This is the java implementation of Naive DFT approach over function. Formula for calculating the coefficient is X(k) = Sum(x(n)*cos(2*PI*k*n/N) – iSum(x(n)*sin(2*PI*k*n/N)) over 0 to N-1. This approach tries to many transforms using different values of k from 0 to N-1.

Here is the source code of the Java Program to Compute Discrete Fourier Transform Using Naive Approach. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

`//This is a java program to perform the DFT using naive approach`

import java.util.Scanner;

public class DFT_Naive_Approach

`{`

double real, img;

public DFT_Naive_Approach()

`{`

this.real = 0.0;

this.img = 0.0;

`}`

public static void main(String args[])

`{`

int N = 10;

Scanner sc = new Scanner(System.in);

System.out.println("Disd=crete Fourier Transform using naive method");

System.out.println("Enter the coefficient of simple linear funtion:");

System.out.println("ax + by = c");

double a = sc.nextDouble();

double b = sc.nextDouble();

double c = sc.nextDouble();

double []function = new double[N];

for(int i=0; i<N; i++)

`{`

function[i] = (((a*(double)i) + (b*(double)i)) - c);

`}`

System.out.println("Enter the max K value: ");

int k = sc.nextInt();

DFT_Naive_Approach []dft_val = new DFT_Naive_Approach[k];

System.out.println("The coefficients are: ");

for(int j=0; j<k; j++)

`{`

dft_val[j] = new DFT_Naive_Approach();

for(int i=0; i<N; i++)

`{`

dft_val[j].real += function[i] * Math.cos((2 * i * j * Math.PI) / N);;

dft_val[j].img += function[i] * Math.sin((2 * i * j * Math.PI) / N);;

`}`

System.out.println("("+dft_val[j].real + ") - " + "("+dft_val[j].img + " i)");

`}`

sc.close();

`}`

`}`

Output:

$ javac DFT_Naive_Approach.java $ java DFT_Naive_Approach Discrete Fourier Transform using naive method Enter the coefficient of simple linear funtion: ax + by = c 1 2 3 Enter the max K value: 20 The coefficients are: (105.0) - (0.0 i) (-15.00000000000001) - (-46.1652530576288 i) (-15.00000000000001) - (-20.6457288070676 i) (-15.000000000000005) - (-10.898137920080407 i) (-15.000000000000004) - (-4.873795443493586 i) (-15.0) - (1.4695761589768243E-14 i) (-14.999999999999996) - (4.873795443493611 i) (-15.000000000000103) - (10.898137920080355 i) (-14.999999999999968) - (20.64572880706762 i) (-14.999999999999922) - (46.16525305762871 i) (105.0) - (-1.7634913907721884E-13 i) (-15.00000000000012) - (-46.16525305762882 i) (-15.000000000000053) - (-20.645728807067577 i) (-14.999999999999911) - (-10.898137920080416 i) (-15.000000000000037) - (-4.87379544349373 i) (-15.0) - (1.0803613098771371E-13 i) (-14.999999999999984) - (4.873795443493645 i) (-14.99999999999996) - (10.89813792008029 i) (-14.999999999999677) - (20.645728807067492 i) (-14.999999999999769) - (46.16525305762875 i)

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