mkcorrts.RdThe time series produced will have the power spectrum given in the columns of
Fxmag.
mkcorrts(fldgen, phase = NULL, method = 1, complexout = FALSE)
| fldgen | A |
|---|---|
| phase | An optional matrix of phases. See notes in the Details section. |
| method | Integer specifying method 1 or method 2 for generating the
phases. Ignored if |
| complexout | The inverse FFT produces complex-valued results; however, the imaginary parts should all be zero. By default we return Re(rslt), but setting this flag causes the result to be left in complex form. This is mostly useful for testing. |
The phase argument allows a user to provide fixed phases to be used in
the field construction. This usually is not desirable because an
arbitrary set of phases will not generally produce properly uncorrelated
outputs. However, it may occasionally be useful to reproduce the input ESM
data, or some other data set for which the phases are known. To make this
sort of exercise easier, the function will accept a matrix containing phases
for all frequencies, including the negative ones, despite the fact that only
the phases for positive frequencies are needed.
Method I assignes uniform random values in [0,2pi) to all phases. This method is simple and fast, but it produces a slight bias in the covariance of the projection coefficients for the EOFs. (The covariance of the projection coefficients for two distinct EOFs should be zero.) Although this produces biases in the grid cell statistics, in many cases they are small enough to be ignorable.
Method II is more conservative in its phase randomization. It uses the Fourier transform of one of the input data sets as a prototype and for each frequency component it generates a random phase shift and adds it to that frequency component for all of the EOFs. This guarantees that the covariance will be zero, but at the cost of making the space of possible realizations much lower dimension, roughly 1/2 N instead of 1/2 M*N (where M is the number of EOFs and N is the number of basis functions).
It should be possible to supply a partial matrix of phases, with some values specified and the rest set to NA. This would allow us, for example, to specify phases for the global mean component (EOF-0) while the other components are randomized.