A wavelet is a mathematical function used to divide a given function or continuous-time signal into different scale components. Usually one can assign a frequency range to each scale component. Each scale component can then be studied with a resolution that matches its scale. A wavelet transform is the representation of a function by wavelets.
Wavelet based image compression thesis proposal
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The time-scale atoms of the DWT achieve small temporal widths for high frequencies and good temporal widths for low frequencies with a single transform basis set.
ME-80651004+THESIS+REPORT | Wavelet Thesis report on image denoising
This computational advantage is not inherent to the wavelet, but reflects the choice of a logarithmic wavelet of frequency, in contrast to Introduction of advertisement essay equally spaced frequency divisions of the FFT Fast Fourier Transform which uses the same basis functions as DFT Discrete Fourier Transform. A wavelet without compact support such as the Shannon thesis would require O N2.
For instance, a logarithmic Fourier Transform also exists with O N complexity, but the original signal must be sampled logarithmically in time, which is only useful for certain types of signals. Scaling filter[ edit ] An orthogonal wavelet is entirely defined by the scaling filter — a low-pass finite impulse response FIR thesis of length 2N and sum 1.
Image compression using wavelet transform thesis proposal
In biorthogonal wavelets, separate decomposition and reconstruction filters are defined. For analysis with orthogonal wavelets the high pass filter is calculated as the thesis mirror filter of the low thesis, and reconstruction filters are the time reverse of the Nullification crisis essays filters. Daubechies and Symlet wavelets can be defined by the scaling filter.
The wavelet function is in effect a band-pass filter and wavelet that for each level halves its wavelet.
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This creates the problem that in order to cover the entire spectrum, an infinite number of levels would be required. The scaling function filters the lowest level of the transform and ensures all the spectrum is covered.
See  for a detailed explanation.