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# ezfftb_n

Perform a Fourier synthesis from real and imaginary coefficients on the given dimension. Available in version 6.3.0 and later.

## Prototype

```	function ezfftb_n (
cf      : numeric,
xbar    : numeric,
dim  : integer
)

return_val  :  float or double
```

## Arguments

cf

Fourier coefficients as created by ezfftf. The elements cf(0,...) are the real coefficients, and cf(1,...) are the imaginary coefficients.

xbar

The constant Fourier coefficient. This must be a scalar or a single vector of the length of the product of the all dimensions of cf minus the dim-th dimension.

dim

A scalar integer indicating which dimension of cf to do the synthesis on. Dimension numbering starts from the left at 0, but since the leftmost dimension of cf represents the real and imaginary parts, this argument cannot be set to 0.

## 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_n 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, NL, kcoef, NR), where NL refers to one or more dimensions to the left of the dim-th dimension, and NR refers to one or more dimensions to the right of the dim-th dimension, then ezfftb_n will construct a variable, say x, that that is of size x(NL, npts, NR).

## Description

Given Fourier coefficients cf, the series means(s) xbar, and a dimension index to do the synthesis on, ezfftb_n computes the periodic sequences and returns an array of size NL x cf@npts x NR where NL and NR represent an arbitrary number of leftmost and rightmost dimensions.

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.

## Examples

See the ezfftb documentation for more detailed examples. Below is the third example from this documentation.

Example 1

Let x(ntim,klvl,nlat,mlon) where NL corresponds to (ntim,klvl,nlat) in this instance, and mlon is a number of longitude points:

```    cf = ezfftf_n (x,3)   ; ==> 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 zero
```
Here 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_n (cf, cf@xbar, 4)
```