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Usage:
hft(hx [,divbyT:T]), hx a REAL matrix considered as complex in Hermitian
form
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Keywords:
time series, complex arithmetic
Usage
hft(hx) where hx is a REAL vector or matrix, computes the real discrete
Fourier transform of each column of hx, considered as a complex series
with Hermitian symmetry in packed Hermitian form.
Any MISSING values in hx are replaced by 0 in computing the result and a
warning message is printed.
hft(hx,divbyt:T) does the same, except the result is divided by the
number of rows of hx.
Inverse transform
hconj(rft(rx,divbyt:T)) is the inverse of hft() in the sense that hx and
hconj(rft(hft(hx),divbyt:T)) are equal except for rounding error.
Limitation on length
The largest prime factor of nrows(hx) must not exceed 29. You can use
primefactors() to find the maximum factor of nrows(hx) and goodfactors()
to find a length >= nrows(hx) which has no prime factors > 29. In
addition, the product of all the "unpaired" prime factors can't be too
large. For example N = 3*5*7*11*13*17*M^2 = 255255*M^2, where M is an
integer, breaks the algorithm and hence is not allowed.
Cross references
See also cft(), rft(), hconj(), primefactors(), goodfactors().
See topic 'complex' for discussion of complex matrices in MacAnova.
See subtopic 'matrices:"complex_matrices" for a list of macros for
working with complex matrices.
Gary Oehlert
2005-08-12