ezfftb
Perform a Fourier synthesis from real and imaginary coefficients.
Prototype
function ezfftb ( cf : numeric, xbar : numeric ) return_val : float or double
Arguments
cfFourier coefficients as created by ezfftf. The elements cf(0,...) are the real coefficients, and cf(1,...) are the imaginary coefficients.
xbarThe constant Fourier coefficient. This must be a scalar (or a single vector of the length of the product of the leftmost dimensions of x).
Return value
A double array is returned if the input cf is double, otherwise a float array is returned.
If cf(2,kcoef), then ezfftb will construct a one-dimensional series using the coefficients and the value of xbar. The length of the one-dimensional series may be odd or even depending upon the input coefficients. If cf(2,N,kcoef), where N refers to one or more dimensions and xbar(N) then ezfftb will construct a variable, say x, that that is of size x(N).
The example will clarify.
Description
There's a bug in V6.1.2 and earlier of this function in which if "npts" is odd, the wrong values are returned. This is fixed in V6.2.0.
Given Fourier coefficients cf and the series mean(s) xbar, ezfftb computes the periodic sequences and returns an array of length N x cf@npts.
If any missing values are encountered in one of the input arrays, then no calculations will be performed on that array, and the corresponding output array will be filled with missing values.
Use ezfftb_n if the dimension to do the transform across is not the rightmost dimension. This function can be significantly faster than ezfftb.
See Also
ezfftb_n, ezfftf, ezfftf_n, cfftf, cfftb
Examples
Example 1
The first example associated with ezfftf performed a Fourier analysis on a series of 24 values. It produced the real and imaginary coef. The following inputs (slightly truncated) coefficients to (approximately) reconstruct the series. Of course, if the full coefficients had been directly input the original values would be reproduced.
cReal = (/1.34, -13.48, 2.17, 3.29, -5.40, 0.08, \ ; real coef
-2.72, 2.70, 2.17,-0.35, 2.95,-1.79 /)
cImag = (/3.73, 6.89, 3.36, 0.36, 3.02, 1.00, \ ; imag coef
4.11, 1.52, 2.53,-2.64, 2.81, 0.00 /)
cf = (/ (/ cReal /) , (/ cImag /) /) ; (2,12)
xbar = 1011.04 ; mean
x = ezfftb(cf, xbar) ; Fourier synthesis
print(x)
; original
(0) 1002 1002
(1) 1017.003 1017
(2) 1018.001 1018
(3) 1019.994 1020
(4) 1017.994 1018
(5) 1026.985 1027
(6) 1027.99 1028
(7) 1030.002 1030
(8) 1011.988 1012
(9) 1011.981 1012
(10) 982.009 982
(11) 1011.994 1012
(12) 1000.98 1001
(13) 996.011 996
(14) 995.016 995
(15) 1010.986 1011
(16) 1027.022 1027
(17) 1025 1025
(18) 1029.99 1029
(19) 1015.996 1016
(20) 995.9965 996
(21) 1005.999 1006
(22) 1002.014 1002
(23) 982.0076 982
Example 2In some instances, it may be appropriate to construct a series about a different mean (commonly, 0.0). The following is the same as Example 1 but reconstruct the series about a mean of 0.0.
X = ezfftb(cf, 0.0) ; Fourier synthesis
Here X would be a one-dimensional array containing:
(/ -9.04, 5.96, 6.96, 8.95, 6.95, 15.94, \
16.95, 18.96, 0.95, 0.94,-29.03, 0.95, \
-10.06,-15.02,-16.02,-0.05, 15.98, 13.96, \
18.95, 4.96,-15.04,-5.04, -9.02,-29.03 /)
Example 3Let x(ntim,klvl,nlat,mlon) and N corresponds to (ntim,klvl,nlat) in this instance, and mlon is a number of longitude points:
cf = ezfftf (x) ; ==> cf(2,ntim,klvl,nlat,mlon/2)
; ==> cf@npts = mlon
; ==> cf@xbar ==> contains the means
length=ntim*klvl*nlat
Reconstruct using only wave 3 and set all the means to 0.0:
cf(:,:,:,:,0:1) = 0.0 ; waves 1 and 2 set to zero cf(:,:,:,:,3:mlon-1) = 0.0 ; waves >3 set to zeroHere cf@xbar will be a one-dimensional array of length ntim*klvl*nlat. We want set all to 0.0 so this is readily done via:
cf@xbar = 0.0 xWave_3 = ezfftb (cf, cf@xbar)