Hardware Implementation of Wavelet Transfrom

In this part, I am trying to explain about the Hardware implementation of wavelet transform. Wavelet transform consist of two parts, they are scaling function and wavelet function. in this case actually the Discrete Wavelet Transform will be presented, DWT itself has many  type for example daubechies, haar, morlet etc. in this blog we are trying to construct the haar wavelet.

at firs the equation for haar wavelet is

it has scaling function and wavelet function. for example, if we have the basic scale function like

so the representation on the graph would be 

 the representation on graph would be 

at easy case, we have a function the answer for haar transform would be 

its easy to say that the result is the average between 5+3 and 5-3. that result of transform will be (4,1). from this formula we can construct the haar into simple convolution process.

<< matrices aprroach >>

in order to simplified the haar transform, we can construct it into some simple matrices. for example if we want to build a haar transform with 8 data input, we need 8 x 1 matrices, shown in figure:

simulation result:

matlab model:

source:

David Salomon, ” Data Compression The Complete Reference”

http://www.bearcave.com/misl/misl_tech/wavelets/matrix/