An Approach to Wavelet Packet Frame Analysis and Noise Suppression Through Wavelet Packet Quantized Coefficients

Wavelet theory has received much interest in recent years because it has ability to analyze signals that have time varying characteristics. The wavelet packet is a frame in a Hilbert space; therefore, the structure of wavelet packet analysis provides a natural tool for denoising. A signal is coherent with respect to a frame, if the energy in the inner product representation is concentrated, that is, well localized in the representation domain. The mapping of coherence is the concentration of energy in the representation domain. Thresholding is a technique performing to zero out small magnitude wavelet packet coefficients and retain the large magnitude wavelet packet coefficients. Noise Suppression of a bumps signal is shown taking threshold value λ= 0.7 and using wavelet packets of Daubechies 4 wavelet, level 4.