hft(hx [,divbyT:T]), hx a REAL matrix considered as complex in Hermitian form |

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. 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. 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. See topic 'complex' for discussion of complex matrices in MacAnova. See also cft(), rft(), hconj(), primefactors(), goodfactors().

Gary Oehlert 2003-01-15