NCL Home > Documentation > Functions > General applied math

cfftb

Performs a backward complex discrete fourier transform [Fourier Synthesis].

Prototype

	function cfftb (
		cf     : numeric,  
		cfopt  : integer   
	)

	return_val  :   typeof(x)

Arguments

An array, possibly modified, returned by cfftf. The array should be unnormalized.

cfopt

Specifies how the reconstructed array will be returned,

cfopt=0, return the reconstructed 'complex' periodic sequence.
cfopt=1, return only the real portion of the synthesized array.
cfopt=2, return only imaginary portion of the synthesized array.

Return value

The returned array will be a real or 'complex' periodic sequence depending upon the value of cfopt. A double array is returned if cf is double, otherwise a float array is returned.

Description

Given a sequence of unnormalized real and imaginary Fourier coefficients, cf, as generated by cfftf, the cfftb function performs a backward complex Fourier transform. This is often called Fourier Synthesis. It will normalize the results before returning the complex sequence.

If any missing values [_FillValue] 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

Example 1

Perform a complex forward transform (fourier analysis: cfftf) of a real periodic sequence. Then perform complex backward transform (fourier synthesis: cfftb) to reconstruct the original series.

    x  = (/ 1002, 1017, 1018, 1020, 1018, 1027, \ 
            1028, 1030, 1012, 1012,  982, 1012, \
            1001,  996,  995, 1011, 1027, 1025, \ 
            1030, 1016,  996, 1006, 1002,  982  /)
    N  = dimsizes(x)
    
    cf = cfftf (x, 0.0, 0)   ; will construct a complex array
                                                ; carr = complex( x, 0.0)
    printVarSummary(cf)
    
    
    xNew = cfftb (cf, 1)    ; return only the real portion

    maxDiff = max(abs(xNew-x))

    print("cfft{f/b}: maxDiff="+maxDiff)

The maxDiff is at machine accuracy (~1e-6 for x of type real).

Example 2

    xr = (/ 1002, 1017, 1018, 1020, 1018, 1027, \ 
            1028, 1030, 1012, 1012,  982, 1012, \
            1001,  996,  995, 1011, 1027, 1025, \ 
            1030, 1016,  996, 1006, 1002,  982  /)
    xi = xr(::-1)
    
    cf = cfftf (xr, xi, 0)   ; will construct a complex array
                                                ; carr = complex( x, 0.0)
    
    x0 = cfftb (cf, 0)    ; return complex (2,...)
    x1 = cfftb (cf, 1)    ; return only the real portion
    x2 = cfftb (cf, 2)    ; return only the imaginary portion

    print(cf)
    print(x0)
    print(x1)
    print(x2)

Edited [reformatted] output: