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 "a.h"
  28 #include "math.h"
  29
  30 /*!
  31  @ingroup A
  32  @addtogroup A_HPF High Pass Filter
  33  @{
  34 */
  35
  36 /*!
  37  @brief instance structure for High Pass Filter
  38 */
  39 typedef struct a_hpf
  40 {
  41     a_float alpha; //!< filter coefficient [0,1]
  42     a_float output; //!< filter output
  43     a_float input; //!< filter input
  44 #if defined(__cplusplus)
  45     A_INLINE void gen(a_float fc, a_float ts)
  46     {
  47         alpha = 1 / (A_FLOAT_TAU * fc * ts + 1);
  48     }
  49     A_INLINE a_float operator()(a_float x)
  50     {
  51         output = alpha * (output + x - input);
  52         return (void)(input = x), output;
  53     }
  54     A_INLINE void zero()
  55     {
  56         output = 0;
  57         input = 0;
  58     }
  59 #endif /* __cplusplus */
  60 } a_hpf;
  61 #if defined(__cplusplus)
  62 namespace a
  63 {
  64 typedef struct a_hpf hpf;
  65 } /* namespace a */
  66 #endif /* __cplusplus */
  67 // clang-format off
  68 #if defined(__cplusplus)
  69 #define A_HPF_INIT(alpha) {a_float_c(alpha), 0, 0}
  70 #define A_HPF_INIT2(fc, ts) {A_HPF_GEN(fc, ts), 0, 0}
  71 #else /* !__cplusplus */
  72 #define A_HPF_INIT(alpha) (a_hpf){a_float_c(alpha), 0, 0}
  73 #define A_HPF_INIT2(fc, ts) (a_hpf){A_HPF_GEN(fc, ts), 0, 0}
  74 #endif /* __cplusplus */
  75 // clang-format on
  76 #define A_HPF_GEN(fc, ts) (1 / (A_FLOAT_TAU * a_float_c(fc) * a_float_c(ts) + 1))
  77
  78 /*!
  79  @brief generate for High Pass Filter
  80  \f{cases}{
  81   \alpha=\frac{RC}{RC+T_s},&\alpha\in[0,1]\\
  82   RC=\frac{1}{2\pi f_c}.
  83  \f}
  84  \f[
  85   \alpha=\frac{1}{2\pi f_c T_s+1}
  86  \f]
  87  @param[in] fc cut-off frequency unit(hz)
  88  @param[in] ts sampling time unit(s)
  89  @return filter coefficient [0,1]
  90 */
  91 A_INTERN a_float a_hpf_gen(a_float fc, a_float ts)
  92 {
  93     return 1 / (A_FLOAT_TAU * fc * ts + 1);
  94 }
  95
  96 /*!
  97  @brief initialize for High Pass Filter
  98  @param[in,out] ctx points to an instance of High Pass Filter
  99  @param[in] alpha filter coefficient [0,1]
 100 */
 101 A_INTERN void a_hpf_init(a_hpf *ctx, a_float alpha)
 102 {
 103     ctx->alpha = alpha;
 104     ctx->output = 0;
 105     ctx->input = 0;
 106 }
 107
 108 /*!
 109  @brief calculate for High Pass Filter
 110  \f[
 111   V_{\mathrm o}(n)=\alpha[V_{\mathrm o}(n-1)+V_{\mathrm i}(n)-V_{\mathrm i}(n-1)]
 112  \f]
 113  @param[in,out] ctx points to an instance of High Pass Filter
 114  @param[in] x input value
 115  @return output value
 116 */
 117 A_INTERN a_float a_hpf_iter(a_hpf *ctx, a_float x)
 118 {
 119     ctx->output = ctx->alpha * (ctx->output + x - ctx->input);
 120     return (void)(ctx->input = x), ctx->output;
 121 }
 122
 123 /*!
 124  @brief zeroing for High Pass Filter
 125  @param[in,out] ctx points to an instance of High Pass Filter
 126 */
 127 A_INTERN void a_hpf_zero(a_hpf *ctx)
 128 {
 129     ctx->output = 0;
 130     ctx->input = 0;
 131 }
 132
 133 /*! @} A_HPF */
 134
 135 #endif /* a/hpf.h */