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okay think of all set for our lecture 25 for so we're 3/4 through and we're firmly into the wavelet filter Bank book and let's see chapter 1 of that book gives the most basic wavelet the horror wavelet and filter Bank and then chapter four and five is really the heart of the book so I'm I'll do a little of chapter one but also draw right away the description of a filter Bank so this subject like the whole course is a mixture of discrete time problems matrix calculations because that's what we actually do and continuous time function problems which illuminate everything so let's see and just to mention again last time I really covered the single individual filters and I'll recap those which were listed at first as to two lectures about filters so so we're lecture ahead of the of the listed program in other words so can i recap what we did about filters soms individual filters and we were interested in low-pass filters high-pass filters g...

PROFESSOR: So let's get set to state Hall's theorem in a way that doesn't mention boys and girls. But let's remember the girl-boy setup to start. So the general setup is a bipartite graph H. And a bipartite graph has two sets of vertices-- the girl vertices and the boy vertices. Formally, there's a set L of H, called the left vertices of H, and a set R of H, called the right vertices of H. The vertices of H altogether are L of H union R of H. Both of these are non-empty. And they don't overlap. Then the edges of H have the property that they only go between L of H and R of H. That is the definition of a bipartite graph. Now, we're interested in a matching in a bipartite graph. So let's be precise again of what's a matching without having to mention boys and girls and like. A match is a total injective function from the left vertices to the right vertices. So that means every L vertex, or girl, has a match m of L that is on the other sid...