ABSTRACT
ABSTRACT: For musical signals, a waveform of a single note has a repeating element, as it contains fundamental frequency and its harmonics. A wavelet designed specifically for a musical instrument by taking this waveform as the scaling function can be used to analyze these musical signals. Since the waveform of a single note which is used as a scaling function does not satisfy orthogonality property, they can be designed as biorthogonal wavelets. In this paper, the filter bank coefficients corresponding to this wavelet are derived from the available analysis low-pass coefficients using the properties satisfied by biorthogonal wavelet. The musical signals can be decomposed and reconstructed using this set of filter bank coefficients. The coefficients thus obtained are modified using lifting technology for better performance. The lifting scheme is an approach to construct so-called second generation wavelets, which are not necessarily transalates and dilations of one function. Signal being corrupted with noise is found to be a major problem in signal processing. The musical signals are denoised using classical wavelets and two sets of filter bank coefficients obtained using the two methods. The denoising is performed by adopting a proper thresholding method. For the performance comparison and measurement of quality of denoising, the Signal to Noise Ratio (SNR) is calculated between original musical signal and the denoised signal. It is found that coefficients give better performance once modified using lifting technology.
