如何用java实现低通滤波器
我正在尝试用Java实现一个低通滤波器。我的要求很简单,我必须消除超过特定频率(一维)的信号。看起来巴特沃斯过滤器适合我的需要如何用java实现低通滤波器,java,filter,waveform,Java,Filter,Waveform,我正在尝试用Java实现一个低通滤波器。我的要求很简单,我必须消除超过特定频率(一维)的信号。看起来巴特沃斯过滤器适合我的需要 现在重要的是CPU时间应该尽可能少。过滤器需要处理将近一百万个样本,我们的用户不喜欢等待太久。是否有Butterworth过滤器的现成实现,具有最佳的过滤算法 > Mark Peters在评论中说:需要过滤很多的过滤器应该用C或C++编写。但是您仍然可以使用Java。看一看。由于C/C++编译为本机代码,因此它将比在Java虚拟机(JVM)中运行字节码快得多,Java虚
现在重要的是CPU时间应该尽可能少。过滤器需要处理将近一百万个样本,我们的用户不喜欢等待太久。是否有Butterworth过滤器的现成实现,具有最佳的过滤算法 > Mark Peters在评论中说:需要过滤很多的过滤器应该用C或C++编写。但是您仍然可以使用Java。看一看。由于C/C++编译为本机代码,因此它将比在Java虚拟机(JVM)中运行字节码快得多,Java虚拟机实际上是一个虚拟处理器,它将字节码转换为本地机器的本机代码(取决于CPU指令集,如x86、x64等)我最近设计了一个简单的巴特沃斯函数()。它们很容易用Java编码,如果你问我的话应该足够快(我想你只需要将filter(double*samples,int-count)更改为filter(double[]samples,int-count) JNI的问题是它需要平台独立性,可能会混淆热点编译器,代码中的JNI方法调用可能仍然会减慢速度。所以我建议尝试Java,看看它是否足够快
在某些情况下,首先使用快速傅里叶变换并在频域中应用滤波可能是有益的,但我怀疑对于一个简单的低通滤波器来说,这比大约6倍和每个样本的几次加法要快。滤波器设计是一门权衡的艺术,要做好这件事,你需要考虑一些细节 必须“不太注意”通过的最大频率是多少,“不太注意”的最大值是多少 “很多”必须衰减的最小频率是多少,“很多”的最小值是多少 在滤波器应通过的频率范围内,可以接受多少纹波(即衰减变化) 你有很多选择,这将花费你大量的计算像matlab或scilab这样的程序可以帮助您比较权衡。您将希望熟悉一些概念,如将频率表示为采样率的小数部分,以及线性和对数(dB)衰减测量值之间的交换 例如,“完美”低通滤波器在频域中是矩形的。在时域中表示为脉冲响应,这将是一个sinc函数(sinx/x),尾部达到正负无穷大。很明显,你不能计算它,所以问题变成了,如果你把sinc函数近似为一个有限的持续时间,你可以计算,这会使你的滤波器性能降低多少
或者,如果你想要一个计算起来非常便宜的有限脉冲响应滤波器,你可以使用一个所有系数都是1的“盒式车”或矩形滤波器。(如果您将其实现为CIC过滤器,利用二进制溢出来执行“循环”累加器,那么这可能会变得更便宜,因为您稍后将获取导数)。但时间上呈矩形的滤波器在频率上看起来像sinc函数——它在通带中有sinx/x衰减(通常会提高到一定的功率,因为通常会有多级版本),在阻带中有一些“反弹”。但在某些情况下,它还是有用的,无论是单独使用还是随后使用另一种类型的过滤器。我有一页介绍了一种非常简单、非常低CPU的低通过滤器,它也能够独立于帧率。我经常使用它来平滑用户输入和绘制帧速率 简而言之,在更新循环中:
//如果您有固定的帧速率
平滑值+=(新值-平滑值)/平滑
//如果你有一个不同的帧速率
平滑值+=timeSinceLastUpdate*(新值-平滑值)/平滑
1
的平滑
值不会导致平滑,而较高的值会逐渐平滑结果
该页面有几个用JavaScript编写的函数,但公式与语言无关。这里有一个低通过滤器,它使用apache数学库中的傅里叶变换
public double[] fourierLowPassFilter(double[] data, double lowPass, double frequency){
//data: input data, must be spaced equally in time.
//lowPass: The cutoff frequency at which
//frequency: The frequency of the input data.
