547:
535:
500:(8): 698–701.
479:
466:10.1109/49.608
460:(2): 314–332.
443:
442:
440:
437:
413:
410:
385:
384:
370:
367:
364:
361:
356:
353:
350:
345:
342:
339:
335:
329:
326:
318:
314:
311:
308:
305:
302:
299:
294:
291:
288:
283:
280:
277:
273:
267:
264:
258:
254:
251:
245:
239:
235:
232:
229:
226:
221:
218:
215:
210:
207:
204:
200:
192:
187:
184:
181:
178:
173:
170:
167:
162:
159:
156:
152:
144:
140:
137:
134:
131:
128:
125:
122:
119:
100:geometric mean
95:
92:
69:power spectrum
60:
59:Interpretation
57:
33:Wiener entropy
9:
6:
4:
3:
2:
726:
715:
712:
710:
707:
706:
704:
690:
686:
681:
676:
671:
666:
662:
658:
654:
647:
639:
635:
630:
625:
620:
615:
611:
607:
606:F1000Research
603:
596:
589:
585:
579:
572:
568:
563:
556:
551:
544:
539:
531:
527:
523:
519:
515:
511:
507:
503:
499:
495:
488:
486:
484:
475:
471:
467:
463:
459:
455:
448:
444:
436:
434:
430:
426:
421:
419:
409:
406:
404:
399:
397:
396:
390:
365:
359:
354:
351:
348:
343:
340:
337:
333:
327:
324:
316:
309:
303:
300:
297:
292:
289:
286:
281:
278:
275:
271:
265:
262:
256:
252:
249:
243:
237:
230:
224:
219:
216:
213:
208:
205:
202:
198:
190:
182:
176:
171:
168:
165:
160:
157:
154:
150:
142:
109:
108:
107:
105:
101:
91:
89:
85:
80:
78:
74:
70:
66:
56:
54:
50:
46:
42:
38:
34:
30:
26:
18:
660:
656:
646:
609:
605:
595:
578:
562:
550:
538:
497:
493:
457:
453:
447:
422:
415:
412:Applications
407:
400:
394:
388:
386:
97:
87:
81:
64:
62:
32:
28:
24:
23:
435:in humans.
393:bin number
94:Formulation
73:white noise
703:Categories
439:References
77:sine waves
522:1070-9908
352:−
334:∑
301:
290:−
272:∑
253:
217:−
199:∑
169:−
151:∏
49:pure tone
689:31417350
638:26594331
530:14778866
425:birdsong
45:decibels
41:spectrum
680:6685481
663:: 794.
629:4648221
612:: 137.
502:Bibcode
474:5999699
403:decibel
55:-like.
687:
677:
636:
626:
528:
520:
472:
418:MPEG-7
387:where
571:IRCAM
526:S2CID
470:S2CID
65:tonal
53:noise
685:PMID
634:PMID
518:ISSN
389:x(n)
675:PMC
665:doi
624:PMC
614:doi
584:doi
510:doi
462:doi
423:In
250:exp
27:or
705::
683:.
673:.
661:13
659:.
655:.
632:.
622:.
608:.
604:.
524:.
516:.
508:.
498:11
496:.
482:^
468:.
456:.
298:ln
90:.
691:.
667::
640:.
616::
610:4
590:.
586::
532:.
512::
504::
476:.
464::
458:6
395:n
369:)
366:n
363:(
360:x
355:1
349:N
344:0
341:=
338:n
328:N
325:1
317:)
313:)
310:n
307:(
304:x
293:1
287:N
282:0
279:=
276:n
266:N
263:1
257:(
244:=
238:N
234:)
231:n
228:(
225:x
220:1
214:N
209:0
206:=
203:n
191:N
186:)
183:n
180:(
177:x
172:1
166:N
161:0
158:=
155:n
143:=
139:s
136:s
133:e
130:n
127:t
124:a
121:l
118:F
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
