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I want to implement Wavelet Transform from the scratch, that mean breaking the wavelet transform into its equations to implement in any Programming language. Matlab Comes with built-in functions to implement Wavelet Transform but It is really hard to understand which processes are exactly involved in the implementation if one wants to develop their own functions.

I know there are Low and High Pass filter involved and the other step called , Down-Sampling but I still have so many doubts on how exactly to combine these filters and samplers to design one's own Wavelet Transform function.

The wavelet tranform block diagram looks like this,

enter image description here

but there are so many Wavelet transform like Haar, db1, db2 etc. Which wavelet tranform does this blog diagram defines anyway.

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I found the Wavelets for Computer Graphics: A Primer a good introduction to the Haar wavelet and its role in image processing.

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You should go for the polyphase implementation of wavelet filter bank. You are referred to the book

Wavelets and Filter Banks, by Gilbert Strang and Truong Nguyen

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