//The apache Fft (Fast Fourier Transform) accepts arrays that are powers of 2.
int minPowerOf2 = 1;
while(minPowerOf2 < data.length)
minPowerOf2 = 2 * minPowerOf2;
//pad with zeros
double[] padded = new double[minPowerOf2];
for(int i = 0; i < data.length; i++)
padded[i] = data[i];
FastFourierTransformer transformer = new FastFourierTransformer(DftNormalization.STANDARD);
Complex[] fourierTransform = transformer.transform(padded, TransformType.FORWARD);
//build the frequency domain array
double[] frequencyDomain = new double[fourierTransform.length];
for(int i = 0; i < frequencyDomain.length; i++)
frequencyDomain[i] = frequency * i / (double)fourierTransform.length;
//build the classifier array, 2s are kept and 0s do not pass the filter
double[] keepPoints = new double[frequencyDomain.length];
keepPoints[0] = 1;
for(int i = 1; i < frequencyDomain.length; i++){
if(frequencyDomain[i] < lowPass)
keepPoints[i] = 2;
else
keepPoints[i] = 0;
}
//filter the fft
for(int i = 0; i < fourierTransform.length; i++)
fourierTransform[i] = fourierTransform[i].multiply((double)keepPoints[i]);
//invert back to time domain
Complex[] reverseFourier = transformer.transform(fourierTransform, TransformType.INVERSE);
//get the real part of the reverse
double[] result = new double[data.length];
for(int i = 0; i< result.length; i++){
result[i] = reverseFourier[i].getReal();
}
return result;
}
公共双[]四层低通滤波器(双[]数据、双低通、双频率){
//数据:输入数据,时间间隔必须相等。
//低通:截止频率
//频率:输入数据的频率。
//apache Fft(快速傅立叶变换)接受2的幂的数组。
int minpower2=1;
while(minPowerOf2/*
* To change this license header, choose License Headers in Project Properties.
* To change this template file, choose Tools | Templates
* and open the template in the editor.
*/
package SoundCruncher;
import java.util.ArrayList;
/**
*
* @author 2sloth
* filter routine from "The scientist and engineer's guide to DSP" Chapter 20
* filterOrder can be any even number between 2 & 20
* cutoffFreq must be smaller than half the samplerate
* filterType: 0=lowPass 1=highPass
* ripplePercent is amount of ripple in Chebyshev filter (0-29) (0=butterworth)
*/
public class Filtering {
double[] filterSignal(ArrayList<Float> signal, double sampleRate ,double cutoffFreq, double filterOrder, int filterType, double ripplePercent) {
double[][] recursionCoefficients = new double[22][2];
// Generate double array for ease of coding
double[] unfilteredSignal = new double[signal.size()];
for (int i=0; i<signal.size(); i++) {
unfilteredSignal[i] = signal.get(i);
}
double cutoffFraction = cutoffFreq/sampleRate; // convert cut-off frequency to fraction of sample rate
System.out.println("Filtering: cutoffFraction: " + cutoffFraction);
//ButterworthFilter(0.4,6,ButterworthFilter.Type highPass);
double[] coeffA = new double[22]; //a coeffs
double[] coeffB = new double[22]; //b coeffs
double[] tA = new double[22];
double[] tB = new double[22];
coeffA[2] = 1;
coeffB[2] = 1;
// calling subroutine
for (int i=1; i<filterOrder/2; i++) {
double[] filterParameters = MakeFilterParameters(cutoffFraction, filterType, ripplePercent, filterOrder, i);
for (int j=0; j<coeffA.length; j++){
tA[j] = coeffA[j];
tB[j] = coeffB[j];
}
for (int j=2; j<coeffA.length; j++){
coeffA[j] = filterParameters[0]*tA[j]+filterParameters[1]*tA[j-1]+filterParameters[2]*tA[j-2];
coeffB[j] = tB[j]-filterParameters[3]*tB[j-1]-filterParameters[4]*tB[j-2];
}
}
coeffB[2] = 0;
for (int i=0; i<20; i++){
coeffA[i] = coeffA[i+2];
coeffB[i] = -coeffB[i+2];
}
// adjusting coeffA and coeffB for high/low pass filter
double sA = 0;
double sB = 0;
for (int i=0; i<20; i++){
if (filterType==0) sA = sA+coeffA[i];
if (filterType==0) sB = sB+coeffB[i];
if (filterType==1) sA = sA+coeffA[i]*Math.pow(-1,i);
if (filterType==1) sB = sB+coeffA[i]*Math.pow(-1,i);
}
// applying gain
double gain = sA/(1-sB);
for (int i=0; i<20; i++){
coeffA[i] = coeffA[i]/gain;
}
for (int i=0; i<22; i++){
recursionCoefficients[i][0] = coeffA[i];
recursionCoefficients[i][1] = coeffB[i];
}
double[] filteredSignal = new double[signal.size()];
double filterSampleA = 0;
double filterSampleB = 0;
// loop for applying recursive filter
for (int i= (int) Math.round(filterOrder); i<signal.size(); i++){
for(int j=0; j<filterOrder+1; j++) {
filterSampleA = filterSampleA+coeffA[j]*unfilteredSignal[i-j];
}
for(int j=1; j<filterOrder+1; j++) {
filterSampleB = filterSampleB+coeffB[j]*filteredSignal[i-j];
}
filteredSignal[i] = filterSampleA+filterSampleB;
filterSampleA = 0;
filterSampleB = 0;
}
return filteredSignal;
}
/* pi=3.14...
