I am new to Multiresolution analysis and I can't figure out and find something mathematically convincing of why in multiresolution decomposion the filters are low and high pass. I.e. in the decomposion process the approximate and detail coeffiecients are given by $$a_{j,k}=\sum_{m}h(m-2k)a_{j-1,m} $$ $$d_{j,k}=\sum_{m}g(m-2k)a_{j-1,m} $$ Why $h(n),g(n)$ represent a pair of low/high pass filters ? Any insight would be highly appreciated.


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