My implementation of a 15 point Fourier Transform. Inspiration for a C++ Fourier Library.

Fourier.cpp

#include <cmath>
#include <iostream>

using namespace std;

								//creating a custom data type for complex no.
struct complx							//The 15 point set is represented here as an
{								//	array of complx data types.
	double real;
	double imag;
};				
								//function computes DFT for in[] and stores in out[].
								//N is the no. of elements in in[] .
void DFT(complx in[], complx out[], int N) 
{
	int x, y;
	
								//this loop will compute each output element.
	for (x = 0; x < N; x++) 
	{	
		complx summation;
		summation.real = 0; summation.imag = 0;

								//loop for summation from i=0 to i=N.
		for (y = 0; y < N; y++) 
		{			
			summation.real+= in[y].real*cos(2*M_PI*y*x/N)+in[y].imag*sin(2*M_PI*y*x/N);
			summation.imag+=-in[y].real*sin(2*M_PI*y*x/N)+in[y].imag*cos(2*M_PI*y*x/N);
		}
		
		out[x] = summation;
	}
}

										//function computes IDFT for in[] stores output to out[]
										//N is the no. of elements in in[]
void IDFT(complx in[], complx out[], int N) 
{
	int i;
									
	for (i = 0; i < N; i++) 
	{	
		in[i].imag *= -1;				//changing the sign of imaginary part
	}
	
	DFT(in, out, N);					//performing SFT function
	for (i = 0; i < N; i++) 
	{	
		out[i].real = out[i].real/N;	//dividing the time domain by N
		out[i].imag = -out[i].imag/N;	//and also changing the sign of the imaginary part
	}
	
}

										//Function to diplay the contents of an array of complx
void display(complx x[], int n)
{
	for (int i = 0; i < n; i++)
	{
		cout<<x[i].real;
		cout<<"     "<<"i ";
		cout<<x[i].imag;
		cout<<endl<<endl;
	}
}
										//function to take user input for a complx array
void user_input(complx x[], int n)
{

	for (int i = 0; i < n; i++)
	{   cout<<endl<<"Point no. "<<i<<endl;
		cin>>x[i].real;
		cout<<"     "<<"i ";
		cin>>x[i].imag;
	}
}
	



int main()
{
	int N=15;							//the no. of elements in input

/*no. of elements can be taken as user input.
15 is taken as per the question.
*/
	int k;	
	complx in[N], out[N];
	
	cout<<endl<<"Enter The input."<<endl;
	cout<<"Enter the real and imaginary part of the "<<N<<" elements :"<<endl;									
	
	user_input(in, N);					//input values
	
	DFT(in, out, N);
	
	cout<<endl<<endl<<"Here is the output after DFT ::"<<endl;
	
	display(out, N);					//displaying output
	
	int option;
	
										//Giving a choice to perform IDFT on the output	
	cout<<endl<<"Do you want to perform a IDFT on the to check if the DFT computation is correct?";
	cout<<endl<<"Enter 1 for YES or 2 for EXIT. "<<endl;
	cin>>option;
	
	if (option == 1)
	{
		IDFT(out, in, N);
	
		cout<<endl<<endl<<"Here is the output after IDFT ::"<<endl;
			
		display(in, N);		
	
	}
	
	else
	{ 
		goto exit;
	}
 
 exit:	
	cout<<endl<<"Thankyou for using the Program. I will now exit."<<endl<<endl;
	
	return 0;	
		
}