# C++ Program to Compute DFT Coefficients Directly

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
Declare three variables which are the coefficient of linear equation and max value
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)
Published on 15-Mar-2019 11:55:11