Critical band

With frequency groups ( plural), Eng. critical bands is called the human auditory frequency range, which are evaluated in common. In German, appeared more frequently the English back-translation "critical frequency bandwidth " on, but this phrase is rather imprecise and is not intended by the original definitions of the literature (see eg Zwicker1961, JASA ). A frequency evaluation in groups is effected for example, in determining the volume of the sound or the direction of the sound. An exception is the evaluation of the pitch, here, the frequency resolution is much larger.

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

• At frequencies below 500 Hz, a frequency range of approximately 100 Hz,
• At frequencies above 500 Hz, the frequency range of a minor third. This is a frequency ratio of 1:1,19.

The Bark scale describes the classification of the audible frequency range into critical bands. A frequency group here has the width of one Bark. See also the ERB scale and the Mel scale.

Formation of the frequency groups in the inner ear

Formation of the frequency groups based on the conversion of sound into nerve impulses in the inner ear. The different frequencies of sound are implemented by the basilar membrane in the inner ear to Auslenkungsmaxima at different spatial positions and excite nerve cells placed here. Each of these nerve cells is responsible for a different pitch sensations.

For the formation of the frequency groups, the length of the basilar membrane in 24 sections of equal length is divided, and the nerve impulses are evaluated together from each of these sections.

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

Signal processing aspects

The formation of groups of frequencies corresponding to a filtering of the sound signal with 100 Hz wide filter or third octave filters. Up to a frequency of 500 Hz, the width is 100 Hz, about the filters have approximately the width of a third. This filtering or grouping of different frequencies has advantages for the hearing.

Response time

Each filter needs some time to settle. This time is inversely proportional to the bandwidth of the filter.

The critical band filters of hearing with a minimum bandwidth of 100 Hz thus require a maximum of 1/100 Hz = 10 ms for transient response. That is, until 10 ms after the onset of a sound signal is the sound impression stable until the hearing may rely on the information.

An evaluation with narrower frequency groups, however, would mean that the hearing will have to wait longer for a reliable acoustic information is available.

Signal Analysis

To determine the direction of a sound source from the hearing evaluates the phase and the envelope of the signals in the frequency groups.

However, this is only particularly simple if the signals in the frequency groups have the character of modulated sinusoidal signals. For this purpose, the signals in the frequency groups must have no overtones and the envelope must be measured at the center frequency of the frequency group change only relatively slowly.

That is to say: To prevent overtones complicate evaluation of the phase, frequency group must be much narrower than an octave, because the first overtone is at the octave. Thus, the envelope changes so slowly that they can be evaluated, the bandwidth of the frequency group must be much smaller than the frequencies contained, that is, the bandwidth must remain significantly below one-half octave.

With a band width of a minor third ( fourth octave ) is satisfied, this boundary condition.

Optimal behavior of hearing

From the viewpoint of signal processing, the hearing behaves optimally with the choice of the frequency groups:

• The frequency groups are large enough ( at least 100Hz ), that a quick analysis of the acoustic signals is possible; with a reaction time of 10 ms.
• The critical bands are narrow enough (up to a minor third ) that a slight analysis of signal phases and envelopes is possible to from this to be able to easily determine the direction of sound incidence.

Table of the 24 frequency groups

Technical application

Signal processing techniques such as MP3 mimic the processing of human hearing. Again, the signals are processed into frequency groups and thereby removes all information that can not perceive hearing within the frequency groups. This leads to a significant reduction in the data rate.