cutoffFreq=fraction of samplerate, default 0.4 FC
filterType: 0=LowPass 1=HighPass LH
rippleP=ripple procent 0-29 PR
iterateOver=1 to poles/2 P%
*/
// subroutine called from "filterSignal" method
double[] MakeFilterParameters(double cutoffFraction, int filterType, double rippleP, double numberOfPoles, int iteration) {
double rp = -Math.cos(Math.PI/(numberOfPoles*2)+(iteration-1)*(Math.PI/numberOfPoles));
double ip = Math.sin(Math.PI/(numberOfPoles*2)+(iteration-1)*Math.PI/numberOfPoles);
System.out.println("MakeFilterParameters: ripplP:");
System.out.println("cutoffFraction filterType rippleP numberOfPoles iteration");
System.out.println(cutoffFraction + " " + filterType + " " + rippleP + " " + numberOfPoles + " " + iteration);
if (rippleP != 0){
double es = Math.sqrt(Math.pow(100/(100-rippleP),2)-1);
// double vx1 = 1/numberOfPoles;
// double vx2 = 1/Math.pow(es,2)+1;
// double vx3 = (1/es)+Math.sqrt(vx2);
// System.out.println("VX's: ");
// System.out.println(vx1 + " " + vx2 + " " + vx3);
// double vx = vx1*Math.log(vx3);
double vx = (1/numberOfPoles)*Math.log((1/es)+Math.sqrt((1/Math.pow(es,2))+1));
double kx = (1/numberOfPoles)*Math.log((1/es)+Math.sqrt((1/Math.pow(es,2))-1));
kx = (Math.exp(kx)+Math.exp(-kx))/2;
rp = rp*((Math.exp(vx)-Math.exp(-vx))/2)/kx;
ip = ip*((Math.exp(vx)+Math.exp(-vx))/2)/kx;
System.out.println("MakeFilterParameters (rippleP!=0):");
System.out.println("es vx kx rp ip");
System.out.println(es + " " + vx*100 + " " + kx + " " + rp + " " + ip);
}
double t = 2*Math.tan(0.5);
double w = 2*Math.PI*cutoffFraction;
double m = Math.pow(rp, 2)+Math.pow(ip,2);
double d = 4-4*rp*t+m*Math.pow(t,2);
double x0 = Math.pow(t,2)/d;
double x1 = 2*Math.pow(t,2)/d;
double x2 = Math.pow(t,2)/d;
double y1 = (8-2*m*Math.pow(t,2))/d;
double y2 = (-4-4*rp*t-m*Math.pow(t,2))/d;
double k = 0;
if (filterType==1) {
k = -Math.cos(w/2+0.5)/Math.cos(w/2-0.5);
}
if (filterType==0) {
k = -Math.sin(0.5-w/2)/Math.sin(w/2+0.5);
}
d = 1+y1*k-y2*Math.pow(k,2);
double[] filterParameters = new double[5];
filterParameters[0] = (x0-x1*k+x2*Math.pow(k,2))/d; //a0
filterParameters[1] = (-2*x0*k+x1+x1*Math.pow(k,2)-2*x2*k)/d; //a1
filterParameters[2] = (x0*Math.pow(k,2)-x1*k+x2)/d; //a2
filterParameters[3] = (2*k+y1+y1*Math.pow(k,2)-2*y2*k)/d; //b1
filterParameters[4] = (-(Math.pow(k,2))-y1*k+y2)/d; //b2
if (filterType==1) {
filterParameters[1] = -filterParameters[1];
filterParameters[3] = -filterParameters[3];
}
// for (double number: filterParameters){
// System.out.println("MakeFilterParameters: " + number);
// }
return filterParameters;
}
}