java实现FFT算法(附完整源码)
时间: 2023-11-30 18:21:28 浏览: 63
下面是Java实现FFT算法的代码:
```java
import java.util.Arrays;
public class FFT {
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;
}
public static void main(String[] args) {
Complex[] x = { new Complex(1, 0), new Complex(2, 0), new Complex(3, 0), new Complex(4, 0) };
// FFT of original data
Complex[] y = fft(x);
// print results
System.out.println("x");
System.out.println("-------------------");
for (int i = 0; i < x.length; i++) {
System.out.println(x[i]);
}
System.out.println();
System.out.println("y = fft(x)");
System.out.println("-------------------");
for (int i = 0; i < y.length; i++) {
System.out.println(y[i]);
}
System.out.println();
System.out.println("y = ifft(y)");
System.out.println("-------------------");
Complex[] z = ifft(y);
for (int i = 0; i < z.length; i++) {
System.out.println(z[i]);
}
System.out.println();
}
public static Complex[] ifft(Complex[] x) {
int N = x.length;
Complex[] y = new Complex[N];
// take conjugate
for (int i = 0; i < N; i++) {
y[i] = x[i].conjugate();
}
// compute forward FFT
y = fft(y);
// take conjugate again
for (int i = 0; i < N; i++) {
y[i] = y[i].conjugate();
}
// divide by N
for (int i = 0; i < N; i++) {
y[i] = y[i].times(1.0 / N);
}
return y;
}
}
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 and angle/phase/argument
public double abs() { return Math.hypot(re, im); } // Math.sqrt(re*re + im*im)
public double phase() { return Math.atan2(im, re); } // between -pi and pi
// 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);
}
// scalar multiplication
// return a new object whose value is (this * alpha)
public Complex times(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;
}
}
```
上面的代码实现了FFT算法和IFFT算法,其中FFT算法使用递归实现,而IFFT算法则是在FFT算法的基础上进行了一些简单的变换。代码中用到了一个名为Complex的复数类,这里直接使用了作者提供的实现。
代码中的FFT算法输入为一个长度为2的n次方的复数数组,输出为进行了FFT变换后的复数数组;IFFT算法输入为一个进行了FFT变换后的复数数组,输出为进行了IFFT变换后的复数数组。
需要注意的是,这里的FFT算法只适用于输入长度为2的n次方的复数数组,输入长度不符合要求时会抛出异常。