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There are two computationally distinct methods
by which we can
compute a spectrum: (1) compute all the coefficients
from (20) and
then form the cosine sum (24) for each ; and
alternately, (2) evaluate for some value of Z on the unit circle,
and multiply the resulting number by its complex conjugate.
Repeat for many values of on the unit circle.
When there are more than about twenty lags,
method (2) is cheaper, because
the fast Fourier transform (coming up soon) can be used.