On Sun, 13 Nov 2005, Charles Henry wrote:
x'' + w^2*x: The eigenfunctions are just e^-iwx and e^iwx, w is the eigenvalue. Our "matrix" in this case is the Hilbert space L2. It's not like you can take the determinate of a set of functions, the linear operator can be factored:
Look, it's not like in the PureData world anyone would bother with infinite sample rates.
What I wanted you to understand is that around here it doesn't matter that it's possible to consider infinite-dimensional spaces, so you don't need to bother with satisfying convergence because the inner product isn't an infinite series, so you don't have to consider function spaces as any different from classic vector spaces, so all your functions are representable by finite-dimensional vectors, so you can always take the determinant of a linear transform -- all that because the sampling rate is always finite and the block size is also always finite too.
Anyway, infinite sample rates are physically impossible, let alone engineerable, let alone noticeable by the human ear.
Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju Freelance Digital Arts Engineer, Montréal QC Canada