Introduction to Acoustics

60
40
20
0
SPL–sound pressure level (dB)
A
B
0.02 0.5 0.1 0.2 0.5 1 2 5 10 20
Frequency (kHz)
Fig. 18.4 Frequency Domain Masking: Curve A is hearing
threshold with no signal present. Curve B is revised threshold
in presence of 1 kHz tone C. Signal D, rising above
curve A but below curve B, will be audible by itself but
masked by signal C
to render an existing component less audible, a process
referred to as masking.
The basic notion of masking is that a louder sound
will tend to render as less audible or inaudible a softer
sound that would otherwise be audible in isolation. The
degree of masking will tend to depend in part on the
frequency spacing of the spectral components in question.
This gives rise to the notion of a prototype masking
curve, delineating the threshold of audibility in the presence
of a sine wave of some frequency and amplitude,
as a function of frequency, as shown in Fig. 18.4.
To at least first-order approximation, the masking
effect of two or more sine waves can be calculated by
summing their respective individual masking curves.
Since, from Fourier theory, any signal can be decomposed
into a sum of sinusoids, a composite masking
curve from an arbitrary signal can be calculated as the
sum of the masking curves of each spectral component.
This constitutes a convolution (filtering operation) of
a prototype masking curve with the signal spectrum. In
practice, the prototype masking curve used for the convolution
is likely to vary as a function of frequency,
amplitude, or signal type (noise versus sine wave). Further,
nonlinearities in the ear may result in significant
deviations from the predicted curve at times.
Although the masking effect of a signal is, quite
logically, maximized while the signal is present, some
residual of the masking effect will extend beyond the
termination of the signal, and even slightly before its
onset. This process is referred to as temporal masking,
and typical behavior is illustrated in Fig. 18.5) [18.18].
C
D
Audio and Electroacoustics 18.2 The Psychoacoustics of Audio and Electroacoustics 749
Sound pressure level (dB)
Pre-masking
90
80
70
60
50
40
Simultaneous masking Post-masking
–60 –40–20
0
20
40
160 180
0
20
Fig. 18.5 Temporal masking characteristic
18.2.3 Timing
40 60 80 100 120 140 160
t (ms)
Because the transduction structure of the ear – the basilar
membrane and associated hair cells – functionally
resembles a filter bank, questions of timing must be considered
as applying to the filtered output signals of that
a)
b) Spikes/s
3200
1600
0
0
c) Spikes/s
800
20 40 60 80 100
Time (ms)
3.44 kHz
400
0
260 Hz
0 20 40 60 80 100
Time (ms)
Fig. 18.6 Neural phase locking at low frequencies and lack
of phase locking at higher frequencies [18.17]
Part E 18.2