最近做音频信号处理的时候，需要对数据做fft变换。关于fft原理：

请参考：FFT算法讲解——麻麻我终于会FFT了！

matlab实现fft函数很简单，直接调用fft即可。但java实现起来就有点难了。参考了比较好两篇java实现的博客：

A.Java实现算法导论中快速傅里叶变换FFT递归算法

B.快速傅里叶变换及java实现

通过比对。A博客只实现了数组长度是2的幂次的函数，其他就没有实现，B博客是实现了所有的，但其中有几处错误。最后实现方法如下：

1)FFT函数

这个函数A和B基本上差不多，但B博客的n为1时，返回要改一下。

public static Complex[] fft(Complex[] x) {

int n = x.length;

// 因为exp(-2i*n*PI)=1，n=1时递归原点

if (n == 1){

// 这里和B博客中有一点变化

return new Complex[]{x[0]};

}

// 如果信号数为奇数，使用dft计算

if (n % 2 != 0) {

return dft(x);

}

// 提取下标为偶数的原始信号值进行递归fft计算

Complex[] even = new Complex[n / 2];

for (int k = 0; k < n / 2; k++) {

even[k] = x[2 * k];

}

Complex[] evenValue = fft(even);

// 提取下标为奇数的原始信号值进行fft计算

// 节约内存

Complex[] odd = even;

for (int k = 0; k < n / 2; k++) {

odd[k] = x[2 * k + 1];

}

Complex[] oddValue = fft(odd);

// 偶数+奇数

Complex[] result = new Complex[n];

for (int k = 0; k < n / 2; k++) {

// 使用欧拉公式e^(-i*2pi*k/N) = cos(-2pi*k/N) + i*sin(-2pi*k/N)

double p = -2 * k * Math.PI / n;

Complex m = new Complex(Math.cos(p), Math.sin(p));

result[k] = evenValue[k].plus(m.multiple(oddValue[k]));

// exp(-2*(k+n/2)*PI/n) 相当于 -exp(-2*k*PI/n)，其中exp(-n*PI)=-1(欧拉公式);

result[k + n / 2] = evenValue[k].minus(m.multiple(oddValue[k]));

}

return result;

}

2)DFT函数

这个函数主要参考B博客的，修改的地方有：

a.当长度为1时，返回值

b.算cos，sin函数参数的时候，把-2 * k* Math.PI / n改为-2 * i * k* Math.PI / n;;

public static Complex[] dft(Complex[] x) {

int n = x.length;

// exp(-2i*n*PI)=cos(-2*n*PI)+i*sin(-2*n*PI)=1

if (n == 1)

return new Complex[]{x[0]};

Complex[] result = new Complex[n];

for (int i = 0; i < n; i++) {

result[i] = new Complex(0, 0);

for (int k = 0; k < n; k++) {

//使用欧拉公式e^(-i*2pi*k/N) = cos(-2pi*k/N) + i*sin(-2pi*k/N)

double p = -2 * i * k* Math.PI / n;

Complex m = new Complex(Math.cos(p), Math.sin(p));

result[i] = result[i].plus(x[k].multiple(m));

}

}

return result;

}

3)Complex代码

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 multiple(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 multiple(double alpha) {

return new Complex(alpha * re, alpha * im);

}

// 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.multiple(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;

}

// See Section 3.3.

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);

}

// See Section 3.3.

public int hashCode() {

return Objects.hash(re, im);

}

}

最后运行情况

matlab

matlab运行结果

上边是输入的数组，下边是fft输出数组。

java

java运行结果