FFT(快速傅立叶算法 for java)
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public class FFT {
public static final int FFT_N_LOG = 10; // FFT_N_LOG <= 13
public static final int FFT_N = 1 << FFT_N_LOG;
private static final float MINY = (float) ((FFT_N << 2) * Math.sqrt(2)); //(*)
private float[] real, imag, sintable, costable;
private int[] bitReverse;
imag = new float[FFT_N];
sintable = new float[FFT_N >> 1];
costable = new float[FFT_N >> 1];
bitReverse = new int[FFT_N];
int i, j, k, reve;
for (i = 0; i < FFT_N; i++) {
k = i;
for (j = 0, reve = 0; j != FFT_N_LOG; j++) {
reve <<= 1;
reve |= (k & 1);
k >>>= 1;
}
bitReverse[i] = reve;
}
double theta, dt = 2 * 3.14159265358979323846 / FFT_N;
for (i = 0; i < (FFT_N >> 1); i++) {
theta = i * dt;
costable[i] = (float) Math.cos(theta);
sintable[i] = (float) Math.sin(theta);
}
}
/**
* 用于频谱显示的快速傅里叶变换
* @param realIO 输入FFT_N个实数,也用它暂存fft后的FFT_N/2个输出值(复数模的平方)。
*/
public void calculate(float[] realIO) {
int i, j, k, ir, exchanges = 1, idx = FFT_N_LOG - 1;
float cosv, sinv, tmpr, tmpi;
for (i = 0; i != FFT_N; i++) {
real[i] = realIO[bitReverse[i]];
imag[i] = 0;
}
for (i = FFT_N_LOG; i != 0; i--) {
for (j = 0; j != exchanges; j++) {
cosv = costable[j << idx];
sinv = sintable[j << idx];
for (k = j; k < FFT_N; k += exchanges << 1) {
ir = k + exchanges;
tmpr = cosv * real[ir] - sinv * imag[ir];
tmpi = cosv * imag[ir] + sinv * real[ir];
real[ir] = real[k] - tmpr;
imag[ir] = imag[k] - tmpi;
real[k] += tmpr;
imag[k] += tmpi;
}
}
exchanges <<= 1;
idx--;
}
j = FFT_N >> 1;
/*
* 输出模的平方(的FFT_N倍):
* for(i = 1; i <= j; i++)
* realIO[i-1] = real[i] * real[i] + imag[i] * imag[i];
*
* 如果FFT只用于频谱显示,可以"淘汰"幅值较小的而减少浮点乘法运算. MINY的值
* 和Spectrum.Y0,Spectrum.logY0对应.
*/
sinv = MINY;
cosv = -MINY;
for (i = j; i != 0; i--) {
tmpr = real[i];
tmpi = imag[i];
if (tmpr > cosv && tmpr < sinv && tmpi > cosv && tmpi < sinv)
realIO[i - 1] = 0;
else
realIO[i - 1] = tmpr * tmpr + tmpi * tmpi;
}
}
}
public static final int FFT_N_LOG = 10; // FFT_N_LOG <= 13
public static final int FFT_N = 1 << FFT_N_LOG;
private static final float MINY = (float) ((FFT_N << 2) * Math.sqrt(2)); //(*)
private float[] real, imag, sintable, costable;
private int[] bitReverse;
public FFT() {
real = new float[FFT_N];imag = new float[FFT_N];
sintable = new float[FFT_N >> 1];
costable = new float[FFT_N >> 1];
bitReverse = new int[FFT_N];
int i, j, k, reve;
for (i = 0; i < FFT_N; i++) {
k = i;
for (j = 0, reve = 0; j != FFT_N_LOG; j++) {
reve <<= 1;
reve |= (k & 1);
k >>>= 1;
}
bitReverse[i] = reve;
}
double theta, dt = 2 * 3.14159265358979323846 / FFT_N;
for (i = 0; i < (FFT_N >> 1); i++) {
theta = i * dt;
costable[i] = (float) Math.cos(theta);
sintable[i] = (float) Math.sin(theta);
}
}
/**
* 用于频谱显示的快速傅里叶变换
* @param realIO 输入FFT_N个实数,也用它暂存fft后的FFT_N/2个输出值(复数模的平方)。
*/
public void calculate(float[] realIO) {
int i, j, k, ir, exchanges = 1, idx = FFT_N_LOG - 1;
float cosv, sinv, tmpr, tmpi;
for (i = 0; i != FFT_N; i++) {
real[i] = realIO[bitReverse[i]];
imag[i] = 0;
}
for (i = FFT_N_LOG; i != 0; i--) {
for (j = 0; j != exchanges; j++) {
cosv = costable[j << idx];
sinv = sintable[j << idx];
for (k = j; k < FFT_N; k += exchanges << 1) {
ir = k + exchanges;
tmpr = cosv * real[ir] - sinv * imag[ir];
tmpi = cosv * imag[ir] + sinv * real[ir];
real[ir] = real[k] - tmpr;
imag[ir] = imag[k] - tmpi;
real[k] += tmpr;
imag[k] += tmpi;
}
}
exchanges <<= 1;
idx--;
}
j = FFT_N >> 1;
/*
* 输出模的平方(的FFT_N倍):
* for(i = 1; i <= j; i++)
* realIO[i-1] = real[i] * real[i] + imag[i] * imag[i];
*
* 如果FFT只用于频谱显示,可以"淘汰"幅值较小的而减少浮点乘法运算. MINY的值
* 和Spectrum.Y0,Spectrum.logY0对应.
*/
sinv = MINY;
cosv = -MINY;
for (i = j; i != 0; i--) {
tmpr = real[i];
tmpi = imag[i];
if (tmpr > cosv && tmpr < sinv && tmpi > cosv && tmpi < sinv)
realIO[i - 1] = 0;
else
realIO[i - 1] = tmpr * tmpr + tmpi * tmpi;
}
}
}
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