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程序
    • 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 濾波器的實現也比 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件的飛速發展，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。采樣率設置為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。
首先設置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窗口如下圖所示。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數據導出到workspace待用。

2.設計FIR濾波器

在matlab命令行輸入fdatool，打開濾波器設計工具。
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，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，這里我們暫時設置為100階；
4.設置采樣頻率為6400Hz，要與simulink中的相符；
5.設置帶通范圍，這里我們設置為帶通范圍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，我們將濾波器導出到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中導出的原始波形、混雜波形，以及設計好的濾波器Hd。
在命令行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中就存儲了濾波后的波形。

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個點才為濾波后的數據起始點。raw200Hz為從scope中導出的200Hz信號數據。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數組即為FIR濾波器系數，將前邊的數據類型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.將混雜信號采樣值復制到C數組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進行FIR計算。
首先講解arm_fir_init_f32 FIR初始化函數，其函數原型為

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實例指針；numTaps為FIR階數；pCoeffs為FIR系數指針；pState為狀態數組指針，其實就是一個計算過程中需要開辟的緩存，用于計算，其長度為numTaps+blockSize-1；blockSize為計算塊的長度，大于1，小于等于原始數據的總長度即可。

配置好arm_fir_init_f32后，即可使用arm_fir_f32進行FIR計算，arm_fir_f32的函數原型為

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

由于設置了blockSize，即每次調用arm_fir_f32計算的數據長度，如blockSize設置為128時，要對總長度為1280的原始數據進行計算，就要循環調用10次arm_fir_f32，其中pSrc和pDst指針也要隨著循環進行后移。
具體FIR程序如下所示：

float32_t output[1280] = {0}; void FIR() {uint32_t timeTick = HAL_GetTick(); //函數進入時間戳uint32_t timePass = 0; //計算用時uint32_t blockSize = 128; //塊長度，原始數據長度為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保存了計算所需要的時間；output為FIR濾波后的數據輸出數組；設置blockSize為128，則numOfblock塊個數就是raw數組的長度1280除以128；pState為臨時使用內存池申請的緩存，如果你的程序中沒有內存池，可以直接開辟一個長度為1280的float數組，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數組數據導出，導入到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調用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，將波形保存在一個數組中，然后再使用FIR進行濾波處理。一般的工程開發過程為：
1.分析原始信號，確定濾波目標；
2.導出單片機采樣數據，在matlab中設計合適的FIR濾波器；
3.導出Matlab濾波器系數到單片機程序；
4.利用arm-dsp庫進行FIR濾波計算。

總結

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