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algo [2020/03/23 15:09] – created niziakalgo [2020/04/20 07:25] (current) – niziak
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 +====== Algorithms ======
 +
 ====== Low-pass filters ====== ====== Low-pass filters ======
  
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 From [[https://en.wikipedia.org/wiki/Low-pass_filter#Simple_infinite_impulse_response_filter|Wiki]]: From [[https://en.wikipedia.org/wiki/Low-pass_filter#Simple_infinite_impulse_response_filter|Wiki]]:
 This discrete-time implementation of a simple RC low-pass filter is the exponentially weighted moving average (aka [[https://en.wikipedia.org/wiki/Exponential_smoothing|Exponential smoothing]]) This discrete-time implementation of a simple RC low-pass filter is the exponentially weighted moving average (aka [[https://en.wikipedia.org/wiki/Exponential_smoothing|Exponential smoothing]])
 +<code>
 +Exponential smoothing:
 +y[i] :=  y[i-1] +  α * (x[i] - y[i-1])
 +where  α = (1-ß) (from above)
 +</code>
 +<code c>
 +#define ALPHA_PERCENT 60
 +int16_t exponential_smoothing(int16_t input, int16_t old_value) {
 +    int32_t val = old_value;
 +    int32_t diff = input - old_value;
 +
 +    val += (ALPHA_PERCENT * diff) / 100;
 +    return val;
 +}
 +</code>
 +
 +===== Moving Average (MA) =====
 +aka moving average / rolling average / running average
 +
 +<code c>
 +#define LPA_NUM     10
 +static int16_t lpa_buf[LPA_NUM];
 +
 +void low_pass_average_init(int16_t init_value) {
 +    for (int i = 0; i < sizeof(lpa_buf)/sizeof(lpa_buf[0]); i++) {
 +        lpa_buf[i] = init_value;
 +    }
 +}
 +
 +int16_t low_pass_average(int16_t input) {
 +    int32_t sum = 0;
 +    for (unsigned int i = (LPA_NUM)-1; i > 0; --i) {
 +        lpa_buf[i] = lpa_buf[i-1];
 +        sum += lpa_buf[i];
 +    }
 +    sum += input;
 +    lpa_buf[0] = input;
 +    return sum/LPA_NUM;
 +}
 +</code>
 +
 +==== Weighted Moving Average ====
 +Time-weighted moving average
 +LWMA - Linearly Weighted Moving Average
 +<code c>
 +#define LPA_NUM     10
 +static int16_t wma_buf[LPA_NUM];
 +static int16_t ma_w[LPA_NUM] = { 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 };
 +
 +void mag_moving_average_init(int16_t init_value) {
 +    for (int i = 0; i < sizeof(ma_buf)/sizeof(ma_buf[0]); i++) {
 +        wma_buf[i] = init_value;
 +    }
 +}
 +
 +nt16_t mag_weighted_moving_average(int16_t input) {
 +    int32_t sum = 0;
 +    int32_t w_sum = 0;
 +    for (unsigned int i = (LPA_NUM)-1; i > 0; --i) {
 +        wma_buf[i] = wma_buf[i-1];
 +        sum += wma_buf[i] * ma_w[i];
 +        w_sum += ma_w[i];
 +    }
 +    wma_buf[0] = input;
 +    sum += wma_buf[0] * ma_w[0];
 +    w_sum += ma_w[0];
 +    return sum / w_sum;
 +}
 +</code>
  
  
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 ===== CuSum ===== ===== CuSum =====
  
-[[https://en.wikipedia.org/wiki/CUSUM|CUSUM]] - Cumulative sum control chart +  * [[https://en.wikipedia.org/wiki/CUSUM|CUSUM]] - Cumulative sum control chart 
 +  * [[https://hal.archives-ouvertes.fr/hal-00914697/document]]