Frequency group

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With frequency groups (plural, English critical bands ) in the human is called listening frequency ranges that are evaluated together. An evaluation in frequency groups takes place z. B. in determining the volume , the sound or the direction of the sound . An exception is the evaluation of the pitch itself: here the frequency resolution is much greater (see pitch resolution ).

In German, the reverse translation of the critical frequency bandwidth from English often appears . However, it appears imprecise and not in the sense of the original definitions in the specialist literature (see e.g. Zwicker1961, JASA).

The human ear divides the audible frequencies into about 24 frequency groups. A frequency group includes here

  • at frequencies below 500  Hz a frequency range of about 100 Hz,
  • at frequencies above 500 Hz the frequency range of a minor third , which corresponds to a frequency ratio of .

This classification is described by the Bark scale , on which a frequency group is just 1 Bark wide. See also ERB scale and Mel scale .

table

Number of
the band
in Bark 		Lower
frequency limit
in Hz		 Upper
frequency limit
in Hz		 Bandwidth
in Hz
1 0 100 100
2 100 200 100
3 200 300 100
4th 300 400 100
5 400 510 110
6th 510 630 120
7th 630 770 140
8th 770 920 150
9 920 1080 160
10 1080 1270 190
11 1270 1480 210
12 1480 1720 240
13 1720 2000 280
14th 2000 2320 320
15th 2320 2700 380
16 2700 3150 450
17th 3150 3700 550
18th 3700 4400 700
19th 4400 5300 900
20th 5300 6400 1100
21st 6400 7700 1300
22nd 7700 9500 1800
23 9500 12000 2500
24 12000 15500 3500

education

In the brain

Since the 1980s it has become increasingly clear that the probable cause of the frequency groups is localized in the auditory midbrain . There the neurons and the catchment area of ​​their dendrites are arranged in layers ( laminae ) in the central core of the inferior colliculus . Here there is a fine scaling according to acoustic frequencies in the area of ​​a layer , while a coarse scaling is present from layer to layer at the distance of a frequency group. This has been demonstrated anatomically and physiologically in cats , mice and rats .

Historical theory: in the inner ear

Relationship between frequency group, location on the basilar membrane, tonality in mel and frequency

The concept of the frequency group with its origin in the inner ear was developed by Harvey Fletcher in the 1940s. It was based solely on psychoacoustic data; anatomical or physiological data were not yet available. Since then, no observations have been made that could support this localization.

The formation of the frequency groups is based on the conversion of sound into nerve impulses in the inner ear. The different frequencies of the sound are converted by the basilar membrane in the inner ear into deflection maxima at different positions and excite the nerve cells located here . Each of them is responsible for a different pitch sensation.

According to the above In theory, the length of the basilar membrane is divided into 24 equally long sections to form the frequency groups, and the nerve impulses from each of these sections are evaluated together.

The width of the frequency groups can be expressed in units of the subjective pitch:

1 frequency group = 100 mel = 1.3 mm on the basilar membrane

Signal processing

The formation of frequency groups corresponds to a filtering of the sound signals:

  • up to a frequency of 500 Hz through 100 Hz wide filters
  • at higher frequencies the filters are approximately the width of a third octave ( third octave filter ).

From the point of view of signal processing , the hearing follows an optimal compromise with this choice of frequency groups (details see below):

  • With at least 100 Hz, the frequency groups are wide enough that a quick evaluation of the sound signals is possible with a response time of 10 ms.
  • On the other hand, the frequency groups are narrow enough (at most a minor third) that an easy analysis of signal phases and envelopes is possible in order to determine the direction of sound incidence .

reaction time

Every filter needs a certain amount of time to settle . This time is inversely proportional to the bandwidth of the filter.

The frequency group filters of the hearing with a minimum bandwidth of 100 Hz therefore require a maximum of 1/100 Hz = 10 ms to settle . That means: the sound impression is only stable 10 ms after the onset of a sound signal, only then can the hearing rely on the information.

An evaluation with narrower frequency groups would mean that the hearing would have to wait longer until reliable acoustic information is available.

Direction determination

The direction of a sound source to determine the enhanced hearing , the phase and the envelope of the signals in the frequency groups.

This is only particularly easy if the signals in the frequency groups have the character of modulated sinusoidal signals . The following must be fulfilled for this:

  • So that an evaluation of the phase is not made more difficult by overtones , a frequency group must be much narrower than an octave , since the first (possible) overtone is one octave above the fundamental.
  • the envelope curve, measured at the center frequency of the frequency group, may only change relatively slowly so that it can be evaluated. For this purpose, the bandwidth of the frequency group must be significantly smaller than the frequencies it contains, i. that is, it must remain well below half an octave.

Both boundary conditions are met with a frequency group width of a minor third (a quarter of an octave).

Technical application

Audio data compression methods such as MP3 mimic the processing of human hearing. Here, too, the signals are processed in frequency groups, removing all information that the hearing cannot perceive within the frequency groups. This leads to a considerable reduction in the data rate .

literature

  • Eberhard Zwicker, Hugo Fastl: Psychoacoustics Facts and Models . ISBN 3-540-65063-6 .
  • Eberhard Zwicker: Subdivision of the Audible Frequency Range into Critical Bands (frequency groups) . In: J. Acoust. Soc. At the. , Volume 33, Issue 2, February 1961, pp. 248-248; doi: 10.1121 / 1.1908630 .

Individual evidence

  1. ^ CE Schreiner, G. Langner: Laminar fine structure of frequency organization in auditory midbrain. In: Nature. Volume 388, Number 6640, July 1997, ISSN  0028-0836 , pp. 383-386, doi: 10.1038 / 41106 , PMID 9237756 .
  2. ↑ M. Egorova, G. Ehret: Tonotopy and inhibition in the midbrain inferior colliculus shape spectral resolution of sounds in neural critical bands. In: The European journal of neuroscience. Volume 28, Number 4, August 2008, ISSN  1460-9568 , pp. 675-692, doi: 10.1111 / j.1460-9568.2008.06376.x , PMID 18702690 .
  3. ↑ MS Malmierca, MA Izquierdo, S. Cristaudo, O. Hernández, D. Pérez-González, E. Covey, DL Oliver: A discontinuous tonotopic organization in the inferior colliculus of the rat. In: The Journal of neuroscience: the official journal of the Society for Neuroscience. Volume 28, number 18, April 2008, ISSN  1529-2401 , pp. 4767-4776, doi: 10.1523 / JNEUROSCI.0238-08.2008 , PMID 18448653 , PMC 2440588 (free full text).