目錄

• • 一、Matlab中的FIR實(shí)驗(yàn)
  • • 1.搭建原始信號(hào)
    • 2.設(shè)計(jì)FIR濾波器
    • 3.FIR濾波
    • 4.濾波前后對(duì)比
  • 二、嵌入式平臺(tái)FIR濾波移植
  • • 1.arm-dsp庫(kù)移植
    • 2.獲得FIR濾波系數(shù)
    • 3.基于arm-dsp的FIR程序
    • 4.濾波結(jié)果-與Matlab比對(duì)
  • 三、總結(jié)

電力電子應(yīng)用中，往往需要對(duì)電流、電壓信號(hào)進(jìn)行采樣，濾除干擾頻段的信號(hào)，或者保留、提取感興趣的頻段的信號(hào)。通過(guò)模擬濾波往往難以達(dá)到較好的效果，因此需要采用數(shù)字濾波器。
常用的數(shù)字濾波器有IIR、FIR濾波器兩種。FIR 濾波器最重要的優(yōu)點(diǎn)就是由于不存在系統(tǒng)極點(diǎn)，FIR 濾波器是絕對(duì)穩(wěn)定的系統(tǒng)。FIR 濾波器還確保了線性相位，這在信號(hào)處理中也非常重要。此外，由于不需要反饋，FIR 濾波器的實(shí)現(xiàn)也比 IIR 濾波器簡(jiǎn)單。FIR 濾波器的缺點(diǎn)在于它的性能不如同樣階數(shù)的 IIR 濾波器，不過(guò)由于數(shù)字計(jì)算硬件的飛速發(fā)展，這一點(diǎn)已經(jīng)不成為問(wèn)題。再加上引入計(jì)算機(jī)輔助設(shè)計(jì)，FIR 濾波器的設(shè)計(jì)也得到極大的簡(jiǎn)化。基于上述原因，FIR 濾波器比 IIR 濾波器的應(yīng)用更廣泛。
這篇博文就通過(guò)Matlab仿真來(lái)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(chǔ)的嵌入式平臺(tái)中。

一、Matlab中的FIR實(shí)驗(yàn)

通過(guò)一個(gè)簡(jiǎn)單的實(shí)驗(yàn)來(lái)使用FIR濾波器：將200Hz正弦信號(hào)疊加到基波50Hz的正弦信號(hào)上，然后利用FIR濾波器提取200Hz信號(hào)。采樣率設(shè)置為6400Hz。

1.搭建原始信號(hào)

在simulink搭建簡(jiǎn)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(shè)置simulink的仿真步長(zhǎng)為固定步長(zhǎng)，1/6400，那么就相當(dāng)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(fù)合，為了在scope中分別查看50Hz和200Hz的原始信號(hào)，2為信號(hào)疊加混合，即50Hz混合200Hz的信號(hào)。

運(yùn)行0.2秒，即10個(gè)50Hz周波，查看scope窗口如下圖所示。可以看到上方為50Hz、200Hz的原始信號(hào)，下方為混合后的信號(hào)。我們現(xiàn)在要做的就是利用FIR濾波器將200Hz信號(hào)從下方的信號(hào)中提取出來(lái)。將scope數(shù)據(jù)導(dǎo)出到workspace待用。

2.設(shè)計(jì)FIR濾波器

在matlab命令行輸入fdatool，打開(kāi)濾波器設(shè)計(jì)工具。
1.選擇帶通濾波、FIR窗口濾波；
2.選擇常用的漢寧窗；
3.指定FIR階數(shù)，一般來(lái)講，階數(shù)越高，濾波效果越好，但運(yùn)算量越大，需要在濾波效果和運(yùn)行速度上做一個(gè)取舍，這里我們暫時(shí)設(shè)置為100階；
4.設(shè)置采樣頻率為6400Hz，要與simulink中的相符；
5.設(shè)置帶通范圍，這里我們?cè)O(shè)置為帶通范圍180~220Hz；
6.點(diǎn)擊Design Filter；
7.點(diǎn)擊Group Delay Response可以查看濾波器的相位延遲，這里是50，這個(gè)數(shù)要記住，后邊要用到。


生成濾波器后，我們將濾波器導(dǎo)出到workspace中。具體操作為：file->export->Export As選擇Objects。默認(rèn)的濾波器名字為Hd。

3.FIR濾波

至此，worksapce中已經(jīng)有了scope中導(dǎo)出的原始波形、混雜波形，以及設(shè)計(jì)好的濾波器Hd。
在命令行中對(duì)混雜信號(hào)進(jìn)行濾波：

fileter(Hd,rawSignal)

