15.01.2013 Views

U. Glaeser

U. Glaeser

U. Glaeser

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

FIGURE 27.5 Critical bandwidth and ERB as functions of the passband center frequency: (a) critical bandwidth<br />

according to Eq. (27.13), (b) ERB according to Eq. (27.14a).<br />

Signal processing, which takes place in the human auditory system, can generally be divided into two<br />

stages: a preliminary phase realized in the acoustic auditory organs (ears) and the advanced phase done<br />

in auditory nervous system (in the brain). The auditory part of the inner ear, known as the cochlea<br />

because of its snaillike shape, performs a kind of the spectral analysis. The acoustic harmonic tones<br />

generate place selective oscillations distributed along the so-called basilar membrane, which extends<br />

down the cochlea. In result, the frequency is mapped into a place on the basilar membrane and a frequency<br />

scale can be laid out at the basilar membrane with low frequencies near the apex and high frequencies<br />

near the base of the cochlea. According to the authors’ results the cochlear response is not a kind of a<br />

Fourier like transformation but, neglecting the nonlinearities, it is rather a kind of the continuous wavelet<br />

transformation (CWT) [5]. Consequently, the cochlear response can be interpreted as if it were produced<br />

by a filter bank composed of highly overlapping bandpass filters with increasing passbands. These filters<br />

are referred to as the peripheral auditory filters.<br />

Two widely accepted approaches are used for estimation of the passbands of the peripheral auditory<br />

filters. The older approach is based on the notion of critical bands ∆f c [12,45,56]. The widths of the critical<br />

bands vary from ca. 100 Hz for low frequencies (lower than 300 Hz) to about one-third of an octave for<br />

high frequencies (Fig. 27.5(a)). The critical bandwidth as a function of its center frequency can be<br />

estimated in hertz using expression<br />

© 2002 by CRC Press LLC<br />

Critical bandwidth , ∆ f c [Hz]<br />

10 3<br />

10 2<br />

ERB<br />

a<br />

b<br />

10 -1<br />

1/<br />

3 - octave bandwidth<br />

(27.13)<br />

in which frequency f is given in kilohertz [45].<br />

The newer approach results from measurements of the frequency response shape of the peripheral<br />

auditory filters and uses a concept of equivalent rectangular bandwidth (ERB) [32,44]. ERB is a bandwidth<br />

of the equivalent ideal (rectangular) passband filter, which has the same center passband frequency as<br />

the respective peripheral auditory filter, transmits the same amount of power when excited with the same<br />

white noise, and has the passband gain equal to the maximum passband gain of the respective auditory<br />

filter. ERB as a function of frequency can be approximated in hertz as<br />

(27.14a)<br />

where frequency f is again given in kilohertz (cf. Fig. 27.5(b)). Sometimes, a slightly simpler formula is<br />

10 0<br />

Center frequency, f [kHz]<br />

∆fc 25 75 1 1.4f 2<br />

= + +<br />

1/<br />

6 - octave bandwidth<br />

( ) 0.69<br />

ERB 6.23f 2 =<br />

+ 93.3f + 28.52<br />

10 1

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!