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P.E. Nachtigall et al.
simply a critical bandwidth (CB), is estimated using a bandpassed white
noise of various widths to mask tonal signals. The bandpassed noise spectral density is held constant. The spectral content of the noise is centered
at the tonal frequency, and the level of the tone is adjusted to determine
the masked threshold. The bandwidth of the noise is adjusted, and a threshold for the tone is again determined. This process is repeated for a number
of frequencies and noise bandwidths. Fletcher's theory of critical bands predicts that only noise in a limited frequency range around a tonal signal is
effective in masking that signal. It follows that, starting with a narrow band
of masking noise, gradually increasing the bandwidth of a bandpass noise
would increase masking of a tone (raise the threshold for detecting it) until
the critical bandwidth was reached, at which point further increases in
masking noise bandwidth would have no additional masking effect. This is,
in fact, the effect observed in studies employing bandpass noises to mask
tonal signals.
As mentioned above, critical bandwidth can be estimated using the critical ratio (CR) methodology, but this measure is indirect and has been
found to produce smaller estimates than more direct measures of critical
bandwidth (CB) in humans (Scharf 1970). The value of CR estimates is that,
when plotted over frequency, a function parallel to the that produced by
more direct measures is produced, and a simple relationship between CRs
and bandwidth can be formulated. In humans, CBs were found to be 2.5
times the size of CBs when expressed in hertz (4dB greater) (Zwicker
et al. 1957).
Moore and Au (1990) measured the CB for a T truncatus at 30,60, and
120 kHz. Bandpass noise was digitally generated having bandwidths from
Q = 1 up to 40, where Q is the ratio of center frequency to bandwidth. CBs
were reported as the noise bandwidth beyond which further increases in
bandwidth had no additional masking effect. The results from this study are
presented in Figure 8.5, along with the CR estimates of bandwidth for the
same species (see also Moore and Au 1983).
To summarize the masked hearing work conducted with T truncatus, Au
(1993) proposed that the frequency processing capabilities as defined by
measures of critical bandwidth could be described as a constant-Q filter
bank. The CR and CB values for T truncatus shown in Figure 8.5 have been
fitted with constant-Q functions. A constant-Q filter bank implies that the
ratio of center frequency to filter bandwidth is a constant. The CR values
were fit with Q = 12.3, and the CB values with Q = 2.2. Au estimated a rough
transfer function between CR and CB for T truncatus to be 5.6 times, or an
increase of 7.5 dB when converting CRs to CB values.
In summary of the frequency selectivity capabilities of cetaceans, we note
that again, the majority of the research in this area has been conducted with
T truncatus. The ability of this species to discriminate tonal signals from
frequency modulated signals is comparable to human capabilities (at lower
frequencies) and the best reported for any mammal above 20kHz (Fay
P.E. Nachtigall et al.
simply a critical bandwidth (CB), is estimated using a bandpassed white
noise of various widths to mask tonal signals. The bandpassed noise spectral density is held constant. The spectral content of the noise is centered
at the tonal frequency, and the level of the tone is adjusted to determine
the masked threshold. The bandwidth of the noise is adjusted, and a threshold for the tone is again determined. This process is repeated for a number
of frequencies and noise bandwidths. Fletcher's theory of critical bands predicts that only noise in a limited frequency range around a tonal signal is
effective in masking that signal. It follows that, starting with a narrow band
of masking noise, gradually increasing the bandwidth of a bandpass noise
would increase masking of a tone (raise the threshold for detecting it) until
the critical bandwidth was reached, at which point further increases in
masking noise bandwidth would have no additional masking effect. This is,
in fact, the effect observed in studies employing bandpass noises to mask
tonal signals.
As mentioned above, critical bandwidth can be estimated using the critical ratio (CR) methodology, but this measure is indirect and has been
found to produce smaller estimates than more direct measures of critical
bandwidth (CB) in humans (Scharf 1970). The value of CR estimates is that,
when plotted over frequency, a function parallel to the that produced by
more direct measures is produced, and a simple relationship between CRs
and bandwidth can be formulated. In humans, CBs were found to be 2.5
times the size of CBs when expressed in hertz (4dB greater) (Zwicker
et al. 1957).
Moore and Au (1990) measured the CB for a T truncatus at 30,60, and
120 kHz. Bandpass noise was digitally generated having bandwidths from
Q = 1 up to 40, where Q is the ratio of center frequency to bandwidth. CBs
were reported as the noise bandwidth beyond which further increases in
bandwidth had no additional masking effect. The results from this study are
presented in Figure 8.5, along with the CR estimates of bandwidth for the
same species (see also Moore and Au 1983).
To summarize the masked hearing work conducted with T truncatus, Au
(1993) proposed that the frequency processing capabilities as defined by
measures of critical bandwidth could be described as a constant-Q filter
bank. The CR and CB values for T truncatus shown in Figure 8.5 have been
fitted with constant-Q functions. A constant-Q filter bank implies that the
ratio of center frequency to filter bandwidth is a constant. The CR values
were fit with Q = 12.3, and the CB values with Q = 2.2. Au estimated a rough
transfer function between CR and CB for T truncatus to be 5.6 times, or an
increase of 7.5 dB when converting CRs to CB values.
In summary of the frequency selectivity capabilities of cetaceans, we note
that again, the majority of the research in this area has been conducted with
T truncatus. The ability of this species to discriminate tonal signals from
frequency modulated signals is comparable to human capabilities (at lower
frequencies) and the best reported for any mammal above 20kHz (Fay