Wavelets are mathematical functions that cut up the data into different frequency components and then study each component with a resolution matched to its scale. They have added advantages over traditional Fourier methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. Wavelets were developed independently in the fields of mathematical, electrical engineering, and quantum physics. Interchanges in these fields have led to many new wavelet applications such as image compression. Effective image compression required a non-expansive discrete wavelet transform (DWT) be employed; consequently, image border extension is a critical issue. Ideally, the image border extension method should not introduce distortion under compression. In this thesis we demonstrated how biorthogonal (9, 7) filter indicate slight performance advantage over length-8 symmetric quadrature mirror filter.
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