include/a/hpf.h

   1 /*!
   2  @file hpf.h
   3  @brief High Pass Filter
   4  @details
   5  high frequencies are passed, low frequencies are attenuated.
   6  \f[
   7   RC\frac{\text{d}(V_{\mathrm i}-V_{\mathrm o})}{\text{dt}}=V_{\mathrm o}
   8  \f]
   9  \f[
  10   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)
  11  \f]
  12  \f[
  13   V_{\mathrm o}(n)=\frac{RC}{RC+T_s}[V_{\mathrm o}(n-1)+V_{\mathrm i}(n)-V_{\mathrm i}(n-1)]
  14  \f]
  15  \f[
  16   \alpha=\frac{RC}{RC+T_s}=\frac{1}{2\pi f_c T_s + 1}
  17  \f]
  18  \f[
  19   V_{\mathrm o}(n)=\alpha[V_{\mathrm o}(n-1)+V_{\mathrm i}(n)-V_{\mathrm i}(n-1)]
  20  \f]
  21  https://en.wikipedia.org/wiki/High-pass_filter
  22 */
  23
  24 #ifndef LIBA_HPF_H
  25 #define LIBA_HPF_H
  26
  27 #include "math.h"
  28
  29 /*!
  30  @ingroup liba
  31  @addtogroup a_hpf High Pass Filter
  32  @{
  33 */
  34
  35 /*!
  36  @brief instance structure for High Pass Filter
  37 */
  38 typedef struct a_hpf
  39 {
  40     a_float alpha; /*!< filter coefficient [0,1] */
  41     a_float output; /*!< filter output */
  42     a_float input; /*!< filter input */
  43 #if defined(__cplusplus)
  44     A_INLINE void gen(a_float fc, a_float ts)
  45     {
  46         alpha = 1 / (A_FLOAT_TAU * fc * ts + 1);
  47     }
  48     A_INLINE a_float operator()(a_float x)
  49     {
  50         output = alpha * (output + x - input);
  51         return (void)(input = x), output;
  52     }
  53     A_INLINE void zero()
  54     {
  55         output = 0;
  56         input = 0;
  57     }
  58 #endif /* __cplusplus */
  59 } a_hpf;
  60 #if defined(__cplusplus)
  61 namespace a
  62 {
  63 typedef struct a_hpf hpf;
  64 } /* namespace a */
  65 #endif /* __cplusplus */
  66 /* clang-format off */
  67 #define A_HPF_1(alpha) {a_float_c(alpha), 0, 0}
  68 #define A_HPF_2(fc, ts) {A_HPF_GEN(fc, ts), 0, 0}
  69 /* clang-format on */
  70 #define A_HPF_GEN(fc, ts) (1 / (A_FLOAT_TAU * a_float_c(fc) * a_float_c(ts) + 1))
  71
  72 /*!
  73  @brief generate for High Pass Filter
  74  \f{cases}{
  75   \alpha=\frac{RC}{RC+T_s},&\alpha\in[0,1]\\
  76   RC=\frac{1}{2\pi f_c}.
  77  \f}
  78  \f[
  79   \alpha=\frac{1}{2\pi f_c T_s+1}
  80  \f]
  81  @param[in] fc cut-off frequency unit(hz)
  82  @param[in] ts sampling time unit(s)
  83  @return filter coefficient [0,1]
  84 */
  85 A_INTERN a_float a_hpf_gen(a_float fc, a_float ts)
  86 {
  87     return 1 / (A_FLOAT_TAU * fc * ts + 1);
  88 }
  89
  90 /*!
  91  @brief initialize for High Pass Filter
  92  @param[in,out] ctx points to an instance of High Pass Filter
  93  @param[in] alpha filter coefficient [0,1]
  94 */
  95 A_INTERN void a_hpf_init(a_hpf *ctx, a_float alpha)
  96 {
  97     ctx->alpha = alpha;
  98     ctx->output = 0;
  99     ctx->input = 0;
 100 }
 101
 102 /*!
 103  @brief calculate for High Pass Filter
 104  \f[
 105   V_{\mathrm o}(n)=\alpha[V_{\mathrm o}(n-1)+V_{\mathrm i}(n)-V_{\mathrm i}(n-1)]
 106  \f]
 107  @param[in,out] ctx points to an instance of High Pass Filter
 108  @param[in] x input value
 109  @return output value
 110 */
 111 A_INTERN a_float a_hpf_iter(a_hpf *ctx, a_float x)
 112 {
 113     ctx->output = ctx->alpha * (ctx->output + x - ctx->input);
 114     return (void)(ctx->input = x), ctx->output;
 115 }
 116
 117 /*!
 118  @brief zeroing for High Pass Filter
 119  @param[in,out] ctx points to an instance of High Pass Filter
 120 */
 121 A_INTERN void a_hpf_zero(a_hpf *ctx)
 122 {
 123     ctx->output = 0;
 124     ctx->input = 0;
 125 }
 126
 127 /*! @} a_hpf */
 128
 129 #endif /* a/hpf.h */