hpf.h File Reference

High Pass Filter. More...

#include "math.h"

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Data Structures
struct	a_hpf
	instance structure for High Pass Filter More...

Macros
#define	A_HPF_1(alpha)
#define	A_HPF_2(fc, ts)
#define	A_HPF_GEN(fc, ts)

Typedefs
typedef struct a_hpf	a_hpf
	instance structure for High Pass Filter
typedef struct a_hpf	a::hpf

Functions
a_real	a_hpf_gen (a_real fc, a_real ts)
	generate for High Pass Filter
void	a_hpf_init (a_hpf *ctx, a_real alpha)
	initialize for High Pass Filter
a_real	a_hpf_iter (a_hpf *ctx, a_real x)
	compute for High Pass Filter
void	a_hpf_zero (a_hpf *ctx)
	zeroing for High Pass Filter

Detailed Description

High Pass Filter.

high frequencies are passed, low frequencies are attenuated.

$$RC\frac{\text{d}(V_{\mathrm{i}}-V_{\mathrm{o}})}{\text{dt}}=V_{\mathrm{o}}$$

$$RC\frac{[V_{\mathrm{i}}(n)-V_{\mathrm{i}}(n-1)]-[V_{\mathrm{o}}(n)-V_{\mathrm{o}}(n-1)]}{T_s}=V_{\mathrm{o}}(n)$$

$$V_{\mathrm{o}}(n)=\frac{RC}{RC+T_s}[V_{\mathrm{o}}(n-1)+V_{\mathrm{i}}(n)-V_{\mathrm{i}}(n-1)]$$

$$\alpha =\frac{RC}{RC+T_s}=\frac{1}{2\pi f_c{T}_s+1}$$

$$V_{\mathrm{o}}(n)=\alpha [V_{\mathrm{o}}(n-1)+V_{\mathrm{i}}(n)-V_{\mathrm{i}}(n-1)]$$

https://en.wikipedia.org/wiki/High-pass_filter