04-05-2017, 09:34 AM
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.
Block diagram for the transformation of the discrete wavelet based on elevation
Discrete Wavelet Transformation (DWT) is an efficient and useful tool for signal and image processing applications and will be adopted in many emerging standards, starting with the new JPEG2000 compression standard. This growing "success" is due to the achievements in the field of mathematics, its multiresolution processing capabilities, and also the wide range of filters that can be provided. These features allow the DWT to adapt to suit a wide range of applications. In the early 1980s, in search of more flexibility and rapid prototyping at low cost, a reconfigurable hardware based on custom logic in the form of Field Programmable Gate Arrays (FPGAs) has been introduced into the CI market. However, while FPGA devices offer an attractive combination of low cost, high performance and apparent flexibility, their programming model is at gate level. To enable a FPGA novice image / signal processing developer to benefit from the advantages offered by such devices, high-level solutions are desired. The objective of this work is to present a framework and the preliminary results of an FPGA based system of discrete Wavelet Transformations. The proposed environment is a Java based graphical user interface (GUI) combined with a wavelet database and a parametric VHDL code generator.
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.
Block diagram for the transformation of the discrete wavelet based on elevation
Discrete Wavelet Transformation (DWT) is an efficient and useful tool for signal and image processing applications and will be adopted in many emerging standards, starting with the new JPEG2000 compression standard. This growing "success" is due to the achievements in the field of mathematics, its multiresolution processing capabilities, and also the wide range of filters that can be provided. These features allow the DWT to adapt to suit a wide range of applications. In the early 1980s, in search of more flexibility and rapid prototyping at low cost, a reconfigurable hardware based on custom logic in the form of Field Programmable Gate Arrays (FPGAs) has been introduced into the CI market. However, while FPGA devices offer an attractive combination of low cost, high performance and apparent flexibility, their programming model is at gate level. To enable a FPGA novice image / signal processing developer to benefit from the advantages offered by such devices, high-level solutions are desired. The objective of this work is to present a framework and the preliminary results of an FPGA based system of discrete Wavelet Transformations. The proposed environment is a Java based graphical user interface (GUI) combined with a wavelet database and a parametric VHDL code generator.