Time-Frequency Analysis of Musical Instruments

This paper describes several approaches to analyzing the frequency, or pitch, content of the sounds produced by musical instruments. The classic method, using Fourier analysis, identifies fundamentals and overtones of individual notes. A second method, using spectrograms, analyzes the changes in fundamentals and overtones over time as several notes are played. Spectrograms produce a time-frequency description of a musical passage. A third method, using scalograms, produces far more detailed time-frequency descriptions within the region of the time-frequency plane typically occupied by musical sounds. Scalograms allow one to zoom in on selected regions of the time-frequency plane in a more flexible manner than is possible with spectrograms, and they have a natural interpretation in terms of a musical scale. All three of these techniques will be employed in analyzing music played on a piano, a flute, and a guitar. The two time-frequency methods, spectrograms and scalograms, will be shown to extend the classic Fourier approach, providing time-frequency portraits of the sounds produced by these instruments. Among other advantages, these time-frequency portraits seem to correlate well with our perceptions of the sounds produced by these instruments and of the differences between each instrument. There are many additional applications of time-frequency methods, such as compression of audio and resolution of closely spaced spectral lines in spectroscopy. Brief discussions of these additional applications are included in the paper.