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Critical bandwidth (Hz)
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Signal processing in the auditory system can be divided into two parts: that done in the peripheral auditory organs (ears) themselves, and that done in the auditory nervous system (brain). The ears process an acoustic pressure signal by first transforming it into a mechanical vibration pattern on the basilar membrane, and then representing this pattern by a series of pulses to be transmitted by the auditory nerve. Perceptual information is extracted at various stages of the auditory nervous system.
For many years, it has been known that the cochlea of the inner ear acts as a mechanical spectrum analyzer. Fletcher's pioneering work in the 1940's pointed to the existence of critical bands in the cochlear response. Studying the masking of a tone by broadband (white) noise, Fletcher (1940) found that only a narrow band of noise surrounding the tone causes masking of the tone, and that when the noise just masks the tone, the power of the noise in this band (the critical band) is equal to the power in the tone.
Fletcher's second result suggested a means for estimating the widths of the critical bands. Noise power is expressed in terms of the power in a band 1 Hz wide; this is called the spectrum level. The ratio of the power level of a single-frequency tone to the spectrum level of the white noise masker thus yields the width of the band effective in masking the tone. Researchers today often call these bands "critical ratios"; they turn out to be about 2.5 times narrower than critical bands determined by other methods.
Critical bands are of great importance in understanding many auditory phenomena: perception of loudness, pitch, and timbre. for example. Their importance is aptly pointed out by Tobias (1970) in his Foreword to an article on Critical Bands:
"Nowhere in auditory theory or in acoustic psychophysiological practice is anything more ubiquitous than the critical band. It turns up in the measurement of pitch, in the study of loudness, in the analysis of masking and fatiguing signals, in the perception of phase, and even in the determination of the pleasantness of music.And likely, in one way or another, it will be a part of the final understanding of how and why we perceive anything that reaches our ears."
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Center frequency (Hz) 100 200 500 1,000 2,000 5,000 |
Critical bandwidth (Hz) 90 90 110 ISO 280 700 1,200 |
Critical bandwidth as a function of the frequency at the critical band center frequency, The critical bandwidth varies from a little less than 100 Hz at low frequency to between two and three musical semitones (12 to 19%) at high frequency (from Rossing, 1982).
The auditory system performs a Fourier analysis of complex sounds into their component frequencies. The cochlea acts as if it were made up of overlapping filters having bandwidths equal to the critical bandwidth. The critical bandwidth varies from slightly less than 100 Hz at low frequency to about 1/3 of an octave at high frequency, as shown in Fig. 1. The audible range of frequencies comprises about 24 critical bands. It should be emphasized that there are not 24 independent filters, however. The ear's critical bands are continuous, in that a tone of any audible frequency will find a critical band centered on it.
Considerable understanding of the way in which the cochlea performs its frequency analysis resulted from the experiments of von Bekesy, who observed the patterns of actual basilar membranes when sound waves of different frequencies were applied. High frequencies created peaks toward the near (oval window) end of the basilar membrane, while low frequencies caused peaks toward the far (apex) end. Bekesy's tuning curves for the basilar membrane led to the place theory of hearing.
Bekesy's tuning curves, measured in cadavers at very high sound intensities, were too broad to account for the observed frequency resolution of the auditory system. Ex-periments by Johnstone and Boyle (1967) and by Rhode and Robles (1974), using the Mossbauer effect to measure basilar membrane motion in animals at much lower ampli-tude, led to sharper tuning curves. Mechanical measurements on the basilar membrane of the cat, using laser interferometry, yielded tuning curves about as sharp as electro-physiological tuning curves measured in the 8th nerve (Khanna and Leonard, 1982). Still, the greater frequency resolution observed in other types of experiments suggests the existence of a "second filter" , which might very well be associated with the hair cells of the basilar membrane.
The first three demonstrations introduce frequency analysis and critical bands. Many of the demonstrations which follow (e.g., on loudness, pitch, masking, etc.) illus-trate these subjects as well.