随手找了个,初步运行了下,貌似能有。不知道有没BUG。 /* * To change this template, choose Tools | Templates * and open the template in the editor. */ package fft;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 % 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; } // compute the inverse FFT of x[], assuming its length is a power of 2 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; } // compute the circular convolution of x and y public static Complex[] cconvolve(Complex[] x, Complex[] y) { // should probably pad x and y with 0s so that they have same length // and are powers of 2 if (x.length != y.length) { throw new RuntimeException("Dimensions don't agree"); } int N = x.length; // compute FFT of each sequence Complex[] a = fft(x); Complex[] b = fft(y); // point-wise multiply Complex[] c = new Complex[N]; for (int i = 0; i < N; i++) { c[i] = a[i].times(b[i]); } // compute inverse FFT return ifft(c); } // compute the linear convolution of x and y public static Complex[] convolve(Complex[] x, Complex[] y) { Complex ZERO = new Complex(0, 0); Complex[] a = new Complex[2*x.length]; for (int i = 0; i < x.length; i++) a[i] = x[i]; for (int i = x.length; i < 2*x.length; i++) a[i] = ZERO; Complex[] b = new Complex[2*y.length]; for (int i = 0; i < y.length; i++) b[i] = y[i]; for (int i = y.length; i < 2*y.length; i++) b[i] = ZERO; return cconvolve(a, b); } // display an array of Complex numbers to standard output public static void show(Complex[] x, String title) { System.out.println(title); System.out.println("-------------------"); for (int i = 0; i < x.length; i++) { System.out.println(x[i]); } System.out.println(); } /********************************************************************* * Test client and sample execution * * % java FFT 4 * x * ------------------- * -0.03480425839330703 * 0.07910192950176387 * 0.7233322451735928 * 0.1659819820667019 * * y = fft(x) * ------------------- * 0.9336118983487516 * -0.7581365035668999 + 0.08688005256493803i * 0.44344407521182005 * -0.7581365035668999 - 0.08688005256493803i * * z = ifft(y) * ------------------- * -0.03480425839330703 * 0.07910192950176387 + 2.6599344570851287E-18i * 0.7233322451735928 * 0.1659819820667019 - 2.6599344570851287E-18i * * c = cconvolve(x, x) * ------------------- * 0.5506798633981853 * 0.23461407150576394 - 4.033186818023279E-18i * -0.016542951108772352 * 0.10288019294318276 + 4.033186818023279E-18i * * d = convolve(x, x) * ------------------- * 0.001211336402308083 - 3.122502256758253E-17i * -0.005506167987577068 - 5.058885073636224E-17i * -0.044092969479563274 + 2.1934338938072244E-18i * 0.10288019294318276 - 3.6147323062478115E-17i * 0.5494685269958772 + 3.122502256758253E-17i * 0.240120239493341 + 4.655566391833896E-17i * 0.02755001837079092 - 2.1934338938072244E-18i * 4.01805098805014E-17i * *********************************************************************/ public static void main(String[] args) { //int N = Integer.parseInt(args[0]); int N = Integer.parseInt("2"); Complex[] x = new Complex[N]; // original data for (int i = 0; i < N; i++) { x[i] = new Complex(i, 0); x[i] = new Complex(-2*Math.random() + 1, 0); } show(x, "x"); // FFT of original data Complex[] y = fft(x); show(y, "y = fft(x)"); // take inverse FFT Complex[] z = ifft(y); show(z, "z = ifft(y)"); // circular convolution of x with itself Complex[] c = cconvolve(x, x); show(c, "c = cconvolve(x, x)"); // linear convolution of x with itself Complex[] d = convolve(x, x); show(d, "d = convolve(x, x)"); } }
/* * To change this template, choose Tools | Templates * and open the template in the editor. */ package fft; /************************************************************************* * Compilation: javac Complex.java * Execution: java Complex * * Data type for complex numbers. * * The data type is "immutable" so once you create and initialize * a Complex object, you cannot change it. The "final" keyword * when declaring re and im enforces this rule, making it a * compile-time error to change the .re or .im fields after * they've been initialized. * * % java Complex * a = 5.0 + 6.0i * b = -3.0 + 4.0i * Re(a) = 5.0 * Im(a) = 6.0 * b + a = 2.0 + 10.0i * a - b = 8.0 + 2.0i * a * b = -39.0 + 2.0i * b * a = -39.0 + 2.0i * a / b = 0.36 - 1.52i * (a / b) * b = 5.0 + 6.0i * conj(a) = 5.0 - 6.0i * |a| = 7.810249675906654 * tan(a) = -6.685231390246571E-6 + 1.0000103108981198i * *************************************************************************/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 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; } // 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()); }}
/*
* To change this template, choose Tools | Templates
* and open the template in the editor.
