Psychoacoustics 493.3.3 Auditory Filters and Critical BandsExperiments show that our ability to detect a signal
depends on the bandwidth of the signal. Fletcher
(1940)^18 found that, when playing a tone in the presence
of a bandpass masker, as the masker bandwidth was
increased while keeping the overall level of the masker
unchanged, the threshold increased as bandwidth
increased up to a certain limit, beyond which the thresh-
old remained constant. One can easily confirm that,
when listening to a bandpass noise with broadening
bandwidth and constant overall level, the loudness is
unchanged, until a certain bandwidth is reached, and
beyond that bandwidth the loudness increases as band-
width increases, although the reading of an SPL meter is
constant. An explanation to account for these effects is
the concept of auditory filters. Fletcher proposed that,
instead of directly listening to each hair cell, we hear
through a set of auditory filters, whose center frequen-
cies can vary or overlap, and whose bandwidth is vary-
ing according to the center frequency. These bands are
referred to as critical bands (CB). Since then, the shape
and bandwidth of the auditory filters have been care-
fully studied. Because the shape of the auditory filters is
not simply rectangular, it is more convenient to use the
equivalent rectangular bandwidth (ERB), which is the
bandwidth of a rectangular filter that gives the same
transmission power as the actual auditory filter. Recent
study by Glasberg and Moore (1990) gives a formula
for ERB for young listeners with normal hearing under
moderate sound pressure levels^21 :where,
the center frequency of the filter F is in kHz,
ERB is in Hz.Sometimes, it is more convenient to use an ERB
number as in Eq. 3-1,^21 similar to the Bark scale
proposed by Zwicker et al.^22 :
(3-1)
where,
the center frequency of the filter F is in kHz.Table 3-1 shows the ERB and Bark scale as a
function of the center frequency of the auditory filter.
The Bark scale is also listed as a percentage of center
frequency, which can then be compared to filters
commonly used in acoustical measurements: octave
(70.7%), half octave (34.8%), one-third octave (23.2%),
and one-sixth octave (11.6%) filters. The ERB is shown
in Fig. 3-11 as a function of frequency. One-third octavefilters which are popular in audio and have been widely
used in acoustical measurements ultimately have their
roots in the study of human auditory response.
However, as Fig. 3-11 shows, the ERB is wider than
octave for frequencies below 200 Hz; is smaller than
octave for frequencies above 200 Hz; and, above 1 kHz,
it approaches octave.3.4 Nonlinearity of the EarWhen a set of frequencies are input into a linear system,
the output will contain only the same set of frequencies,
although the relative amplitudes and phases can be
adjusted due to filtering. However, for a nonlinear sys-
tem, the output will include new frequencies that are not
present in the input. Because our auditory system has
developed mechanisms such as acoustic reflex in the
middle ear and the active processes in the inner ear, it is
nonlinear. There are two types of nonlinear-ERB=24.7 4.37 F 1+ERB Number=21.4log 4.37F 1+Table 3-1. Critical Bandwidths of the Human Ear
Critical Band
NoCenter
Frequency
HzBark Scale Equivalent
Rectangular
Band (ERB), Hz(Hz) %1 50 100 200 33
21501006743
32501004052
43501002962
54501102472
65701202184
77001402097
8 840 150 18 111
9 1000 160 16 130
10 1170 190 16 150
11 1370 210 15 170
12 1600 240 15 200
13 1850 280 15 220
14 2150 320 15 260
15 2500 380 15 300
16 2900 450 16 350
17 3400 550 16 420
18 4000 700 18 500
19 4800 900 19 620
20 5800 1100 19 780
21 7000 1300 19 990
22 8500 1800 21 1300
23 10,500 2500 24 1700
24 13,500 3500 26 2400(^1) » 3
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