Abstract

The spectral envelope conveys sound quality and the time envelope is responsible for speech intelligibility. The spectral envelope can be identified in terms of the poles and zeros according to the linear system theory. This chapter deals with the poles and zeros creating spectral envelopes by taking an example of spectral records on piano string vibration. Sinusoidal modeling of spectral peaks due to poles in the frequency domain represents spectral fine structure of a temporally changing response such as a piano tone. Time-waveform decomposition in the transient state into pulse sequences in the time domain is explored in order to find the zeros that make the spectral envelope in the frequency domain. The two approaches to sound quality or signal signatures in the time and frequency domains are formulated on the basis of the least square error (LSE) criterion. The zeros are mainly responsible for the source signatures. The exciting source, such as a piano hammer, makes the outer spectral envelopes of the vibration response, while the inner envelope is rendered by the zeros due to a single cycle of the cyclic source-wave traveling on the piano string.

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