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[DSP学习笔记]基于TMS320F28335的FFT及加窗函数实现_ref_rfft_f32
作者：小丑西瓜9 | 2024-03-22 11:14:55
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ref_rfft_f32
一、新建工程
首先我们先将C2000 wave中我们所需要的函数库给导入到我们的新建工程中（可见于我实现FIR滤波文章中导入函数库的操作）。
工程中可见有以下文件。（仅FFT可删除滤波有关文件）
接着新建我们所需的文件INPUT.c于Window.c。
二、输入信号
借助MATLAB我们来生成所需的输入信号于窗函数
生成输入信号的MATLAB程序如下：
- %生成固定点数固定频率的正弦信号
- %fs为采样率
- %f为多频信号频率
- %N为采样点数
- %amp为信号幅值
- %phase为信号初相位
- function [input,t] = mult_freq_signal_test(fs,f,N,amp,phase)
- dt = 1/fs; %采样周期
- t = dt*N; %采样时间
- temp = (0:dt:(N-1)*dt)';
- y = amp.*sin(2*pi*f.*temp+phase/180*pi);
- Num = size(f,2); %获取f频率个数
- input = y*ones(Num,1);
- subplot(1,2,1);
- plot(temp/dt,input);
- title('信号时域');
- xlabel('点数 N');ylabel('幅值 A');
- subplot(1,2,2);
- Y = fftshift(fft(input));%做傅里叶变换并把零频点移到频谱中心
- F = (-N/2:N/2-1)*(fs/N);%设置横坐标
- plot(F,abs(Y)/max(abs(Y)));
- title('信号频域');
- xlabel('频率 f');ylabel('幅值 A')
- end
- %与mult_freq_signal_test.m函数式文件配合使用，将生成的输出信号保存到本地
- fs=8e4; %设采样率为80K
- f = [1e4,1.5e4,3e4]; %频率矩阵（1*N）测试信号频率为10K,15K,30K
- phase = [20,0,40]; %初相位分别为为20，0，40
- amp = [0.5/3*4095,0.3/3*4095,0.4/3*4095];%对应幅值为0.5V，0.3V，0.4V信号的采集值（ADC为0-3V）
- N=1024; %采样点数
-
- y=mult_freq_signal_test(fs,f,N,amp,phase);
-
- y=reshape(y,[4,N/4]);
- y=y+1.2/3*4095; %用于增加直流偏置，无需直流偏置时可注释，直流偏置为1V
- y=y';
-
- %writematrix(y,'record.txt','delimiter',',');%将生成的初始信号保存到.m文件路径下的record.txt
-
- fileID = fopen('record.txt','w');
- for i=1:1:N/4
- fprintf(fileID,'%.6f,%.6f,%.6f,%.6f,\n',y(i,1),y(i,2),y(i,3),y(i,4));
- end
- fclose(fileID);%将生成的初始信号保存到.m文件路径下的record.txt
将record.txt的文件内容复制到INPUT.c中，如下：
- //#############################################################################
- //! \file input.c
- //! \brief Input Vector (2048)
- //! \author Vishal Coelho
- //! \date 19-Jan-2023
- //!
- //
- // Group: C2000
- // Target Family: $DEVICE$
- //
- //#############################################################################
- //
- //
- // $Copyright: Copyright (C) 2020 Texas Instruments Incorporated -
- // http://www.ti.com/ ALL RIGHTS RESERVED $
- //#############################################################################
-
- #include <stdint.h>
-
-
- #pragma DATA_SECTION(FFT_input, "FFT_buffer3")
-
-
- // Matrix is 2 times its required sizeas it will be used to store
- // 1024 floats at a later point
- uint16_t FFT_input[2048] = {
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- 2222.390783,2682.470769,2150.640175,2313.650403,
- 644.109217,815.149034,1704.480279,1183.969400,
- 2222.390783,1925.813432,1571.519721,2627.068134,
- 1463.109217,1128.566765,1125.359825,427.312063,
- 2222.390783,2682.470769,2150.640175,2313.650403,
- 644.109217,815.149034,1704.480279,1183.969400,
- 2222.390783,1925.813432,1571.519721,2627.068134,
- 1463.109217,1128.566765,1125.359825,427.312063,
