Below is a diagram of how I plan to do the DWT. How can this be done using Matlab? I do not want to this by sub band coding.

DWT diagram

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Rasula On BEST ANSWER

This is how got used to the discrete wavelet transform in MATLAB https://au.mathworks.com/help/wavelet/, the above is the link for the Wavelet toolbox for MATLAB. Check out the below functions.

dwt-https://au.mathworks.com/help/wavelet/ref/dwt.html?s_tid=doc_ta

wavedec- https://au.mathworks.com/help/wavelet/ref/wavedec.html?s_tid=doc_ta

PS if you do not want the decimation of samples at each stage, try out the stationary wavelet transform in MATLAB. ( makes your results redundant according to my understanding.) https://au.mathworks.com/help/wavelet/ref/swt.html