Study of Wavelet Transforms In De-Noising (Using Cauchy Distribution)

Degraded signal has an adverse effect on the performance of the system and therefore it must be removed before further processing of signals. Spectral analysis through the Fourier transform is the simplest way to remove the noise, but it is limited to only stationary signals. Non stationary signals require continuous analysis of the signal in time and frequency domain. Wavelets provide better time, frequency localization and multi-resolution analysis compared to the Fourier transform. In this paper, we use the Cauchy probability density function for the study of different wavelets in denoising of audio signals. Compared to Gaussian Density Function, Cauchy distribution shown the non Gaussian statistics with heavy tailed distribution. Soft and Hard thresholding are estimated at each decomposition level and performance are evaluated in terms of signal-tonoise ratio (SNR).