嵌入式STM32利用arm-dsp库进行FIR滤波
Posted 菜老越
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目录
电力电子应用中，往往需要对电流、电压信号进行采样，滤除干扰频段的信号，或者保留、提取感兴趣的频段的信号。通过模拟滤波往往难以达到较好的效果，因此需要采用数字滤波器。
常用的数字滤波器有IIR、FIR滤波器两种。FIR 滤波器最重要的优点就是由于不存在系统极点，FIR 滤波器是绝对稳定的系统。FIR 滤波器还确保了线性相位，这在信号处理中也非常重要。此外，由于不需要反馈，FIR 滤波器的实现也比 IIR 滤波器简单。FIR 滤波器的缺点在于它的性能不如同样阶数的 IIR 滤波器，不过由于数字计算硬件的飞速发展，这一点已经不成为问题。再加上引入计算机辅助设计，FIR 滤波器的设计也得到极大的简化。基于上述原因，FIR 滤波器比 IIR 滤波器的应用更广泛。
这篇博文就通过Matlab仿真来直观的介绍FIR滤波器的用途，并将FIR滤波器移植到以STM32F4为基础的嵌入式平台中。
一、Matlab中的FIR实验
通过一个简单的实验来使用FIR滤波器：将200Hz正弦信号叠加到基波50Hz的正弦信号上，然后利用FIR滤波器提取200Hz信号。采样率设置为6400Hz。
1.搭建原始信号
在simulink搭建简易混合电路，将幅值为1的50Hz正弦波与幅值为1的200Hz正弦波混合。
首先设置simulink的仿真步长为固定步长，1/6400，那么就相当于采样率为6400Hz，如图所示。
搭建电路如下图所示。其中1为多路复合，为了在scope中分别查看50Hz和200Hz的原始信号，2为信号叠加混合，即50Hz混合200Hz的信号。
运行0.2秒，即10个50Hz周波，查看scope窗口如下图所示。可以看到上方为50Hz、200Hz的原始信号，下方为混合后的信号。我们现在要做的就是利用FIR滤波器将200Hz信号从下方的信号中提取出来。将scope数据导出到workspace待用。
2.设计FIR滤波器
在matlab命令行输入fdatool，打开滤波器设计工具。
1.选择带通滤波、FIR窗口滤波；
2.选择常用的汉宁窗；
3.指定FIR阶数，一般来讲，阶数越高，滤波效果越好，但运算量越大，需要在滤波效果和运行速度上做一个取舍，这里我们暂时设置为100阶；
4.设置采样频率为6400Hz，要与simulink中的相符；
5.设置带通范围，这里我们设置为带通范围180~220Hz；
6.点击Design Filter；
7.点击Group Delay Response可以查看滤波器的相位延迟，这里是50，这个数要记住，后边要用到。
生成滤波器后，我们将滤波器导出到workspace中。具体操作为：file->export->Export As选择Objects。默认的滤波器名字为Hd。
3.FIR滤波
至此，worksapce中已经有了scope中导出的原始波形、混杂波形，以及设计好的滤波器Hd。
在命令行中对混杂信号进行滤波：
fileter(Hd,rawSignal)
其中rawSignal为混杂信号，即scope中下方的波形。运行后，ans中就存储了滤波后的波形。
4.滤波前后对比
将滤波后的波形与原始的200Hz信号进行比对：
plot(1:200,ans(51:250),1:200,raw200Hz(1:200))
其中，滤波后的信号要从51开始，因为滤波器在设计时的FIR相位延迟为50，即第51个点才为滤波后的数据起始点。raw200Hz为从scope中导出的200Hz信号数据。绘图后如下图所示。可以看出FIR滤波震荡稳定后，能较好的带通200Hz信号，幅值、相位均与原信号相同，50Hz信号被滤掉。
二、嵌入式平台FIR滤波移植
1.arm-dsp库移植
arm-dsp库的移植可以参考我之前的博客【嵌入式】利用arm-DSP库进行FFT计算，获得信号的频谱、幅值及相位(上)中的二-1节内容。
2.获得FIR滤波系数
还是在fdatool中，当设计玩滤波器后，点击Targets->Generate C Header.
