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【嵌入式】STM32利用arm-dsp庫進行FIR濾波

2021-04-30 18:55:47 其他

目錄

    • 一、Matlab中的FIR實驗
      • 1.搭建原始信號
      • 2.設計FIR濾波器
      • 3.FIR濾波
      • 4.濾波前后對比
    • 二、嵌入式平臺FIR濾波移植
      • 1.arm-dsp庫移植
      • 2.獲得FIR濾波系數
      • 3.基于arm-dsp的FIR程式
      • 4.濾波結果-與Matlab比對
    • 三、總結

電力電子應用中，往往需要對電流、電壓信號進行采樣，濾除干擾頻段的信號，或者保留、提取感興趣的頻段的信號，通過模擬濾波往往難以達到較好的效果，因此需要采用數字濾波器，
常用的數字濾波器有IIR、FIR濾波器兩種，FIR 濾波器最重要的優點就是由于不存在系統極點，FIR 濾波器是絕對穩定的系統，FIR 濾波器還確保了線性相位，這在信號處理中也非常重要，此外，由于不需要反饋，FIR 濾波器的實作也比 IIR 濾波器簡單，FIR 濾波器的缺點在于它的性能不如同樣階數的 IIR 濾波器，不過由于數字計算硬體的飛速發展，這一點已經不成為問題，再加上引入計算機輔助設計，FIR 濾波器的設計也得到極大的簡化，基于上述原因，FIR 濾波器比 IIR 濾波器的應用更廣泛，
這篇博文就通過Matlab仿真來直觀的介紹FIR濾波器的用途，并將FIR濾波器移植到以STM32F4為基礎的嵌入式平臺中，

一、Matlab中的FIR實驗

通過一個簡單的實驗來使用FIR濾波器：將200Hz正弦信號疊加到基波50Hz的正弦信號上，然后利用FIR濾波器提取200Hz信號，采樣率設定為6400Hz，

1.搭建原始信號

在simulink搭建簡易混合電路，將幅值為1的50Hz正弦波與幅值為1的200Hz正弦波混合，
首先設定simulink的仿真步長為固定步長，1/6400，那么就相當于采樣率為6400Hz，如圖所示，

搭建電路如下圖所示，其中1為多路復合，為了在scope中分別查看50Hz和200Hz的原始信號，2為信號疊加混合，即50Hz混合200Hz的信號，

運行0.2秒，即10個50Hz周波，查看scope視窗如下圖所示，可以看到上方為50Hz、200Hz的原始信號，下方為混合后的信號，我們現在要做的就是利用FIR濾波器將200Hz信號從下方的信號中提取出來，將scope資料匯出到workspace待用，

2.設計FIR濾波器

在matlab命令列輸入fdatool，打開濾波器設計工具，
1.選擇帶通濾波、FIR視窗濾波；
2.選擇常用的漢寧窗；
3.指定FIR階數，一般來講，階數越高，濾波效果越好，但運算量越大，需要在濾波效果和運行速度上做一個取舍，這里我們暫時設定為100階；
4.設定采樣頻率為6400Hz，要與simulink中的相符；
5.設定帶通范圍，這里我們設定為帶通范圍180~220Hz；
6.點擊Design Filter；
7.點擊Group Delay Response可以查看濾波器的相位延遲，這里是50，這個數要記住，后邊要用到，


生成濾波器后，我們將濾波器匯出到workspace中，具體操作為：file->export->Export As選擇Objects，默認的濾波器名字為Hd，

3.FIR濾波

至此，worksapce中已經有了scope中匯出的原始波形、混雜波形，以及設計好的濾波器Hd，
在命令列中對混雜信號進行濾波：

fileter(Hd,rawSignal)

其中rawSignal為混雜信號，即scope中下方的波形，運行后，ans中就存盤了濾波后的波形，

4.濾波前后對比

將濾波后的波形與原始的200Hz信號進行比對：

plot(1:200,ans(51:250),1:200,raw200Hz(1:200))

