Efficient Algorithms for Discrete Wavelet Transform

<p>Transforms are an important part of an engineer’s toolkit for solving signal processing and polynomial computation problems. In contrast to the Fourier transform-based approaches where a fixed window is used uniformly for a range of frequencies, the wavelet transform uses short windows at high frequencies and long windows at low frequencies. This way, the characteristics of non-stationary disturbances can be more closely monitored. In other words, both time and frequency information can be obtained by wavelet transform. Instead of transforming a pure <i>time description</i> into a pure <i>frequency description</i>, the wavelet transform finds a good promise in a <i>time-frequency</i> description. </p><p>Due to its inherent time-scale locality characteristics, the discrete wavelet transform (DWT) has received considerable attention in digital signal processing (speech and image processing), communication, computer science and mathematics.^ Wavelet transforms are known to have excellent energy compaction characteristics and are able to provide perfect reconstruction. Therefore, they are ideal for signal/image processing. The shifting (or translation) and scaling (or dilation) are