### ASA 127th Meeting M.I.T. 1994 June 6-10

## 4aMU4. Musical signal spectrum analysis with the matrix pencil method.

**Jean Laroche
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*Dept. Signal C134-4, Telecom Paris, 46 Rue Barrault, 75634 Paris Cedex 13,
France
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The matrix pencil spectrum analysis method provides an interesting
alternative to classical Fourier analysis. The method is based on the
assumption that the signal can be represented as a sum of exponentially damped
sinusoids whose parameters (frequency, damping factor, amplitude and phase) are
estimated by a matrix-based algorithm. In spite of its computational cost, the
matrix pencil method achieves extremely good results in the case of highly
damped signals, short data records, or close frequencies. The matrix pencil
method is first briefly described and compared to other spectrum analysis
techniques (Fourier transform, Prony method). Several implementations are
proposed and their computational costs evaluated. The good performance of the
method is illustrated by analysis examples involving low-frequency beats of
piano tones. These beats are decomposed as sums of closely spaced damped
sinusoids, which makes it possible to verify some of results on the coupling
between orthogonal vibrating modes of strings [G. Weinreich, ``Coupled piano
strings,'' J. Acoust. Soc. Am. 62, 1474 (1977)]. The matrix pencil method is
also applied to the analysis of the bridge admittance of a guitar and is used
to model the admittance as a set of simple mechanical systems in parallel.