打开生成的fdacoefs.h，里边的BL即为FIR滤波器阶数。B数组即为FIR滤波器系数，将前边的数据类型real64_T改为float即可。
/*
* Filter Coefficients (C Source) generated by the Filter Design and Analysis Tool
* Generated by MATLAB(R) 8.3 and the Signal Processing Toolbox 6.21.
* Generated on: 28-Apr-2021 15:33:18
*/
/*
* Discrete-Time FIR Filter (real)
* -------------------------------
* Filter Structure : Direct-Form FIR
* Filter Length : 101
* Stable : Yes
* Linear Phase : Yes (Type 1)
*/
/* General type conversion for MATLAB generated C-code */
#include "tmwtypes.h"
/*
* Expected path to tmwtypes.h
* F:\\MatLab\\extern\\include\\tmwtypes.h
*/
const int BL = 101;
const real64_T B[101] =
-0.002364379994766,-0.002555816813742, -0.00271143828077,-0.002821346700614,
-0.002865814202786,-0.002816683118228,-0.002640000779638,-0.002299699197689,
-0.001762028066288,-0.001000368319048,4.399291056296e-18, 0.001237622441001,
0.002691519514449, 0.004319142530531, 0.006055934652271, 0.007816685262717,
0.009498734985135, 0.01098694698435, 0.01216021777687, 0.01289916830821,
0.01309454373426, 0.01265576722454, 0.01151904640175, 0.009654425543614,
0.007071214384679, 0.003821304224151,-5.964020643576e-18,-0.004255853855223,
-0.008772504883931, -0.01334655058446, -0.01775451146912, -0.02176424083345,
-0.02514755140538, -0.02769333338392, -0.02922037668388, -0.0295890978537,
-0.02871141129903, -0.02655807388539, -0.02316296707884, -0.01862395375005,
-0.01310014718858, -0.00680564532364,-1.977442795623e-17, 0.007024104515362,
0.01395531112556, 0.02047939405639, 0.02629552027152, 0.03113204072429,
0.03476090062898, 0.03700983073789, 0.03777160643401, 0.03700983073789,
0.03476090062898, 0.03113204072429, 0.02629552027152, 0.02047939405639,
0.01395531112556, 0.007024104515362,-1.977442795623e-17, -0.00680564532364,
-0.01310014718858, -0.01862395375005, -0.02316296707884, -0.02655807388539,
-0.02871141129903, -0.0295890978537, -0.02922037668388, -0.02769333338392,
-0.02514755140538, -0.02176424083345, -0.01775451146912, -0.01334655058446,
-0.008772504883931,-0.004255853855223,-5.964020643576e-18, 0.003821304224151,
0.007071214384679, 0.009654425543614, 0.01151904640175, 0.01265576722454,
0.01309454373426, 0.01289916830821, 0.01216021777687, 0.01098694698435,
0.009498734985135, 0.007816685262717, 0.006055934652271, 0.004319142530531,
0.002691519514449, 0.001237622441001,4.399291056296e-18,-0.001000368319048,
-0.001762028066288,-0.002299699197689,-0.002640000779638,-0.002816683118228,
-0.002865814202786,-0.002821346700614, -0.00271143828077,-0.002555816813742,
-0.002364379994766
;
3.基于arm-dsp的FIR程序
1.将混杂信号采样值复制到C数组raw中。
const float raw[1280] = 0,0.244157996343546,0.480700572694650,0.702300707474964,0.902197103202676,1.07444979220581,1.21416420976575,1.31767513379545,1.38268343236509,1.40834037383351,
1.39527626933728,1.34557235649577,1.26267701420615,1.15126953751204,1.01707671652874,0.866649276863147,0.707106781186548,0.545860803338831,0.390327020997647,0.247637298461043,
0.124362831115998,0.0262589976977269,-0.0419582681629318,-0.0767959872797872,-0.0761204674887133,-0.0392412152202096,0.0330608032209223,0.138561640891999,0.273678499216683,0.433606276945179,
