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Discrete Fourier Transform

Language: C++

Processor: Not Relevant

Submitted by Miguel De Jesus on Dec 14 2010

Discrete Fourier Transform

This is an implementation of a Discrete Fourier Transform, also known as DFT.  This code is ideal for DSP beginners and students.  This implementation is based on the assumption that the input signal is a sequence of real numbers.  The result is a sequence of complex numbers containing the DFT frequency samples.

#include<iostream>
#include<iomanip>
#include<cmath>
using namespace std;

#define pi 3.14159265

// class complex
class complex
{
public:
//This class member function set the values of the class members real and imag
void setvals(double r, double i)
{
real=r;
imag=i;
}

//This function get the values (by reference) of the class members real and imag
void getvals(double &r, double &i)
{
r=real;
i=imag;
}

private:
/* The class members real and imag represents the real and imaginary parts
of a complex number, respectively.*/

double real;
double imag;

}; // end of class complex

//**********************************************************************************************
/* function dft receives two parameters x and N. x is the input sequence containing
the discrete-time samples and N is the number of DFT points.  The complex type paramater
xk receives a sequence of N-points frequency samples (this is the DFT of the input sequence*/

void dft(double x[], int N, complex xk[])
{
double r,i;

for(int k=0;k<N;k++) //k is the index of the N-point frequency sequence
{
xk[k].setvals(0,0); //initialize the values of the counters to zero

for(int n=0;n<N;n++) //n is the index of the discrete-time sequence
{
xk[k].getvals(r,i); // get the values of real and imag

/*This is the computation of the real and imaginary parts of the DFT.
The class member function setvals is used to update the value of the accumulators
contaning the real and imaginary parts of the DFT samples*/

xk[k].setvals(r + x[n]*cos(2*pi*k/N*n),i + x[n]*sin(2*pi*k/N*n));
} //end inner for-loop

} //end outer for-loop

}//end dft function

//************************************************************************************************
//Declaration of the main() function
int main()
{
int size; // The number of DFT samples
double r,i; // r = real part of the DFT; i = imaginary part of the DFT

cout<<"Enter the desired number of DFT samples: ";
cin>>size;

double *x = new double[size];  //dynamic array x represent the discrete-time samples
complex *xk = new complex[size]; // dynamic array xk represent the DFT samples

cout<<"\nEnter the sequence x[n]: ";
for(int h=0;h<size;h++)
{
cin>>x[h];
}

//Computation of the DFT of x
dft(x, size, xk);

system("CLS"); //clear screen

cout<<"Discrete Fourier Transform: "<<endl<<endl;

for(int h=0;h<size;h++)
{
cout.precision(3); // display three (3) decimal places
xk[h].getvals(r,i); //get the DFT samples values
cout<<"xk["<<h<<"] = "<<fixed<< r <<" + "<<fixed<< i <<"j"<<endl;  // print the DFT samples
}

cout<<endl;

return 0;
}// end main function

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posted by Miguel De Jesus
Miguel De Jesus possessed a BS in Electrical Engineering. He also pursued graduate studies obtaining a MSEE with specialization in Digital Signal Processing from the Polytechnic University of Puerto Rico. He has experience in research and development in several DSP areas such as time/frequency analysis, array processing, and parallel processing.

lmorales wrote:

12/15/2010

It is interesting the way you compute the real and imaginary parts of the DFT inside the parameter list of the function setvals.

Karthik wrote:

12/31/2010

Super Work ........