include/a/lpf.h

   1 /*!
   2  @file lpf.h
   3  @brief Low Pass Filter
   4  @details
   5  low frequencies are passed, high frequencies are attenuated.
   6  \f[
   7   RC\frac{\text{d}V_{\mathrm o}}{\text{dt}}+V_{\mathrm o}=V_{\mathrm i}
   8  \f]
   9  \f[
  10   RC\frac{V_{\mathrm o}(n)-V_{\mathrm o}(n-1)}{T_s}+V_{\mathrm o}(n)=V_{\mathrm i}(n)
  11  \f]
  12  \f[
  13   V_{\mathrm o}(n)=\frac{RC}{RC+T_s}V_{\mathrm o}(n-1)+\frac{T_s}{RC+T_s}V_{\mathrm i}(n)
  14  \f]
  15  \f[
  16   V_{\mathrm o}(n)=(1-\alpha)V_{\mathrm o}(n-1)+\alpha V_{\mathrm i}(n)
  17  \f]
  18  \f[
  19   \alpha=\frac{T_s}{RC+T_s}=\frac{T_s}{{\frac{1}{2\pi f_c}}+T_s}
  20  \f]
  21  https://en.wikipedia.org/wiki/Low-pass_filter
  22 */
  23
  24 #ifndef LIBA_LPF_H
  25 #define LIBA_LPF_H
  26
  27 #include "math.h"
  28
  29 /*!
  30  @ingroup liba
  31  @addtogroup a_lpf Low Pass Filter
  32  @{
  33 */
  34
  35 /*!
  36  @brief instance structure for Low Pass Filter
  37 */
  38 typedef struct a_lpf
  39 {
  40     a_float alpha; /*!< filter coefficient [0,1] */
  41     a_float output; /*!< filter output */
  42 #if defined(__cplusplus)
  43     A_INLINE void gen(a_float fc, a_float ts)
  44     {
  45         alpha = ts / (A_FLOAT_1_TAU / fc + ts);
  46     }
  47     A_INLINE a_float operator()(a_float x)
  48     {
  49         output *= 1 - alpha;
  50         output += x * alpha;
  51         return output;
  52     }
  53     A_INLINE void zero() { output = 0; }
  54 #endif /* __cplusplus */
  55 } a_lpf;
  56 #if defined(__cplusplus)
  57 namespace a
  58 {
  59 typedef struct a_lpf lpf;
  60 } /* namespace a */
  61 #endif /* __cplusplus */
  62 /* clang-format off */
  63 #define A_LPF_1(alpha) {a_float_c(alpha), 0}
  64 #define A_LPF_2(fc, ts) {A_LPF_GEN(fc, ts), 0}
  65 /* clang-format on */
  66 #define A_LPF_GEN(fc, ts) (a_float_c(ts) / (A_FLOAT_1_TAU / a_float_c(fc) + a_float_c(ts)))
  67
  68 /*!
  69  @brief generate for Low Pass Filter
  70  \f{cases}{
  71   \alpha=\frac{T_s}{RC+T_s},&\alpha\in[0,1]\\
  72   RC=\frac{1}{2\pi f_c}.
  73  \f}
  74  \f[
  75   \alpha=\frac{T_s}{\frac{1}{2\pi f_c}+T_s}
  76  \f]
  77  @param[in] fc cut-off frequency unit(hz)
  78  @param[in] ts sampling time unit(s)
  79  @return filter coefficient [0,1]
  80 */
  81 A_INTERN a_float a_lpf_gen(a_float fc, a_float ts)
  82 {
  83     return ts / (A_FLOAT_1_TAU / fc + ts);
  84 }
  85
  86 /*!
  87  @brief initialize for Low Pass Filter
  88  @param[in,out] ctx points to an instance of Low Pass Filter
  89  @param[in] alpha filter coefficient [0,1]
  90 */
  91 A_INTERN void a_lpf_init(a_lpf *ctx, a_float alpha)
  92 {
  93     ctx->alpha = alpha;
  94     ctx->output = 0;
  95 }
  96
  97 /*!
  98  @brief calculate for Low Pass Filter
  99  \f[
 100   V_{\mathrm o}(n)=(1-\alpha)V_{\mathrm o}(n-1)+\alpha V_{\mathrm i}(n)
 101  \f]
 102  @param[in,out] ctx points to an instance of Low Pass Filter
 103  @param[in] x input value
 104  @return output value
 105 */
 106 A_INTERN a_float a_lpf_iter(a_lpf *ctx, a_float x)
 107 {
 108     ctx->output *= 1 - ctx->alpha;
 109     ctx->output += x * ctx->alpha;
 110     return ctx->output;
 111 }
 112
 113 /*!
 114  @brief zeroing for Low Pass Filter
 115  @param[in,out] ctx points to an instance of Low Pass Filter
 116 */
 117 A_INTERN void a_lpf_zero(a_lpf *ctx) { ctx->output = 0; }
 118
 119 /*! @} a_lpf */
 120
 121 #endif /* a/lpf.h */