0.612501294307107,0.803705134189045,1.00000000000000,1.19388577822130,1.37786815903729,1.54474674298438,1.68789206158978,1.80150086549709,1.88081986824350,1.92232934558625,
1.92387953251129,1.88477457352667,1.80580079685964,1.68919822230282,1.53857639348909,1.35877776450025,1.15569388572783,0.936041447371087,0.707106781186548,0.476468632830889,
0.251709851798556,0.0401290714728317,-0.151536548166946,-0.317366868109323,-0.452482795685290,-0.553230186972949,-0.617316567634911,-0.643895427011010,-0.633594855256824,-0.588489432399282,
-0.512016459170419,-0.408839758564241,-0.284666292035529,-0.146022647688710,-3.67394039744206e-16,0.146022647688711,0.284666292035529,0.408839758564241,0.512016459170420,0.588489432399282,
0.633594855256825,0.643895427011010,0.617316567634910,0.553230186972948,0.452482795685289,0.317366868109324,0.151536548166945,-0.0401290714728307,-0.251709851798557,-0.476468632830890,
-0.707106781186549,-0.936041447371088,-1.15569388572783,-1.35877776450025,-1.53857639348909,-1.68919822230282,-1.80580079685964,-1.88477457352667,-1.92387953251129,-1.92232934558625,
-1.88081986824350,-1.80150086549709,-1.68789206158978,-1.54474674298438,-1.37786815903729,-1.19388577822130,-1.00000000000000,-0.803705134189046,-0.612501294307106,-0.433606276945178,
-0.273678499216683,-0.138561640891999,-0.0330608032209226,0.0392412152202102,0.0761204674887134,0.0767959872797871,0.0419582681629319,-0.0262589976977280,-0.124362831115999,-0.247637298461043,
-0.390327020997648,-0.545860803338834,-0.707106781186550,-0.866649276863148,-1.01707671652874,-1.15126953751204,-1.26267701420615,-1.34557235649577,-1.39527626933728,-1.40834037383351,
-1.38268343236509,-1.31767513379545,-1.21416420976575,-1.07444979220581,-0.902197103202674,-0.702300707474963,-0.480700572694650,-0.244157996343547,-1.22464679914735e-15,0.244157996343549,
0.480700572694652,0.702300707474965,0.902197103202676,1.07444979220581,1.21416420976575,1.31767513379545,1.38268343236509,1.40834037383351,1.39527626933728,1.34557235649577,
1.26267701420615,1.15126953751204,1.01707671652874,0.866649276863147,0.707106781186549,0.545860803338832,0.390327020997646,0.247637298461042,0.124362831115998,0.0262589976977273,
-0.0419582681629314,-0.0767959872797872,-0.0761204674887132,-0.0392412152202096,0.0330608032209218,0.138561640892000,0.273678499216684,0.433606276945180,0.612501294307107,0.803705134189047,
1.00000000000000,1.19388577822130,1.37786815903729,1.54474674298439,1.68789206158978,1.80150086549709,1.88081986824350,1.92232934558625,1.92387953251129,1.88477457352667,
1.80580079685964,1.68919822230282,1.53857639348909,1.35877776450025,1.15569388572782,0.936041447371084,0.707106781186545,0.476468632830888,0.251709851798555,0.0401290714728308,
-0.151536548166945,-0.317366868109323,-0.452482795685288,-0.553230186972950,-0.617316567634911,-0.643895427011010,-0.633594855256824,-0.588489432399281,-0.512016459170419,-0.408839758564240,
-0.284666292035529,-0.146022647688706,-1.10218211923262e-15,0.146022647688709,0.284666292035527,0.408839758564238,0.512016459170421,0.588489432399282,0.633594855256825,0.643895427011010,