*/
package fft;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 % 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;
}
// compute the inverse FFT of x[], assuming its length is a power of 2
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; } // compute the circular convolution of x and y
public static Complex[] cconvolve(Complex[] x, Complex[] y) { // should probably pad x and y with 0s so that they have same length
// and are powers of 2
if (x.length != y.length) { throw new RuntimeException("Dimensions don't agree"); } int N = x.length; // compute FFT of each sequence
Complex[] a = fft(x);
Complex[] b = fft(y); // point-wise multiply
Complex[] c = new Complex[N];
for (int i = 0; i < N; i++) {
c[i] = a[i].times(b[i]);
} // compute inverse FFT
return ifft(c);
}
// compute the linear convolution of x and y
public static Complex[] convolve(Complex[] x, Complex[] y) {
Complex ZERO = new Complex(0, 0); Complex[] a = new Complex[2*x.length];
for (int i = 0; i < x.length; i++) a[i] = x[i];
for (int i = x.length; i < 2*x.length; i++) a[i] = ZERO; Complex[] b = new Complex[2*y.length];
for (int i = 0; i < y.length; i++) b[i] = y[i];
for (int i = y.length; i < 2*y.length; i++) b[i] = ZERO; return cconvolve(a, b);
} // display an array of Complex numbers to standard output
public static void show(Complex[] x, String title) {
System.out.println(title);
System.out.println("-------------------");
for (int i = 0; i < x.length; i++) {
System.out.println(x[i]);
}
System.out.println();
}
/*********************************************************************
* Test client and sample execution
*
* % java FFT 4
* x
* -------------------
* -0.03480425839330703
* 0.07910192950176387
* 0.7233322451735928
* 0.1659819820667019
*
* y = fft(x)
* -------------------
* 0.9336118983487516
* -0.7581365035668999 + 0.08688005256493803i
* 0.44344407521182005
* -0.7581365035668999 - 0.08688005256493803i
*
* z = ifft(y)
* -------------------
* -0.03480425839330703
* 0.07910192950176387 + 2.6599344570851287E-18i
* 0.7233322451735928
* 0.1659819820667019 - 2.6599344570851287E-18i
*
* c = cconvolve(x, x)
* -------------------
* 0.5506798633981853
* 0.23461407150576394 - 4.033186818023279E-18i
* -0.016542951108772352
* 0.10288019294318276 + 4.033186818023279E-18i
*
* d = convolve(x, x)
* -------------------
* 0.001211336402308083 - 3.122502256758253E-17i
* -0.005506167987577068 - 5.058885073636224E-17i
* -0.044092969479563274 + 2.1934338938072244E-18i
* 0.10288019294318276 - 3.6147323062478115E-17i
* 0.5494685269958772 + 3.122502256758253E-17i
* 0.240120239493341 + 4.655566391833896E-17i
* 0.02755001837079092 - 2.1934338938072244E-18i
* 4.01805098805014E-17i
*
*********************************************************************/ public static void main(String[] args) {
//int N = Integer.parseInt(args[0]);
int N = Integer.parseInt("2");
Complex[] x = new Complex[N]; // original data
for (int i = 0; i < N; i++) {
x[i] = new Complex(i, 0);
x[i] = new Complex(-2*Math.random() + 1, 0);
}
show(x, "x"); // FFT of original data
Complex[] y = fft(x);
show(y, "y = fft(x)"); // take inverse FFT
Complex[] z = ifft(y);
show(z, "z = ifft(y)"); // circular convolution of x with itself
Complex[] c = cconvolve(x, x);
show(c, "c = cconvolve(x, x)"); // linear convolution of x with itself
Complex[] d = convolve(x, x);
show(d, "d = convolve(x, x)");
}
}
* To change this template, choose Tools | Templates
* and open the template in the editor.
*/
package fft;
/*************************************************************************
* Compilation: javac Complex.java
* Execution: java Complex
*
* Data type for complex numbers.
*
* The data type is "immutable" so once you create and initialize
* a Complex object, you cannot change it. The "final" keyword
* when declaring re and im enforces this rule, making it a
* compile-time error to change the .re or .im fields after
* they've been initialized.
*
* % java Complex
* a = 5.0 + 6.0i
* b = -3.0 + 4.0i
* Re(a) = 5.0
* Im(a) = 6.0
* b + a = 2.0 + 10.0i
* a - b = 8.0 + 2.0i
* a * b = -39.0 + 2.0i
* b * a = -39.0 + 2.0i
* a / b = 0.36 - 1.52i
* (a / b) * b = 5.0 + 6.0i
* conj(a) = 5.0 - 6.0i
* |a| = 7.810249675906654
* tan(a) = -6.685231390246571E-6 + 1.0000103108981198i
*
*************************************************************************/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 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;
} // 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());
}}