其中rawSignal為混雜信號(hào)，即scope中下方的波形。運(yùn)行后，ans中就存儲(chǔ)了濾波后的波形。

4.濾波前后對(duì)比

將濾波后的波形與原始的200Hz信號(hào)進(jìn)行比對(duì)：

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

其中，濾波后的信號(hào)要從51開(kāi)始，因?yàn)闉V波器在設(shè)計(jì)時(shí)的FIR相位延遲為50，即第51個(gè)點(diǎn)才為濾波后的數(shù)據(jù)起始點(diǎn)。raw200Hz為從scope中導(dǎo)出的200Hz信號(hào)數(shù)據(jù)。繪圖后如下圖所示。可以看出FIR濾波震蕩穩(wěn)定后，能較好的帶通200Hz信號(hào)，幅值、相位均與原信號(hào)相同，50Hz信號(hào)被濾掉。

二、嵌入式平臺(tái)FIR濾波移植

1.arm-dsp庫(kù)移植

arm-dsp庫(kù)的移植可以參考我之前的博客【嵌入式】利用arm-DSP庫(kù)進(jìn)行FFT計(jì)算，獲得信號(hào)的頻譜、幅值及相位(上)中的二-1節(jié)內(nèi)容。

2.獲得FIR濾波系數(shù)

還是在fdatool中，當(dāng)設(shè)計(jì)玩濾波器后，點(diǎn)擊Targets->Generate C Header.
打開(kāi)生成的fdacoefs.h，里邊的BL即為FIR濾波器階數(shù)。B數(shù)組即為FIR濾波器系數(shù)，將前邊的數(shù)據(jù)類型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程序

1.將混雜信號(hào)采樣值復(fù)制到C數(shù)組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, 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2.利用arm_fir_init_f32和arm_fir_f32進(jìn)行FIR計(jì)算。
首先講解arm_fir_init_f32 FIR初始化函數(shù)，其函數(shù)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(shí)例指針；numTaps為FIR階數(shù)；pCoeffs為FIR系數(shù)指針；pState為狀態(tài)數(shù)組指針，其實(shí)就是一個(gè)計(jì)算過(guò)程中需要開(kāi)辟的緩存，用于計(jì)算，其長(zhǎng)度為numTaps+blockSize-1；blockSize為計(jì)算塊的長(zhǎng)度，大于1，小于等于原始數(shù)據(jù)的總長(zhǎng)度即可。

配置好arm_fir_init_f32后，即可使用arm_fir_f32進(jìn)行FIR計(jì)算，arm_fir_f32的函數(shù)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(shè)置了blockSize，即每次調(diào)用arm_fir_f32計(jì)算的數(shù)據(jù)長(zhǎng)度，如blockSize設(shè)置為128時(shí)，要對(duì)總長(zhǎng)度為1280的原始數(shù)據(jù)進(jìn)行計(jì)算，就要循環(huán)調(diào)用10次arm_fir_f32，其中pSrc和pDst指針也要隨著循環(huán)進(jìn)行后移。
具體FIR程序如下所示：

float32_t output[1280] = {0}; void FIR() {uint32_t timeTick = HAL_GetTick(); //函數(shù)進(jìn)入時(shí)間戳uint32_t timePass = 0; //計(jì)算用時(shí)uint32_t blockSize = 128; //塊長(zhǎng)度，原始數(shù)據(jù)長(zhǎng)度為1280uint32_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(jì)算所需要的時(shí)間；output為FIR濾波后的數(shù)據(jù)輸出數(shù)組；設(shè)置blockSize為128，則numOfblock塊個(gè)數(shù)就是raw數(shù)組的長(zhǎng)度1280除以128；pState為臨時(shí)使用內(nèi)存池申請(qǐng)的緩存，如果你的程序中沒(méi)有內(nèi)存池，可以直接開(kāi)辟一個(gè)長(zhǎng)度為1280的float數(shù)組，或者直接使用malloc動(dòng)態(tài)申請(qǐng)。
運(yùn)行后，timePass等于2，說(shuō)明對(duì)1280個(gè)點(diǎn)進(jìn)行100階的FIR濾波只需要2ms，速度已經(jīng)非常快了。

4.濾波結(jié)果-與Matlab比對(duì)

將output數(shù)組數(shù)據(jù)導(dǎo)出，導(dǎo)入到matlab中，與matlab的FIR濾波結(jié)果進(jìn)行比對(duì)，發(fā)現(xiàn)一模一樣完全重合，證明了stm32調(diào)用arm-dsp庫(kù)FIR濾波的準(zhǔn)確性、可靠性和高效性。

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

三、總結(jié)

實(shí)際工程應(yīng)用中，往往是單片機(jī)對(duì)信號(hào)進(jìn)行采樣，將波形保存在一個(gè)數(shù)組中，然后再使用FIR進(jìn)行濾波處理。一般的工程開(kāi)發(fā)過(guò)程為：
1.分析原始信號(hào)，確定濾波目標(biāo)；
2.導(dǎo)出單片機(jī)采樣數(shù)據(jù)，在matlab中設(shè)計(jì)合適的FIR濾波器；
3.導(dǎo)出Matlab濾波器系數(shù)到單片機(jī)程序；
4.利用arm-dsp庫(kù)進(jìn)行FIR濾波計(jì)算。

總結(jié)

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