0.617316567634910,0.553230186972946,0.452482795685290,0.317366868109319,0.151536548166948,-0.0401290714728279,-0.251709851798559,-0.476468632830885,-0.707106781186550,-0.936041447371081,
-1.15569388572783,-1.35877776450025,-1.53857639348909,-1.68919822230282,-1.80580079685964,-1.88477457352667,-1.92387953251129,-1.92232934558625,-1.88081986824350,-1.80150086549709,
-1.68789206158978,-1.54474674298438,-1.37786815903728,-1.19388577822130,-0.999999999999995,-0.803705134189046,-0.612501294307103,-0.433606276945176,-0.273678499216681,-0.138561640891998,
-0.0330608032209183,0.0392412152202098,0.0761204674887133,0.0767959872797871,0.0419582681629321,-0.0262589976977290,-0.124362831115996,-0.247637298461045,-0.390327020997644,-0.545860803338833,
-0.707106781186549,-0.866649276863148,-1.01707671652874,-1.15126953751204,-1.26267701420615,-1.34557235649577,-1.39527626933728,-1.40834037383351,-1.38268343236509,-1.31767513379545,
-1.21416420976575,-1.07444979220581,-0.902197103202675,-0.702300707474956,-0.480700572694651,-0.244157996343539,-2.44929359829471e-15,0.244157996343543,0.480700572694655,0.702300707474960,
0.902197103202678,1.07444979220581,1.21416420976575,1.31767513379545,1.38268343236509,1.40834037383351,1.39527626933728,1.34557235649577,1.26267701420615,1.15126953751204,
1.01707671652873,0.866649276863145,0.707106781186546,0.545860803338830,0.390327020997642,0.247637298461043,0.124362831115994,0.0262589976977277,-0.0419582681629329,-0.0767959872797874,
-0.0761204674887129,-0.0392412152202090,0.0330608032209198,0.138561640892000,0.273678499216683,0.433606276945179,0.612501294307106,0.803705134189050,0.999999999999998,1.19388577822130,
1.37786815903728,1.54474674298439,1.68789206158978,1.80150086549709,1.88081986824350,1.92232934558625,1.92387953251129,1.88477457352667,1.80580079685964,1.68919822230281,
1.53857639348910,1.35877776450024,1.15569388572782,0.936041447371085,0.707106781186546,0.476468632830881,0.251709851798556,0.0401290714728245,-0.151536548166944,-0.317366868109322,
-0.452482795685292,-0.553230186972947,-0.617316567634911,-0.643895427011010,-0.633594855256824,-0.588489432399281,-0.512016459170419,-0.408839758564241,-0.284666292035525,-0.146022647688712,
3.49210031947972e-15,0.146022647688708,0.284666292035531,0.408839758564242,0.512016459170420,0.588489432399282,0.633594855256826,0.643895427011010,0.617316567634909,0.553230186972949,
0.452482795685286,0.317366868109326,0.151536548166942,-0.0401290714728269,-0.251709851798558,-0.476468632830900,-0.707106781186549,-0.936041447371096,-1.15569388572783,-1.35877776450025,
-1.53857639348909,-1.68919822230282,-1.80580079685964,-1.88477457352667,-1.92387953251129,-1.92232934558625,-1.88081986824350,-1.80150086549709,-1.68789206158977,-1.54474674298438,
-1.37786815903728,-1.19388577822130,-0.999999999999996,-0.803705134189033,-0.612501294307104,-0.433606276945171,-0.273678499216682,-0.138561640891994,-0.0330608032209219,0.0392412152202076,
0.0761204674887132,0.0767959872797880,0.0419582681629324,-0.0262589976977287,-0.124362831115996,-0.247637298461045,-0.390327020997654,-0.545860803338832,-0.707106781186554,-0.866649276863147,
