// 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 % 2 != 0) {
throw new RuntimeException("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;
}
// sample client for testing
public static void main(String[] args) {
Complex a = new Complex(5.0, 6.0);
Complex b = new Complex(-3.0, 4.0);
System.out.println("a = " + a);
System.out.println("b = " + b);
System.out.println("Re(a) = " + a.re());
System.out.println("Im(a) = " + a.im());
System.out.println("b + a = " + b.plus(a));
System.out.println("a - b = " + a.minus(b));
System.out.println("a * b = " + a.times(b));
System.out.println("b * a = " + b.times(a));
System.out.println("a / b = " + a.divides(b));
System.out.println("(a / b) * b = " + a.divides(b).times(b));
System.out.println("conj(a) = " + a.conjugate());
System.out.println("|a| = " + a.abs());
System.out.println("tan(a) = " + a.tan());
}
public Numeric mul(Object y) {
if (y instanceof Complex) {
Complex yc = (Complex) y;
if (yc.unit() == Unit.Empty) {
double y_re = yc.reValue();
double y_im = yc.imValue();
return new DComplex(real * y_re - imag * y_im, real * y_im + imag * y_re);
}
return Complex.times(this, yc);
}
return ((Numeric) y).mulReversed(this);
}
// 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 % 2 != 0) {
// throw new RuntimeException("N is not a power of 2");
Log.e(TAG, "N=" + Integer.toString(N) + " is not a power of 2");
return null;
}
// 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);
if (q == null) return null;
// 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);
if (r == null) return null;
// 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;
}
// return a / b
public Complex divides(Complex b) {
Complex a = this;
return a.times(b.reciprocal());
}