其中，濾波后的信號要從51開始，因為濾波器在設計時的FIR相位延遲為50，即第51個點才為濾波后的資料起始點，raw200Hz為從scope中匯出的200Hz信號資料，繪圖后如下圖所示，可以看出FIR濾波震蕩穩定后，能較好的帶通200Hz信號，幅值、相位均與原信號相同，50Hz信號被濾掉，

二、嵌入式平臺FIR濾波移植

1.arm-dsp庫移植

arm-dsp庫的移植可以參考我之前的博客【嵌入式】利用arm-DSP庫進行FFT計算，獲得信號的頻譜、幅值及相位(上)中的二-1節內容，

2.獲得FIR濾波系數

還是在fdatool中，當設計玩濾波器后，點擊Targets->Generate C Header.
打開生成的fdacoefs.h，里邊的BL即為FIR濾波器階數，B陣列即為FIR濾波器系數，將前邊的資料型別real64_T改為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程式

1.將混雜信號采樣值復制到C陣列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,
-1.01707671652874,-1.15126953751203,-1.26267701420615,-1.34557235649577,-1.39527626933728,-1.40834037383351,-1.38268343236509,-1.31767513379545,-1.21416420976575,-1.07444979220580,
-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,
-0.617316567634911,-0.643895427011011,-0.633594855256824,-0.588489432399284,-0.512016459170413,-0.408839758564237,-0.284666292035531,-0.146022647688717,8.08638275819206e-15,0.146022647688712,
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2.利用arm_fir_init_f32和arm_fir_f32進行FIR計算，
首先講解arm_fir_init_f32 FIR初始化函式，其函式原型為

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為fir實體指標；numTaps為FIR階數；pCoeffs為FIR系數指標；pState為狀態陣列指標，其實就是一個計算程序中需要開辟的快取，用于計算，其長度為numTaps+blockSize-1；blockSize為計算塊的長度，大于1，小于等于原始資料的總長度即可，

配置好arm_fir_init_f32后，即可使用arm_fir_f32進行FIR計算，arm_fir_f32的函式原型為

void arm_fir_f32(
const arm_fir_instance_f32 * S,
float32_t * pSrc,
float32_t * pDst,
uint32_t blockSize)

由于設定了blockSize，即每次呼叫arm_fir_f32計算的資料長度，如blockSize設定為128時，要對總長度為1280的原始資料進行計算，就要回圈呼叫10次arm_fir_f32，其中pSrc和pDst指標也要隨著回圈進行后移，
具體FIR程式如下所示：

float32_t output[1280] = {0};
void FIR()
{
	uint32_t timeTick = HAL_GetTick();		//函式進入時間戳
	uint32_t timePass = 0;					//計算用時
	uint32_t blockSize = 128;				//塊長度，原始資料長度為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保存了計算所需要的時間；output為FIR濾波后的資料輸出陣列；設定blockSize為128，則numOfblock塊個數就是raw陣列的長度1280除以128；pState為臨時使用記憶體池申請的快取，如果你的程式中沒有記憶體池，可以直接開辟一個長度為1280的float陣列，或者直接使用malloc動態申請，
運行后，timePass等于2，說明對1280個點進行100階的FIR濾波只需要2ms，速度已經非常快了，

4.濾波結果-與Matlab比對

將output陣列資料匯出，匯入到matlab中，與matlab的FIR濾波結果進行比對，發現一模一樣完全重合，證明了stm32呼叫arm-dsp庫FIR濾波的準確性、可靠性和高效性，

 plot(1:1280,ans(1:1280),1:1280,stm32out)

三、總結

實際工程應用中，往往是單片機對信號進行采樣，將波形保存在一個陣列中，然后再使用FIR進行濾波處理，一般的工程開發程序為：
1.分析原始信號，確定濾波目標；
2.匯出單片機采樣資料，在matlab中設計合適的FIR濾波器；
3.匯出Matlab濾波器系數到單片機程式；
4.利用arm-dsp庫進行FIR濾波計算，

轉載請註明出處，本文鏈接：https://www.uj5u.com/qita/281714.html

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