IAP15W4K58S4
Keil uVision V5.29.0.0
PK51 Prof.Developers Kit Version:9.60.0.0
串口示波器：Vofa+ 1.3.10

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理论推导

低通滤波器
见一阶RC低通滤波器的数学模型及算法实现 —— 奔跑的chanchanchan
$$Y_n=A\cdot X_n+(1-A)\cdot Y_{n-1}$$
$$A=\frac{\Delta T}{RC+\Delta T}=\frac{\Delta T}{\frac{1}{2\pi f}+\Delta T}=\frac{1}{1+\frac{1}{2\pi f\Delta T}}$$
高通滤波器
见一阶RC高通滤波器详解（仿真+matlab+C语言实现）—— 小麦大叔
$$Y_n=A\cdot Y_{n-1}+A\cdot (X_n-X_{n-1})$$
$$A=\frac{RC}{RC+\Delta T}=\frac{\frac{1}{2\pi f}}{\frac{1}{2\pi f}+\Delta T}=\frac{1}{1+2\pi f\Delta T}$$

产生测试信号

sin_cal.c

#include "sin_cal.h"
#include <math.h>void sin_Init(sin_Type *Sin, float f, float delta_ms)
{Sin->angle = 0;Sin->delta = 2 * 3.141592653589793f * f * delta_ms / 1000.f;Sin->out = 0;
}float sin_cal(sin_Type *Sin)
{Sin->angle += Sin->delta;if (Sin->angle > 6.283185307179586f)Sin->angle -= 6.283185307179586f;Sin->out = sin(Sin->angle);return Sin->out;
}

sin_cal.h

#ifndef __SIN_CAL_H__
#define __SIN_CAL_H__typedef struct
{float angle;float delta;float out;
} sin_Type;void sin_Init(sin_Type *Sin, float f, float delta_ms);	//f为设定的频率，delta_ms为时间间隔
float sin_cal(sin_Type *Sin);#endif

生成波形

初始化

//...
sin_Type Sin_1, Sin_2;
//...sin_Init(&Sin_1, 1, 5);		//1  Hz的正弦波sin_Init(&Sin_2, 25, 5);	//25 Hz的正弦波
//...

定时器中断周期为1ms，每5ms输出一次数据

extern sin_Type Sin_1, Sin_2;/********************* Timer0中断函数************************/
void timer0_int (void) interrupt TIMER0_VECTOR
{static int count = 0;float Data;if(++count >= 5){count = 0;sin_cal(&Sin_1);sin_cal(&Sin_2);Data = Sin_1.out+Sin_2.out;printf("%f\r\n", Data);}
}

如图，生成了1Hz和25Hz的混合波形：

一阶滤波器

FirstOrderFilter.c

#include "FirstOrderFilter.h"void fof_Init(fof_Type *fof, float f, float delta_ms, char HPForLPF) 
{fof->in_old = 0;fof->out = 0;fof->type = HPForLPF;fof->a = 2 * 3.141592653589793f * f * delta_ms / 1000.f;if(!HPForLPF){fof->a = 1.f / fof->a;}fof->a = 1.f / (1.f + fof->a);
}float FirstOrderFilter(fof_Type *fof, float in)
{if(fof->type){fof->out = fof->a * fof->out + fof->a * (in - fof->in_old);fof->in_old = in;}elsefof->out = fof->a * in + (1 - fof->a) * fof->out;return fof->out;
}

FirstOrderFilter.h

#ifndef __FOF_H__
#define __FOF_H__typedef struct
{float a;float in_old;float out;char type;
} fof_Type;void fof_Init(fof_Type *fof, float f, float delta_ms, char HPForLPF);	//f为截止频率，delta_ms为时间间隔，HPForLPF为类型选择
float FirstOrderFilter(fof_Type *fof, float in);#endif

测试

//...
fof_Type fof_1, fof_2;
//...fof_Init(&fof_1, 1, 5, 0);	//低通滤波器，截止频率为1Hzfof_Init(&fof_2, 25, 5, 1);	//高通滤波器，截止频率为25Hz
//...

extern fof_Type fof_1, fof_2;
extern sin_Type Sin_1, Sin_2;/********************* Timer0中断函数************************/
void timer0_int (void) interrupt TIMER0_VECTOR
{static int count = 0;float Data;if(++count >= 5){count = 0;sin_cal(&Sin_1);sin_cal(&Sin_2);Data = Sin_1.out+Sin_2.out;printf("%f, %f, %f\r\n", Data, FirstOrderFilter(&fof_1, Data), FirstOrderFilter(&fof_2, Data));}
}

下图为滤波效果

低通滤波器

对于低通滤波器，截止频率处的1Hz信号能量衰减至0.688，与$\frac{1}{\sqrt{2}}\approx 0.707$相差2.7%，

截止频率外的25Hz的信号经滤波已衰减至0.040

高通滤波器

对于高通滤波器，截止频率处的25Hz信号能量衰减至0.594，与$\frac{1}{\sqrt{2}}\approx 0.707$相差16%，

截止频率外的1Hz的信号经滤波已衰减至0.039