Time Frequency Representation Of Musical Signals Using The Discrete Hermite Transform

Time-frequency representations of musical signals help with the visualization and understanding of the building blocks of music. Difficulties with different representations limit the amount of information that can be extracted from the signal processing techniques used. The discrete Hermite transform has already proven to be an excellent choice in biomedical signal processing applications. We will show that the discrete Hermite transfrom is an excellent choice for the analysis of musical signals as well. The discrete Hermite basis functions are approximately sinusoidal with shorter function supports than the Fourier techniques. This gives them better frequency resolution than both classic Fourier transforms and current wavelet transforms for musical signals. We will show that the discrete Hermite transform and the time-frequency display it produces, the Hermitian distribution, will be an invaluable resource to the sign processing community.