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# cft()

Usage:
 ```cft(cx [,divbyT:T]), cx a REAL matrix representing complex data ```

Keywords: time series, complex arithmetic
```cft(cx) where cx is a REAL vector or matrix, computes the fully complex
form of the discrete Fourier transforms of successive pairs of columns
of cx, considered as the real and imaginary parts of complex series.
The real and imaginary parts of the results are in alternating columns.

Any MISSING values in cx are replaced by 0 in computing the result and a
warning message is printed.

cft(cx,divbyt:T) does the same except the transform is divided by the
number of rows of cx.

cconj(cft(cconj(cx),divbyt:T)) is the inverse of cft() in the sense that
cx and cconj(cft(cconj(cft(cx)),divbyt:T)) are equal except for rounding
error.

The largest prime factor of nrows(cx) must not exceed 29.  You can use
primefactors() to find the maximum factor of nrows(cx) and goodfactors()
to find a length >= nrows(cx) 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 hft(), rft(), cconj(), primefactors(), goodfactors().
```

Gary Oehlert 2003-01-15