Bark: Difference between revisions

Latest revision as of 19:43, 17 February 2007

The Bark is the standard unit corresponding to one of the 24 critical bands representing the width of human hearing system. Human hearing critical bands are narrow at low frequencies, but become wider at higher frequencies.

(in Hz) $0,100,200,300,400,510,630,770,920,1080,1270,1480,1720,2000,2320,2700,3150,3700,4400,5300,6400,7700,9500,12000,15500$

converting a f to it's bark equivalent:

$Bark=13\cdot \arctan {\left({\frac {0.0076f}{1000}}\right)}+3.5\cdot \arctan {\left({\frac {f}{7500}}\right)^{2}}$

Figure: Human hearing critical bands versus Layer 3 32 equal width subbands

Example: Widths of the critical bands gets wider towards the higher frequencies. MP3 32 equal width subbands (shown on top), based upon PQF filterbank cover the 22.05kHz bandwidth. The width of 1 MP3 subband is about $689Hz(32*689=22.05kHz)$ . Ogg Vorbis uses Bark Scale mapping in it's filterbank decomposition. Both Bark and ERB bilinear transforms are equivalent in representing the critical bands of human auditory system.

References

Smith, O. Julius. Abel, Johnathen. "Bark and ERB Bilinear Transforms". Dec 1999

<http://citeseer.ist.psu.edu/smith99bark.html> (17 Feb 2007)

Smith, O. Julius. "The Bark Frequency Scale (condensed)". 3 Jan. 2006.

<http://ccrma.stanford.edu/~jos/bbt/Bark_Frequency_Scale.html> (17 Feb 2007)

@@ Line 1: / Line 1: @@
-The bark is the standard unit corresponding to one of the 24 [[critical bands]] representing the width of human hearing system. Human hearing critical bands are narrow at low [[frequency|frequencies]], but become wider at higher [[frequency|frequencies]].
+The ''Bark'' is the standard unit corresponding to one of the 24 [[critical band|critical bands]] representing the width of human hearing system. Human hearing critical bands are narrow at low [[frequency|frequencies]], but become wider at higher [[frequency|frequencies]].
-(in Hz) 0, 100, 200, 300, 400, 510, 630, 770, 920, 1080, 1270, 1480, 1720, 2000, 2320, 2700, 3150, 3700, 4400, 5300, 6400, 7700, 9500, 12000, 15500
+''(in Hz) <math>0, 100, 200, 300, 400, 510, 630, 770, 920, 1080, 1270, 1480, 1720, 2000, 2320, 2700, 3150, 3700, 4400, 5300, 6400, 7700, 9500, 12000, 15500 </math>''
-converting a ''f'' to it's bark equivalent:
+converting a ''f''  to it's bark equivalent:
-<math>Bark = 13*\arctan{(0.76f / 1000)} + 3.5*\arctan{((f / 7500)^2)}</math>
+<math>Bark = 13 \cdot \arctan{\left( \frac{0.0076f}{1000} \right)} + 3.5 \cdot \arctan{\left( \frac{f} {7500} \right)^2}</math>
 [[Image:Cribands.png|none|frame|Figure: Human hearing critical bands versus Layer 3 32 equal width subbands]]
-Example: Widths of the [[critical band|critical bands]] gets wider towards the higher [[frequency|frequencies]]. [[MP3]] 32 equal width [[subband|subbands]] (shown on top), based upon PQF filterbank cover the 22.05kHz [[bandwidth]]. The width of 1 [[MP3]] [[subband]] is about 689Hz (32*689=22.05kHz). Both Bark and ERB bilinear transforms are equivalent in representing the critical bands of human auditory system.
+Example: Widths of the [[critical band|critical bands]] gets wider towards the higher [[frequency|frequencies]]. [[MP3]] 32 equal width [[subband|subbands]] (shown on top), based upon PQF filterbank cover the 22.05kHz [[bandwidth]]. The width of 1 [[MP3]] [[subband]] is about <math> 689Hz (32*689=22.05kHz)</math>. [[Ogg Vorbis]] uses Bark Scale mapping in it's filterbank decomposition. Both Bark and ERB bilinear transforms are equivalent in representing the critical bands of human auditory system.
-==Additional Reading:==
+==References==
-* [http://citeseer.ist.psu.edu/smith99bark.html Bark and ERB Bilinear Transforms, Julius O. Smith (1999)]
+* Smith, O. Julius. Abel, Johnathen. "Bark and ERB Bilinear Transforms". Dec 1999
-* [http://ccrma.stanford.edu/~jos/bbt/Bark_Frequency_Scale.html The Bark Frequency Scale (condensed), Julius O. Smith (2005)]
+:<http://citeseer.ist.psu.edu/smith99bark.html> (17 Feb 2007)
+* Smith, O. Julius. "The Bark Frequency Scale (condensed)". 3 Jan. 2006.
+:<http://ccrma.stanford.edu/~jos/bbt/Bark_Frequency_Scale.html> (17 Feb 2007)
+[[Category:Psychoacoustics]]