SSM wavelets for analysis of music signals using Particle Swarm Optimization

The waveform of a single note played by musical instruments has a repeating element, as it contains fundamental frequency and its harmonics. This waveform can be used as the scaling function for analysing the signals produced by that particular musical instrument, provided it satisfies the necessary and sufficient condition for a scaling function. In this paper, the filter coefficients corresponding to this scaling function is obtained using Particle Swarm Optimization(PSO) technique. For known wavelets, like Daubechies, the scaling function can be iteratively found from the filter coefficients. However, it is difficult to generate the filter coefficients from the wavelets without the knowledge of some characteristics of the scaling function or the wavelet. In this context, the PSO model which has been developed here gives very accurate values of the filter coefficients for any given scaling function. Further, ordinary PSO is modified for better optimization resulting in a new wavelet for music signals called as Sinith-Shikha-Murthy (SSM) wavelet. The working of the proposed models are verified using Daubechies wavelet. The filter coefficients corresponding to the signal generated by musical instruments flute and violin are also found. The regeneration of the scaling function iteratively using the obtained filter coefficients confirmed the results.