Centroid wavelength

The centroid wavelength (index c for centroid = center of gravity ) is used in digital signal processing as a measure to characterize a frequency spectrum . It indicates where the "center" of the spectrum is. ${\displaystyle \lambda _{c}}$

The centroid wavelength is calculated as the weighted arithmetic mean of the wavelengths , weighted with their amplitudes using the distribution function : ${\displaystyle \lambda }$ ${\displaystyle s(\lambda )}$

${\displaystyle \lambda _{c}={\frac {\int _{-\infty }^{\infty }\lambda \cdot s(\lambda )\,{\textrm {d}}\lambda }{\int _{-\infty }^{\infty }s(\lambda )\,{\textrm {d}}\lambda }}}$

Alternative use

Sometimes the center wavelength is formed from the median of the spectrum. However, this usually leads to different results if the signal is not normally distributed .

application

The focal wavelength is used in digital audio technology or acoustics to determine the timbre .

In radiometry , the centroid wavelength is used to identify light sources , e.g. B. LEDs to characterize.

Individual evidence

1. ↑ A Large Set of Audio Features for Sound Description (PDF; 9.1 MB) - technical report published by IRCAM in 2003. Section 6.1.1 describes the spectral centroid.
2. ^ Emery Schubert, Joe Wolfe, Alex Tarnopolsky: Spectral centroid and timbre in complex, multiple instrumental textures . In: Proceedings of the 8th International Conference on Music Perception & Cognition, North Western University, Illinois . In: International Conference on Music Perception & Cognition. School of Music and Music Education; School of Physics, University of New South Wales, 2004.
3. ↑ John M. Gray, John W. Gordon: Perceptual effects of spectral modifications on musical timbres . In: The Journal of the Acoustical Society of America . tape 63 , no. 5 , 1978, p. 1493-1500 , doi : 10.1121 / 1.381843 .

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