public class FFT {
// compute the FFT of x[], assuming its length is a power of 2
public static Complex[] fft(Complex[] x) {
int n = x.length;
// base case
if (n == 1) return new Complex[] { x[0] };
// radix 2 Cooley-Tukey FFT
if ((n&(n-1))!=0) {
throw new IllegalArgumentException("n is not a power of 2");
}
// fft of even terms
Complex[] even = new Complex[n/2];
for (int k = 0; k < n/2; k++) {
even[k] = x[2*k];
}
Complex[] q = fft(even);
// fft of odd terms
Complex[] odd = even; // reuse the array
for (int k = 0; k < n/2; k++) {
odd[k] = x[2*k + 1];
}
Complex[] r = fft(odd);
// combine
Complex[] y = new Complex[n];
for (int k = 0; k < n/2; k++) {
double kth = -2 * k * Math.PI / n;
Complex wk = new Complex(Math.cos(kth), Math.sin(kth));
y[k] = q[k].plus(wk.times(r[k]));
y[k + n/2] = q[k].minus(wk.times(r[k]));
}
return y;
}
public static void show(Complex[] input, String title) {
System.out.println(title);
System.out.println("-------------------");
for (int i = 0; i < input.length; i++) {
System.out.println(input[i]);
}
System.out.println();
}
public static void main(String[] args) {
int number_of_Bins = 65536;
Complex[] input = new Complex[number_of_Bins];
int wave_Frequency = 16384;
int wave_Period=3;
int wave_Amplitude=3;
// original data
for (int i = 0; i < number_of_Bins; i++) {
input[i] = new Complex(0, wave_Amplitude*(Math.sin(2*Math.PI*wave_Frequency*wave_Period*i/number_of_Bins)));
}
// FFT of original data
try
{
Complex[] output = fft(input);
double magnitude_temp=0;
double maximum_Magnitude=0;
for(int i=0;i<output.length;i++)
{
magnitude_temp=Math.sqrt(((output[i].re())*(output[i].re()))+((output[i].im())*(output[i].im())));
if(magnitude_temp>maximum_Magnitude)
{
maximum_Magnitude = magnitude_temp;
}
}
System.out.println("Maximum Magnitude(Peak Frequency) of output is "+Math.ceil(maximum_Magnitude)/6);
}
catch(IllegalArgumentException exception)
{
System.out.println("Error: "+exception.getMessage());
}
}
# Supporting Class to execute complex numbers operations
import java.util.Objects;
public class Complex {
private final double re; // the real part
private final double im; // the imaginary part
// create a new object with the given real and imaginary parts
public Complex(double real, double imag) {
re = real;
im = imag;
}
// return a string representation of the invoking Complex object
public String toString() {
if (im == 0) return re + "";
if (re == 0) return im + "i";
if (im < 0) return re + " - " + (-im) + "i";
return re + " + " + im + "i";
}
// return abs/modulus/magnitude
public double abs() {
return Math.hypot(re, im);
}
// return angle/phase/argument, normalized to be between -pi and pi
public double phase() {
return Math.atan2(im, re);
}
// return a new Complex object whose value is (this + b)
public Complex plus(Complex b) {
Complex a = this; // invoking object
double real = a.re + b.re;
double imag = a.im + b.im;
return new Complex(real, imag);
}
// return a new Complex object whose value is (this - b)
public Complex minus(Complex b) {
Complex a = this;
double real = a.re - b.re;
double imag = a.im - b.im;
return new Complex(real, imag);
}
// return a new Complex object whose value is (this * b)
public Complex times(Complex b) {
Complex a = this;
double real = a.re * b.re - a.im * b.im;
double imag = a.re * b.im + a.im * b.re;
return new Complex(real, imag);
}
// return a new object whose value is (this * alpha)
public Complex scale(double alpha) {
return new Complex(alpha * re, alpha * im);
}
// return a new Complex object whose value is the conjugate of this
public Complex conjugate() {
return new Complex(re, -im);
}
// return a new Complex object whose value is the reciprocal of this
public Complex reciprocal() {
double scale = re*re + im*im;
return new Complex(re / scale, -im / scale);
}
// return the real or imaginary part
public double re() { return re; }
public double im() { return im; }
// return a / b
public Complex divides(Complex b) {
Complex a = this;
return a.times(b.reciprocal());
}
// return a new Complex object whose value is the complex exponential of this
public Complex exp() {
return new Complex(Math.exp(re) * Math.cos(im), Math.exp(re) * Math.sin(im));
}
// return a new Complex object whose value is the complex sine of this
public Complex sin() {
return new Complex(Math.sin(re) * Math.cosh(im), Math.cos(re) * Math.sinh(im));
}
// return a new Complex object whose value is the complex cosine of this
public Complex cos() {
return new Complex(Math.cos(re) * Math.cosh(im), -Math.sin(re) * Math.sinh(im));
}
// return a new Complex object whose value is the complex tangent of this
public Complex tan() {
return sin().divides(cos());
}
// a static version of plus
public static Complex plus(Complex a, Complex b) {
double real = a.re + b.re;
double imag = a.im + b.im;
Complex sum = new Complex(real, imag);
return sum;
}
public boolean equals(Object x) {
if (x == null) return false;
if (this.getClass() != x.getClass()) return false;
Complex that = (Complex) x;
return (this.re == that.re) && (this.im == that.im);
}
public int hashCode() {
return Objects.hash(re, im);
}
}
}