C++ Program to Compute DFT Coefficients Directly

In discrete Fourier transform (DFT), a finite list is converted of equally spaced samples of a function into the list of coefficients of a finite combination of complex sinusoids. They ordered by their frequencies, that has those same sample values, to convert the sampled function from its original domain (often time or position along a line) to the frequency domain.

Algorithm

Begin
   Declare three variables which are the coefficient of linear equation and max value
   Read the variables
   Define a class with two variables real, img
   Create a constructor and set real, img to zero
   Take a variable M and initialize it to some integer
   Create function[M]
   For i=0 to M do
      function[i] = (((a * (double) i) + (b * (double) i)) - c)
   Declare function sine[M]
   Declare function cosine[M]
   for i = 0 to M do
      cosine[i] = cos((2 * i * k * PI) / M)
      sine[i] = sin((2 * i * k * PI) / M)
   for i = 0 to M do
      dft_value.real += function[i] * cosine[i]
      dft_value.img += function[i] * sine[i]
   Print the value
End

Example Code

#include<iostream>
#include<math.h>
using namespace std;
#define PI 3.14159265
class DFT_Coeff {
   public:
   double real, img;
   DFT_Coeff() {
      real = 0.0;
      img = 0.0;
   }
};
int main(int argc, char **argv) {
   int M = 10;
   cout << "Enter the coeff of simple linear function:\n";
   cout << "ax + by = c\n";
   double a, b, c;
   cin >> a >> b >> c;
   double function[M];
   for (int i = 0; i < M; i++) {
      function[i] = (((a * (double) i) + (b * (double) i)) - c);
   }
   cout << "Enter the max K value: ";
   int k;
   cin >> k;
   double cosine[M];
   double sine[M];
   for (int i = 0; i < M; i++) {
      cosine[i] = cos((2 * i * k * PI) / M);
      sine[i] = sin((2 * i * k * PI) / M);
   }
   DFT_Coeff dft_value;
   cout << "The coeffs are: ";
   for (int i = 0; i < M; i++) {
      dft_value.real += function[i] * cosine[i];
      dft_value.img += function[i] * sine[i];
   }
   cout << "(" << dft_value.real << ") - " << "(" << dft_value.img << " i)";
}

Output

Enter the coeff of simple linear function:
ax + by = c
4 6 7
Enter the max K value:
4
The coeffs are: (-50) - (-16.246 i)