convolution:
when we multiply polynomials, their elements are convolved. interesting.
multiplying decimal numbers is a convolution:
100 + 50 + 7 + .4
split function into even and odd parts. why important?
sum of all samples in an odd signal is zero. integral of odd function is zero.
projecting signal onto a sinusoidal basis vector.
inverse transform: superposition of all projections
DFT: coordinate transform, projection, matrix mult.
DFT repeats every N samples
if you project a vector onto a basis, to reconstruct it, you add up the bases.
ahh... project signal onto every possible sine wave. then reconstruct it by adding
up all the projections.
it's really just a dot product of the signal with the sample kernel, namely
e^(-jwt). interesting. we take every element of x(n), multiply by e^(-jwt), and add
them up. example how a lot of little concepts can give you something non-trivial.
