Analysis of the signal complexity in sitar performances

Abstract

The sitar is perhaps the most well known of the Indian plucked string musical instruments. It has a varying number of strings but 1620 is usual. When played by an expert, the sitar produces a melodious sound effect. The mode of attachment of strings and or the interaction of the large number of strings, some of them being playing strings, some drone and others sympathetic, create the total acoustic environment, which also includes the global resonance structure of the instrument. This creates a sound whose complexity is difficult to model by usual mathematical methods. Fractal dimension is an effective tool for analysis in such cases. In the present paper D0 (fractal dimension), D2 (correlation dimension) and also the higher moments are studied for acoustic signals obtained from actual sitar performances. Four such performances are used for the present study. The obeying of power law indicates the presence of non-linearity in the production system. The presence of multifractality is noticed through an examination of relationship between q and Dq and the functional relationship between the Dq's. It was observed that fractal dimension might be used as a measure of signal complexity. © 2010 World Scientific Publishing Company.