Fwd: [PD] basic DSP stuff
matju at artengine.ca
Mon Nov 14 01:26:47 CET 2005
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
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