- 2222.390783,2682.470769,2150.640175,2313.650403,
- 644.109217,815.149034,1704.480279,1183.969400,
- 2222.390783,1925.813432,1571.519721,2627.068134,
- 1463.109217,1128.566765,1125.359825,427.312063,
- 2222.390783,2682.470769,2150.640175,2313.650403,
- 644.109217,815.149034,1704.480279,1183.969400,
- 2222.390783,1925.813432,1571.519721,2627.068134,
- 1463.109217,1128.566765,1125.359825,427.312063,
- 2222.390783,2682.470769,2150.640175,2313.650403,
- 644.109217,815.149034,1704.480279,1183.969400,
- 2222.390783,1925.813432,1571.519721,2627.068134,
- 1463.109217,1128.566765,1125.359825,427.312063,
- 2222.390783,2682.470769,2150.640175,2313.650403,
- 644.109217,815.149034,1704.480279,1183.969400,
- 2222.390783,1925.813432,1571.519721,2627.068134,
- 1463.109217,1128.566765,1125.359825,427.312063,
- 2222.390783,2682.470769,2150.640175,2313.650403,
- 644.109217,815.149034,1704.480279,1183.969400,
- 2222.390783,1925.813432,1571.519721,2627.068134,
- 1463.109217,1128.566765,1125.359825,427.312063,
- 2222.390783,2682.470769,2150.640175,2313.650403,
- 644.109217,815.149034,1704.480279,1183.969400,
- 2222.390783,1925.813432,1571.519721,2627.068134,
- 1463.109217,1128.566765,1125.359825,427.312063,
- 2222.390783,2682.470769,2150.640175,2313.650403,
- 644.109217,815.149034,1704.480279,1183.969400,
- 2222.390783,1925.813432,1571.519721,2627.068134,
- 1463.109217,1128.566765,1125.359825,427.312063,
- 2222.390783,2682.470769,2150.640175,2313.650403,
- 644.109217,815.149034,1704.480279,1183.969400,
- 2222.390783,1925.813432,1571.519721,2627.068134,
- 1463.109217,1128.566765,1125.359825,427.312063,
- };
-
-
-
-
- // End of File
三、窗函数
接下我们进行窗函数的生成。
1.加窗之前，首先我们要明白我们为什么要加窗。
在实际应用中，我们采集到的信号通常是较长的非周期时间序列，在进行FFT时，需要对信号进行截断。截断后得到的信号通常是非周期信号，所以FFT结果就变成了连续的谱线，周期信号的频率-幅值不再是一条垂直的直线，而是一条曲线，同时幅值下降，泄露到曲线其他频率点，即我们常说的频谱泄露。而窗函数一个周期函数，窗函数与截断信号相乘后，会变成比较接近周期函数的波形(实际上就是利用窗函数进行调制)。加窗后的信号进行FFT后，得到的频谱曲线会更窄，趋向于垂直直线。因此对频谱泄露有一定改善。
2.知道为什么要加窗后，我们再来根据实际情况来选择我们所需要的窗函数。
通常情况下，我们不对输入信号进行处理，而直接截断情况下相当于给信号加了一个矩形窗。
如果我们对于FFT后的结果要求精确的幅值，平顶窗是我们的首选。
如果我们对应FFT后的结果要求精确的频率点，则可以选择汉宁窗。
如果检测两个频率相近、幅度不同的信号，可以选用布莱克曼窗。
如果对应频率于幅值均有一定要求，则可以选用凯赛窗。
3.选择完窗函数，我们还要对FFT后的结果乘以他们对应的恢复系数（窗函数对信号有衰减），如下表：
了解完以上知识，我们便可以继续我们的实验。
在MATLAB命令行窗口敲入window，进入下列界面并完成下列配置。（本次测试选用汉宁窗）
点击文件，导出
导出到工作区，我使用默认的变量名。我们便在工作区得到了从我们所需要的窗函数。
但是，我们工程实际应用，还需对得到的窗函数进行处理，将其转化为Q16型。
官方例程中提出，如下
通过编写MATLAB文件实现，并保存到本地的window.txt文件中。
- %将窗设计器生成的窗系数打印到window.txt文件中
-
- fileID = fopen('window.txt','w');
- N=1024;%生成窗点数
-
- Win=reshape(Win',N,1);
- Windows=uint16(floor(Win.*(2^16))); % convert to Q16
-
- Windows=reshape(Windows,[4,N/4]);
- Windows=Windows';
- for i=1:1:N/8
- fprintf(fileID,'%d,%d,%d,%d,\n',Windows(i,1),Windows(i,2),Windows(i,3),Windows(i,4));
- end
- fclose(fileID);%将生成的初始信号保存到.m文件路径下的window.txt
将window.txt的内容复制到window.c中，如下：
- //#############################################################################
