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Automatic Music Composition plays a crucial role in the musical research and can become a tool for the incorporation of artificial intelligence in computer musicology. This paper finds an efficient method for identifying the wavelets and filter bank coefficients in musical instruments using NLMS algorithm and the usage of these wavelets for Automatic music Composition using Hidden Markov Model. In this paper, a technique to identify the scaling function and the wavelet functions of the wavelets present in musical instruments, violin and flute, is presented. NLMS algorithm is used to identify the filter bank coefficients of wavelet-like elements, found repeating in musical notes of the instruments. Pre-trained hidden markov models for each raga of South Indian Music is used for the composition. The HMM selected has twelve states which represent the twelve notes in South Indian music. Fundamental frequency tracking algorithm, followed by quantization is done. The resulting sequence of frequency jumps of different musical clips of same musical pattern (Raga) is presented to Hidden Markov Model of a particular Raga for training. The HMM model of that Raga along with the filter coefficient is used to regenerate a piece of music in that particular raga. The methodology is tested in the context of South Indian Classical Music, using the wavelet of classical music instruments, Flute and Violin.