Java implementation Fast Fourier Transform FFT (Base-2 FFT for Time Extraction, Inverse Calculation, Butterfly Operation)
import java.util.Scanner;
import java.math.*;
//log function
class Log{
static public double log(double value, double base) {
return Math.log(value) / Math.log(base);
}
}
//power function
class Pow{
public static int powNM(int n,int m){
if(m == 1)
return n;
else
return n*powNM(n,m-1);
//Math.pow(m,n);
}
}
public class DFT_FFT {
public static void main (String []args){
//init varaibles
final double PI=3.141;
int N1=0; //series length
int M=0; //series level 2^M
int arraylength; //
int i=0; //input array loop count
int t=0; //output array loop count
///////////////////////////////////////////////////////////////
//check
Scanner sc=new Scanner (System.in);
while(N1<2){
System.out.println("check your series length！");
N1=sc.nextInt();
}
///////////////////////////////////////////////////////////////
//判断长度并初始化数组
//确定N=2^M的级数M
M=(Log.log(N1, 2)==(int) Log.log(N1, 2))?(int) Log.log(N1, 2) : ((int)Log.log(N1, 2))+1;
//确定数字长度
arraylength=(int)Pow.powNM(2, M);
System.out.printf("序列长度N1为%d时，数组长度为%d，级数M为%d !\n",N1,arraylength,M);
float []Array=new float [ arraylength ]; //实部
float []IArray=new float [ arraylength ]; //虚部
///////////////////////////////////////////////////////////////
//输入序列
float jc; //暂存转换后的数据
String xy;
System.out.printf("请依次输入序列的%d个值：\n",N1);
System.out.println("////////////////");
while(i<N1){
System.out.printf("x[%d]实部：\n",i);
xy=sc.next();
if((xy.charAt(0)<48|xy.charAt(0)>57)){ //输入不是数字
System.out.println("阿汪先生(a_wang_xian_sheng)的博客！");
break; //跳出循环输入
}
if((xy.charAt(0)>=48|xy.charAt(0)<=57)){ //输入数字
jc = Float.parseFloat(xy); //String转化成float类型
Array[i]=jc; //保存String转存下来的数字
}
System.out.printf("x[%d]虚部：\n",i); //输入虚部
IArray[i]=sc.nextFloat(); //录入数字
i++;
}
System.out.println("////////////////");
System.out.println("输入结果如下：");
while(t<arraylength){
System.out.printf("x[%d]=",t);
System.out.print(Array[t]);
System.out.printf("+j(%f)\n",IArray[t]);
t++;
}
//////////////////////////////////////////////////////////////
int w=0; //倒序处理时的外循环次数
int j=0; //倒序处理时的内循环次数
float ws=0; //倒序处理时的数组间值传递变量
int p=0; //倒序处理时下一倒位序的确定变量
int w1=0; //倒序处理时的外循环次数
int j1=0; //倒序处理时的内循环次数
float ws1=0; //倒序处理时的数组间值传递变量
int p1=0; //倒序处理时下一倒位序的确定变量
//倒序处理(实部)
for(w=1,j=arraylength/2;w<arraylength-1;w++)
{
if(w<j) //如果i<j,即进行变址
{
ws=Array[j];
Array[j]=Array[w];
Array[w]=ws;
}
p=arraylength/2; //求j的下一个倒位序
while(p<=j) //如果k<=j,表示j的最高位为1
{
j=j-p; //把最高位变成0
p=p/2; //k/2，比较次高位，依次类推，逐个比较，直到某个位为0
}
j=j+p; //把0改为1
}
//倒序处理(虚部)
for(w1=1,j1=arraylength/2;w1<arraylength-1;w1++)
{
if(w1<j1) //如果i<j,即进行变址
{
ws1=IArray[j1];
IArray[j1]=IArray[w1];
IArray[w1]=ws1;
}
p1=arraylength/2; //求j的下一个倒位序
while(p1<=j1) //如果k<=j,表示j的最高位为1
{
j1=j1-p1; //把最高位变成0
p1=p1/2; //k/2，比较次高位，依次类推，逐个比较，直到某个位为0
}
j1=j1+p1; //把0改为1
}
//////////////////////////////////////////////////////////////
//蝶形运算变量定义并初始化
int L=1;//蝶形运算级数，用于循环
int N=2;//蝶形运算数据量，用于循环 ，WN(k)*X(k+N/2)中的N
int distance=1;//蝶形运算两节点间的距离，用于循环（distance=N/2）
int group=arraylength/2; //蝶形运算的组数，长度为数组长度的一半
double tempr1,tempr2,tempi1,tempi2;//临时变量
int k=0; //WN(k)*X(k+N/2)中的k
//蝶形运算
for(;L<=M;L++){//第L级的蝶形运算
for(i=0;i<group;i++){//第group组的蝶形运算
for(k=0;k<distance;k++){//第k次蝶形运算
float theta=(float)(-2*PI*k/N);//旋转因子,WN(k)
tempr1=Array[N*i+k];
tempi1=IArray[N*i+k];
tempr2=Math.cos(theta)*Array[N*i+k+distance]-Math.sin(theta)*IArray[N*i+k+distance]; //CB的实数
tempi2=Math.sin(theta)*Array[N*i+k+distance]+Math.cos(theta)*IArray[N*i+k+distance]; //CB的复数
Array[N*i+k]=(float)(tempr1+tempr2);//(A+CB)的实数
IArray[N*i+k]=(float)(tempi1+tempi2);//(A+CB)的复数
Array[N*i+k+distance]=(float)(tempr1-tempr2);//(A-CB)的实数
IArray[N*i+k+distance]=(float)(tempi1-tempi2);//(A-CB)的复数
}
}
N=N*2; //下一级蝶形运算中循环分母N*2
distance*=2; //下一级蝶形运算两节点间的距离增加
group/=2; //下一级蝶形运算的组数减半
}
//////////////////////////////////////////////////////////////
//输出运算结果
int t1=0; //数组输出的循环次数
System.out.println("////////////////");
System.out.println("FFT运算结果如下：");
while(t1<arraylength){
System.out.printf("X[%d]= %f\t+j(%f)\n",t1,Array[t1],IArray[t1]);
t1++;
}
}
}
Program effect
1.Plural input
2. When entering the real part, enter any non-numeric character (string) to automatically end the entry process and the remaining sequence bits are automatically zero-added;
Checking in Matlab
x=[1 2 3 0]; X=fft(x,4); X
Some notes:
1. Plural input is possible. If the number of input digits is less than 2 ^ N times, it will be filled automatically.
2. When entering the real part, enter any non-numeric character to automatically end the entry process and zero-padded the remaining sequence bits automatically;
3. The inversion operation uses the Reid algorithm;
4. The limitation of the number of digits in the computer operation results in the error of the above two programs, and the problem is not large;
5. Modify the N in the factor W_N ^ K to calculate the FFT operation of any N points. The N in this program is (2 ^ M), which has certain limitations.
// As long as the input is individually assigned, the FFT operation of any N points (may be odd points) in the sequence can be realized.
Orignal link:https://blog.csdn.net/qq_43499622/article/details/102759545