C++ Perform to a 2D FFT Inplace Given a Complex 2D Array

Fast Fourier transform (FFT) is an algorithm to compute the discrete Fourier transform (DFT) and its inverse. Basically Fourier analysis converts time (or space) to frequency and vice versa. A FFT rapidly computes transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors.

Algorithm

Begin    Declare the size of the array    Take the elements of the array    Declare three arrays    Initialize height =size of array and width=size of array    Create two outer loops to iterate on output data    Create two outer loops to iterate on input data    Compute real, img and amp. End

Example Code

#include <iostream> #include <math.h> using namespace std; #define PI 3.14159265 int n; int main(int argc, char **argv) {    cout << "Enter the size: ";    cin >> n;    double Data[n][n];    cout << "Enter the 2D elements ";    for (int i = 0; i < n; i++)       for (int j = 0; j < n; j++)          cin >> Data[i][j];    double realOut[n][n];    double imgOut[n][n];    double ampOut[n][n];    int height = n;    int width = n;    for (int yWave = 0; yWave < height; yWave++) {       for (int xWave = 0; xWave < width; xWave++) {          for (int ySpace = 0; ySpace < height; ySpace++) {             for (int xSpace = 0; xSpace < width; xSpace++) {                realOut[yWave][xWave] += (Data[ySpace][xSpace] * cos(2 *                   PI * ((1.0 * xWave * xSpace / width) + (1.0 * yWave * ySpace /                   height)))) / sqrt(width * height);                imgOut[yWave][xWave] -= (Data[ySpace][xSpace] * sin(2 * PI                   * ((1.0 * xWave * xSpace / width) + (1.0 * yWave * ySpace / height)))) /                   sqrt( width * height);                ampOut[yWave][xWave] = sqrt(                   realOut[yWave][xWave] * realOut[yWave][xWave] +                   imgOut[yWave][xWave] * imgOut[yWave][xWave]);             }             cout << realOut[yWave][xWave] << " + " <<             imgOut[yWave][xWave] << " i (" << ampOut[yWave][xWave] << ")\n";          }       }    } }

Output

Enter the size: 2 Enter the 2D elements 4 5 6 7 4.5 + 6.60611e-310 i (4.5) 11 + 6.60611e-310 i (11) -0.5 + -8.97448e-09 i (0.5) -1 + -2.15388e-08 i (1) 4.5 + 6.60611e-310 i (4.5) -2 + -2.33337e-08 i (2) -0.5 + -8.97448e-09 i (0.5) 0 + 5.38469e-09 i (5.38469e-09)