Spectral
Centroid
The
spectral
centroid (Beauchamp 1982) is commonly associated
with the measure of the brightness
of a sound (Grey and Gordon
1978). This measure is obtained by evaluating the "center of gravity" using
the Fourier transform's frequency and magnitude information (Equation 2.7).
Generally speaking, it has been found that increased loudness also increases
the amount of high spectrum content of a signal thus making a sound brighter.
(2.7)
X[k]
is the magnitude corresponding to bin k and N is the length
of the DFT. This measure has also been used in MDS (multidimensional scaling)
based systems. Figure 2.10 shows examples of the spectral centroid
for the french horn and the electric bass guitar.
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Figure 2.10 Spectral centroid of
french horn and electric bass at 44.1 kHz
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Spectral
Smoothness
The
spectral
smoothness (McAdams 1999) measures the smoothness of the frame to frame
spectral envelope obtained via the short time Fourier transform. The algorithm
basically takes the average of adjacent amplitudes of the spectral bins
and compares them to the current amplitude at bin k as shown in
equation 2.8.
(2.8)
Figure 2.11 shows examples of the spectral
smoothness for white noise, sine wave and electric bass sampled at 44,100
Hz.
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Figure 2.11 White noise, sine wave
and electric bass spectral smoothness
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