Download or view Fourier2d.frink in plain text format
/* This file contains routines for 2-dimensional Fourier transforms of discrete
data.
Note that these algorithms are now built into Frink and this file is no
longer necessary! */
// The (optional) second argument divFactor sets the scaling factor for
// the results. This means that the scaling factor (the whole
// expression to the left of the summation symbol above) becomes:
//
// FFT InverseFFT
//
// divFactor = 0: 1/sqrt[n] 1/sqrt[n]
// divFactor = -1: 1/n 1 (default)
// divFactor = 1: 1 1/n
//
//
// The (optional) third argument direction sets the sign used in the
// exponent.
//
// FFT | InverseFFT
// |
// direction = 1: e^( 2 pi i j k / n) | e^(-2 pi i j k / n) (default)
// direction = -1: e^(-2 pi i j k / n) | e^( 2 pi i j k / n)
/* Return the Fourier transform of a 2-D array. */
DFT2D[values, divFactor=-1, direction=1] :=
{
rows = length[values]
cols = length[values@0]
result1 = new array
for rowNum = 0 to rows-1
result1@rowNum = DFT[values@rowNum, divFactor, direction]
result1 = transpose[result1]
result2 = new array
for colNum = 0 to cols-1
result2@colNum = DFT[result1@colNum, divFactor, direction]
return transpose[result2]
}
// Produces the inverse of the FFT given by the FFT function. In fact, it just
// calls the FFT function with appropriately-reversed parameters.
//
// If you specified the optional second or third arguments for the FFT
// function, you will need to pass in the *same* arguments to this function
// to get the inverse operation. This function takes care of reversing them
// appropriately.
InverseDFT2D[x, divFactor=-1, direction=1] := DFT2D[x, -divFactor, -direction]
/** Returns the transpose of a 2D matrix. */
transpose[values] :=
{
rows = length[values]
cols = length[values@0]
result = new array[[cols, rows]]
for rowNum = 0 to rows-1
for colNum = 0 to cols-1
result@colNum@rowNum = values@rowNum@colNum
return result
}
Download or view Fourier2d.frink in plain text format
This is a program written in the programming language Frink.
For more information, view the Frink
Documentation or see More Sample Frink Programs.
Alan Eliasen was born 19963 days, 7 hours, 37 minutes ago.