Abstract
The concept of a harmonic wavelet is generalized to describe a family of mixed wavelets with the structure
w
m, n
(x)
= {exp (i
n
2π
x
) – exp (i
m
2π
x
)}/i(
n – m
) 2π
x
. It is shown that this family provides a complete set of orthogonal basis functions for signal analysis. By choosing the (real) numbers
m
and
n
(not necessarily integers) appropriately, wavelets whose frequency content ascends according to the musical scale can be generated. These musical wavelets provide greater frequency discrimination than is possible with harmonic wavelets whose frequency interval is always an octave. An example of the wavelet analysis of music illustrates possible applications.
Reference9 articles.
1. Jeans Sir James 1937 Science and music. Cambridge University Press.
2. A theory for multiresolution signal decomposition: the wavelet representation
3. Wavelet analysis of vibration. In Proc. Structural Dynamics and Vibration Symp., ASME Energy-Sources Technology Conference;Newland D. E.;Houston PD-vol.,1993
4. Harmonic wavelet analysis
5. Newland D. E. 1993c Random vibrations spectral and wavelet analysis 3rd edn. Harlow: Longman and New York: John Wiley.
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