- //! \file window.c
- //! \brief window Vector (512)
- //! \author yang
- //! \date 19-Jan-2023
- //! 此窗函数为汉宁窗，由MATLAB生成，加窗后FFT结果需乘以恢复系数，汉宁窗恢复系数为2
- //
- // Group: C2000
- // Target Family: $DEVICE$
- //
- //#############################################################################
- #include "dsp.h"
-
- const uint16_t Window[512]={
- 0,0,2,5,
- 9,15,22,30,
- 39,50,61,74,
- 88,104,121,138,
- 158,178,200,222,
- 246,272,298,326,
- 355,385,416,449,
- 483,518,554,592,
- 630,670,711,754,
- 797,842,888,935,
- 983,1033,1084,1136,
- 1189,1243,1299,1355,
- 1413,1472,1533,1594,
- 1657,1720,1785,1851,
- 1919,1987,2057,2128,
- 2199,2273,2347,2422,
- 2499,2576,2655,2735,
- 2816,2898,2982,3066,
- 3152,3238,3326,3415,
- 3505,3596,3688,3782,
- 3876,3972,4068,4166,
- 4265,4364,4465,4567,
- 4670,4774,4880,4986,
- 5093,5201,5311,5421,
- 5532,5645,5758,5873,
- 5988,6105,6222,6341,
- 6460,6581,6702,6825,
- 6948,7072,7198,7324,
- 7451,7580,7709,7839,
- 7970,8102,8235,8369,
- 8504,8640,8776,8914,
- 9052,9192,9332,9473,
- 9615,9758,9901,10046,
- 10191,10338,10485,10633,
- 10782,10931,11082,11233,
- 11385,11538,11692,11846,
- 12002,12158,12315,12472,
- 12631,12790,12950,13110,
- 13272,13434,13597,13760,
- 13924,14090,14255,14422,
- 14589,14757,14925,15094,
- 15264,15434,15606,15777,
- 15950,16123,16296,16471,
- 16646,16821,16997,17174,
- 17351,17529,17708,17887,
- 18066,18246,18427,18608,
- 18790,18972,19155,19339,
- 19522,19707,19891,20077,
- 20263,20449,20636,20823,
- 21010,21198,21387,21576,
- 21765,21955,22145,22336,
- 22527,22718,22910,23102,
- 23295,23487,23681,23874,
- 24068,24262,24457,24652,
- 24847,25042,25238,25434,
- 25630,25827,26024,26221,
- 26418,26616,26813,27011,
- 27210,27408,27607,27806,
- 28005,28204,28403,28603,
- 28802,29002,29202,29402,
- 29603,29803,30003,30204,
- 30405,30606,30806,31007,
- 31208,31409,31611,31812,
- 32013,32214,32415,32617,
- 32818,33019,33220,33422,
- 33623,33824,34025,34226,
- 34427,34628,34829,35030,
- 35231,35431,35632,35832,
- 36033,36233,36433,36633,
- 36832,37032,37232,37431,
- 37630,37829,38028,38226,
- 38425,38623,38821,39018,
- 39216,39413,39610,39807,
- 40003,40199,40395,40591,
- 40786,40981,41176,41370,
- 41564,41758,41951,42144,
- 42337,42529,42721,42913,
- 43104,43294,43485,43675,
- 43864,44054,44242,44431,
- 44618,44806,44993,45179,
- 45365,45551,45736,45921,
- 46105,46288,46471,46654,
- 46836,47017,47198,47379,
- 47559,47738,47917,48095,
- 48272,48449,48626,48802,
- 48977,49151,49325,49499,
- 49672,49844,50015,50186,
- 50356,50526,50694,50862,
- 51030,51197,51363,51528,
- 51693,51857,52020,52182,
- 52344,52505,52665,52825,
- 52984,53142,53299,53455,
- 53611,53766,53920,54073,
- 54226,54378,54529,54679,
- 54828,54976,55124,55271,
- 55416,55561,55706,55849,
- 55991,56133,56273,56413,
- 56552,56690,56827,56963,
- 57099,57233,57366,57499,
- 57630,57761,57891,58020,
