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the binary representation of the amplitude value. The bit depth depends on the
software; for instance, an 8-bit sample can resolve 256 (2
8
) different amplitude
values, and a 16-bit sample can resolve 65,536 (2
16
) values. A high value of bit
depth reduces the quantization noise introduced when the approximation between
analog value and digitized version is too coarse.
9.4 Time Domain and Frequency Domain of Sound
Sound can be represented in a time domain and in a frequency domain. In the time
domain the instantaneous pressure is represented as a function of the time (Fig.
9.8
).
In a frequency domain the pressure expressed as amplitude and phase is plotted
against frequency. The pressure is converted by a microphone in volts and the
amplitude is expressed in voltage. The frequency domain of a pure tone is represented
by a vertical line with length corresponding to the amplitude. Any sound can be
represented by a series of pure tones different in amplitude and phase. The spectral
representation of sounds is more intuitive because in mammals the cochlea
transforms the eardrum vibration into neural pulses that are the frequency domain
representation of sounds. The frequency domain is represented by a magnitude
spectrum and by a phase spectrum that has a few applications in bioacoustics.
The Fourier transform (FT) is a mathematical procedure that transforms a short
segment of sound from a temporal domain to a frequency domain. A specific
version of the FT, the discrete Fourier transform (DFT), is used when the signal
and spectrum are represented by a sequence of discrete digital values. The obtained
output of this transformation is represented by a sequence of values evenly spaced
from 0 Hz to half the sampling frequency. The DFT is implemented applying the
Fig. 9.8
Representation of
the time domain (
a
) and
frequency domain (
b
)ofa
pure tone. In (
a
) the
instantaneous pressure is
represented with time; in (
b
)
the pressure is represented
as amplitude along the
frequency axes. In this case
a pure tone belongs only to a
frequency class
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