# C++ Program to Compute Discrete Fourier Transform Using Naive Approach

C++Server Side ProgrammingProgramming

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
Take a variable M and initialize it to some integer
Declare an array function[M]
For i = 0 to M-1 do
function[i] = (((a * (double) i) + (b * (double) i)) - c)
Done
Declare function sine[M]
Declare function cosine[M]
for i =0 to M-1 do
cosine[i] = cos((2 * i * k * PI) / M)
sine[i] = sin((2 * i * k * PI) / M)
Done
Declare DFT_Coeff dft_value[k]
for j = 0 to k-1 do
for i = 0 to M-1 do
dft_value.real += function[i] * cosine[i]
dft_value.img += function[i] * sine[i]
Done
Done
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 coefficient 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);
//System.out.print( " "+function[i] + " ");
}
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[k];
cout << "The coefficients are: ";
for (int j = 0; j < k; j++) {
for (int i = 0; i < M; i++) {
dft_value[j].real += function[i] * cosine[i];
dft_value[j].img += function[i] * sine[i];
}
cout << "(" << dft_value[j].real << ") - " << "(" << dft_value[j].img <<" i)\n";
}
}

## Output

Enter the coefficient of simple linear function:
ax + by = c
4 5 6
Enter the max K value: 10
The coefficients are:
(345) - (-1.64772e-05 i)
(345) - (-1.64772e-05 i)
(345) - (-1.64772e-05 i)
(345) - (-1.64772e-05 i)
(345) - (-1.64772e-05 i)
(345) - (-1.64772e-05 i)
(345) - (-1.64772e-05 i)
(345) - (-1.64772e-05 i)
(345) - (-1.64772e-05 i)
(345) - (-1.64772e-05 i)