- 58147,58274,58400,58525,
- 58649,58772,58894,59015,
- 59135,59254,59372,59489,
- 59605,59720,59834,59947,
- 60058,60169,60279,60388,
- 60496,60602,60708,60813,
- 60916,61019,61120,61221,
- 61320,61418,61515,61611,
- 61706,61800,61893,61985,
- 62075,62165,62253,62340,
- 62426,62511,62595,62678,
- 62760,62840,62919,62998,
- 63075,63151,63226,63299,
- 63372,63443,63513,63582,
- 63650,63717,63782,63847,
- 63910,63972,64033,64092,
- 64151,64208,64264,64319,
- 64373,64425,64477,64527,
- 64576,64624,64670,64716,
- 64760,64803,64844,64885,
- 64924,64962,64999,65035,
- 65069,65102,65134,65165,
- 65195,65223,65250,65276,
- 65301,65324,65346,65367,
- 65387,65406,65423,65439,
- 65454,65467,65480,65491,
- 65501,65509,65517,65523,
- 65528,65532,65534,65535,
- };
四、FFT以及计算幅值
接下来进行编写对FFT进行初始化的函数。
- void RFFT_Init()
- {
- RFFT_f32_setInputPtr(hnd_rfft, (float *)FFT_input);
- RFFT_f32_setOutputPtr(hnd_rfft, FFT_output);
- RFFT_f32_setStages(hnd_rfft, FFT_STAGES);
- RFFT_f32_setFFTSize(hnd_rfft, FFT_SIZE);
- RFFT_f32_setMagnitudePtr(hnd_rfft, FFT_magnitude_phase);
- RFFT_f32_setPhasePtr(hnd_rfft, FFT_magnitude_phase);
-
- RFFT_f32_setTwiddlesPtr(hnd_rfft, FFT_twiddleFactors);
- RFFT_f32_sincostable(hnd_rfft);
-
- RFFT_ADC_f32_setTailPtr(hnd_rfft_adc, &(hnd_rfft->OutBuf));
- RFFT_ADC_f32_setInBufPtr(hnd_rfft_adc, FFT_input);
-
- RFFT_adc_f32_win(FFT_input, Window, FFT_SIZE );
- }
进行FFT以及对FFT结果进行计算的函数。
- void RFFT_Caculate()
- {
- float* mag;
-
- RFFT_adc_f32(hnd_rfft_adc);
- RFFT_f32_mag(hnd_rfft); //计算幅度
- mag=RFFT_f32_getMagnitudePtr(hnd_rfft);
-
- RFFT_Analyse(mag);
- }
需注意的是，FFT的返回值不是幅值，我们需对其进行转换。
首先对FFT的结果进行取模，使用RFFT_f32_mag（）函数，得到幅度。
接着对幅度再进行相应的处理，如下表：
即，直流分量的幅值等于幅度除以采样点数，其余的的幅值等于幅值除以采样点数的一半。
对幅度进行分析的函数
- void RFFT_Analyse(float *src)
- {
- Uint16 i;
- float FFT_Value; //FFT_Value为该频率点的FFT后的幅度
- Uint16 peak_index[RFFT_Analyse_MaxNum];//存放的峰值个数为RFFT_Analyse_MaxNum个
-
- memset(peak_index, 0U, RFFT_Analyse_MaxNum*sizeof(Uint16)); //初始化将指定区块为0值
- memset(rfft_analyse.freq, 0U, RFFT_Analyse_MaxNum*sizeof(float));
- memset(rfft_analyse.Amp, 0U, RFFT_Analyse_MaxNum*sizeof(float));
-
- rfft_analyse.Wave_Num=RFFT_Peak_Find(src,FFT_SIZE/2,peak_index);
-
- for(i=0;i<rfft_analyse.Wave_Num;i++)
- {
- rfft_analyse.freq[i]=(float) Fs / FFT_SIZE * peak_index[i];//计算频率，已调试过，为准确频率
- FFT_Value=*(src+peak_index[i]);
- rfft_analyse.Amp[i] = 2 * FFT_Value / FFT_SIZE * 3 * 2; //将幅度转换为幅值公式：幅值=（幅度/(采样点数/2)）该点不为FFT后结果的第一个点和最后一个点，乘3是ADC的转化范围为0-3V，乘2是汉宁窗的幅度恢复系数
- }
- rfft_analyse.DC_Amp=src[0]/FFT_SIZE * 3 * 2; //直流分量的幅值=幅度/采样点数，乘2是汉宁窗的幅度恢复系数
- }
在主函数中，对RFFT_Init（）和RFFT_Caculate（）完成调用，即可。
五、核验结果
准备阶段结束，进入仿真。
仿真结果如下：
频率点：
对应幅值：
直流分量：
可以看到加窗后FFT的结果于输入信号相吻合，测试结束。
需要工程文件的可以私信我，本文如有错误，也请多多指出。
本文编写时，参考了以下相关文章：
【1】窗函数总结_wxyczhyza的博客-CSDN博客_窗函数衰减【2】TMS320F28335调用官方库进行FFT频谱分析_PeepFuture橙子的博客-CSDN博客
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