On Fri, 17 Feb 2006, Charles Henry wrote:
so, we start with two vectors x, a reference signal and m, the actual signal that is observed If it's possible for a filter to input x, and output m, then, we have that the filter is (pointwise) m^ / x^ but this runs into problems that your matrix solvers (time-domain approach) don't have
Does something count as a "filter" if it can output something in m that doesn't exist in x? The assumption here is that the frequency band F(m)(f) is some multiple of the frequency band F(x)(f), where F is a fourier.
The space of all allowable filters has to be at most (2N-1)-dimensional, and has a N-dimensional subspace that correspond to circulants and the above assumption. The quotient space, (N-1)-dimensional, is something else; I'm not sure how it works; but it's really not like any frequency band can affect any other, because then your filter group would be (N^2)-dimensional.
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