Critical band

In audiology and psychoacoustics the concept of critical bands, introduced by Harvey Fletcher in 1933[1] and refined in 1940,[2] describes the frequency bandwidth of the "auditory filter" created by the cochlea, the sense organ of hearing within the inner ear.

Psychophysiologically, beating and auditory roughness sensations can be linked to the inability of the auditory frequency-analysis mechanism to resolve inputs whose frequency difference is smaller than the critical bandwidth and to the resulting irregular "tickling"[3] of the mechanical system (basilar membrane) that resonates in response to such inputs.

[5] The auditory filters are associated with points along the basilar membrane and determine the frequency selectivity of the cochlea, and therefore the listener's discrimination between different sounds.

[4][6] They are non-linear, level-dependent and the bandwidth decreases from the base to apex of the cochlea as the tuning on the basilar membrane changes from high to low frequency.

An ERB passes the same amount of energy as the auditory filter it corresponds to and shows how it changes with input frequency.

[6][7] The ERB can be converted into a scale that relates to frequency and shows the position of the auditory filter along the basilar membrane.

[9] The shapes of auditory filters are found by analysis of psychoacoustic tuning, which are graphs that show a subject's threshold for detection of a tone as a function of masker parameters.

[10] In the notched-noise method the subject is presented with a notched noise as the masker and a sinusoid (pure tone) as the signal.

To get a true representation of the auditory filters in one subject, many psychoacoustic tuning curves need to be calculated with the signal at different frequencies.

For each psychoacoustic tuning curve being measured, at least five but preferably between thirteen and fifteen thresholds must be calculated, with different notch widths.

[10] This is because the threshold is recorded when the subject first hears the tone, instead of when they respond to a certain stimulus level a certain percentage of the time.

The cochlea is a snail-shaped formation that enables sound transmission via a sensorineural route, rather than through a conductive pathway.

[11] The diagram below illustrates the complex layout of the compartments and their divisions:[4] The basilar membrane widens as it progresses from base to apex.

[11] When a vibration is carried through the cochlea, the fluid within the three compartments causes the basilar membrane to respond in a wave-like manner.

[11] Outer hair cells have stereocilia projecting towards the tectorial membrane, which sits above the organ of Corti.

When this occurs, the stereocilia separate and a channel is formed that allows chemical processes to take place.

This is because the frequency selectivity and the tuning of the basilar membrane is reduced as the outer hair cells are damaged.

When only the outer hair cells are damaged the filter is broader on the low frequency side.

A Band-pass filter showing the centre frequency(Fc), the lower(F1) and upper(F2) cut off frequencies and the bandwidth. The upper and lower cut-off frequencies are defined as the point where the amplitude falls to 3 dB below the peak amplitude. The bandwidth is the distance between the upper and lower cut-off frequencies, and is the range of frequencies passed by the filter.
ERB related to centre frequency: The diagram shows the ERB versus centre frequency according to the formula by Glasberg & Moore (1990) . [ 8 ] [ 6 ]
Cross-section through the cochlea, showing the different compartments (as described above)
Simplified schematic of the basilar membrane, showing the change in characteristic frequency from base to apex
Asymmetry of the auditory filter. The diagram shows the increasing asymmetry of the auditory filter with increasing input level. The highlighted filters show the shape for 90 dB input level (pink) and a 20 dB input level (green). Diagram adapted from Moore and Glasberg, [ 13 ] which showed rounded (roex) filter shapes.
Off-frequency listening. Diagram A shows the auditory filter centred on the signal and how some of the masker falls within that filter, resulting in a low SNR. Diagram B shows a filter further along the basilar membrane, which is not centered on the signal but contains a substantial amount of that signal and less masker. This shift reduces the effect of the masker by increasing the SNR. Diagram adapted from Gelfand (2004). [ 4 ]
The auditory filter of a "normal" cochlea
The auditory filter of an impaired cochlea