matlab source code for discrete wavelet transform pdf
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source code for discrete wavelet transform
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In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transformations, a key advantage over Fourier transforms is the temporal resolution: it captures both frequency and location information (time location).


The first DWT was invented by the Hungarian mathematician Alfréd Haar. For an input represented by a list of numbers {\ displaystyle 2n} 2n, the Haar waveform can be considered to match input values, storing the difference and passing the sum. This process is repeated recursively, matching the sums to test the next scale, which leads to differences {\ displaystyle 2n -1} 2n -1 and a final sum.

Compression is one of the main techniques of image processing. It is one of the most useful and commercially successful technologies in the field of digital image processing. Image compression is the representation of an image in digital form with the fewest number of bits, maintaining an acceptable level of image quality. More and more images are acquired and stored digitally or several film scanners are used to convert traditional raw images into digital format. Data $ compression is the technique to reduce redundancies in data representation in order to reduce data storage requirements and therefore communication costs. Reducing the storage requirement is equivalent to increasing the capacity of the storage medium to increase the transmission speed and therefore the communication bandwidth. Efficient ways to store large amounts of data and due to limitations of bandwidth and storage, images must be compressed before transmission and storage. At some later time, the compressed image is decompressed to reconstruct the original image or approximate it.
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