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-0.902197103202676,-0.702300707474957,-0.480700572694636,-0.244157996343540,-3.67394039744206e-15,0.244157996343551,0.480700572694645,0.702300707474966,0.902197103202670,1.07444979220581,
1.21416420976574,1.31767513379545,1.38268343236509,1.40834037383351,1.39527626933728,1.34557235649576,1.26267701420615,1.15126953751203,1.01707671652873,0.866649276863140,
0.707106781186547,0.545860803338837,0.390327020997637,0.247637298461039,0.124362831115999,0.0262589976977311,-0.0419582681629346,-0.0767959872797873,-0.0761204674887137,-0.0392412152202092,
0.0330608032209192,0.138561640891999,0.273678499216688,0.433606276945178,0.612501294307099,0.803705134189056,1.00000000000000,1.19388577822130,1.37786815903728,1.54474674298439,
1.68789206158978,1.80150086549709,1.88081986824350,1.92232934558625,1.92387953251129,1.88477457352667,1.80580079685964,1.68919822230281,1.53857639348908,1.35877776450024,
1.15569388572783,0.936041447371070,0.707106781186539,0.476468632830891,0.251709851798565,0.0401290714728182,-0.151536548166950,-0.317366868109321,-0.452482795685291,-0.553230186972947,
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0.284666292035526,0.408839758564242,0.512016459170423,0.588489432399281,0.633594855256825,0.643895427011010,0.617316567634909,0.553230186972943,0.452482795685287,0.317366868109326,
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2.利用arm_fir_init_f32和arm_fir_f32进行FIR计算。
首先讲解arm_fir_init_f32 FIR初始化函数，其函数原型为
void arm_fir_init_f32(
arm_fir_instance_f32 * S,
uint16_t numTaps,
float32_t * pCoeffs,
float32_t * pState,
uint32_t blockSize)
其中：S为fir实例指针；numTaps为FIR阶数；pCoeffs为FIR系数指针；pState为状态数组指针，其实就是一个计算过程中需要开辟的缓存，用于计算，其长度为numTaps+blockSize-1；blockSize为计算块的长度，大于1，小于等于原始数据的总长度即可。
配置好arm_fir_init_f32后，即可使用arm_fir_f32进行FIR计算，arm_fir_f32的函数原型为
void arm_fir_f32(
const arm_fir_instance_f32 * S,
float32_t * pSrc,
float32_t * pDst,
uint32_t blockSize)
由于设置了blockSize，即每次调用arm_fir_f32计算的数据长度，如blockSize设置为128时，要对总长度为1280的原始数据进行计算，就要循环调用10次arm_fir_f32，其中pSrc和pDst指针也要随着循环进行后移。
具体FIR程序如下所示：
float32_t output[1280] = 0;
void FIR()
uint32_t timeTick = HAL_GetTick(); //函数进入时间戳
uint32_t timePass = 0; //计算用时
uint32_t blockSize = 128; //块长度，原始数据长度为1280
uint32_t numOfBlock = 1280 / blockSize; //
uint32_t i;
arm_fir_instance_f32 S;
float32_t *pState;
pState = (float32_t *)Mem.malloc((blockSize + BL - 1) * sizeof(float32_t));
if(pState != NULL)
arm_fir_init_f32(&S,BL,(float32_t *)B,pState,blockSize);
for(int i=0; i < numOfBlock; i++)
arm_fir_f32(&S, raw + (i * blockSize), output + (i * blockSize), blockSize);
timePass = HAL_GetTick() - timeTick;
Mem.free(pState);
其中，timePass保存了计算所需要的时间；output为FIR滤波后的数据输出数组；设置blockSize为128，则numOfblock块个数就是raw数组的长度1280除以128；pState为临时使用内存池申请的缓存，如果你的程序中没有内存池，可以直接开辟一个长度为1280的float数组，或者直接使用malloc动态申请。
运行后，timePass等于2，说明对1280个点进行100阶的FIR滤波只需要2ms，速度已经非常快了。
4.滤波结果-与Matlab比对
将output数组数据导出，导入到matlab中，与matlab的FIR滤波结果进行比对，发现一模一样完全重合，证明了stm32调用arm-dsp库FIR滤波的准确性、可靠性和高效性。
plot(1:1280,ans(1:1280),1:1280,stm32out)
三、总结
实际工程应用中，往往是单片机对信号进行采样，将波形保存在一个数组中，然后再使用FIR进行滤波处理。一般的工程开发过程为：
1.分析原始信号，确定滤波目标；
2.导出单片机采样数据，在matlab中设计合适的FIR滤波器；
3.导出Matlab滤波器系数到单片机程序；
4.利用arm-dsp库进行FIR滤波计算。
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