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+/**
+ * @file      LPF.h
+ * @brief     implements four FIR low-pass filters
+ * @details   Finite length LPF<br>
+ 1) Size is the depth 2 to 16<br>
+ 2) y(n) = (sum(x(n)+x(n-1)+...+x(n-size-1))/size<br>
+ 3) To use a filter<br>
+   a) initialize it once<br>
+   b) call the filter at the sampling rate<br>
+ * @version   from TI-RSLK MAX v1.1
+ * @author    Daniel Valvano and Jonathan Valvano
+ * @copyright Copyright 2020 by Jonathan W. Valvano, valvano@mail.utexas.edu,
+ * @warning   AS-IS
+ * @note      For more information see  http://users.ece.utexas.edu/~valvano/
+ * @date      January 15, 2020
+
+
+ ******************************************************************************/
+
+/* This example accompanies the books
+   "Embedded Systems: Introduction to ARM Cortex M Microcontrollers",
+      ISBN: 978-1469998749, Jonathan Valvano, copyright (c) 2020
+   "Embedded Systems: Real Time Interfacing to ARM Cortex M Microcontrollers",
+      ISBN: 978-1463590154, Jonathan Valvano, copyright (c) 2020
+   "Embedded Systems: Real-Time Operating Systems for ARM Cortex-M Microcontrollers",
+      ISBN: 978-1466468863, Jonathan Valvano, copyright (c) 2020
+
+ Copyright 2020 by Jonathan W. Valvano, valvano@mail.utexas.edu
+    You may use, edit, run or distribute this file
+    as long as the above copyright notice remains
+ THIS SOFTWARE IS PROVIDED "AS IS".  NO WARRANTIES, WHETHER EXPRESS, IMPLIED
+ OR STATUTORY, INCLUDING, BUT NOT LIMITED TO, IMPLIED WARRANTIES OF
+ MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE APPLY TO THIS SOFTWARE.
+ VALVANO SHALL NOT, IN ANY CIRCUMSTANCES, BE LIABLE FOR SPECIAL, INCIDENTAL,
+ OR CONSEQUENTIAL DAMAGES, FOR ANY REASON WHATSOEVER.
+ For more information about my classes, my research, and my books, see
+ http://users.ece.utexas.edu/~valvano/
+ */
+#include <stdint.h>
+/**
+ * Newton's method sqrt
+ * @param s is an integer
+ * @return sqrt(s) is an integer
+ * @brief  square root
+ */
+uint32_t sqrt2(uint32_t s);
+
+/**
+ * Initialize first LPF<br>
+ * Set all data to an initial value<br>
+ * @param initial value to preload into MACQ
+ * @param size depth of the filter, 2 to 16
+ * @return none
+ * @brief  Initialize first LPF
+ */
+void LPF_Init(int32_t initial, int32_t size);
+
+/**
+ * First LPF, calculate one filter output<br>
+ * Called at sampling rate
+ * @param newdata new ADC data
+ * @return result filter output
+ * @brief  FIR low pass filter
+ */
+int32_t LPF_Calc(int32_t newdata);
+int32_t Noise1(void);
+
+/**
+ * Initialize second LPF<br>
+ * Set all data to an initial value<br>
+ * @param initial value to preload into MACQ
+ * @param size depth of the filter, 2 to 16
+ * @return none
+ * @brief  Initialize second LPF
+ */
+void LPF_Init2(int32_t initial, int32_t size);
+/**
+ * Second LPF, calculate one filter output<br>
+ * Called at sampling rate
+ * @param newdata new ADC data
+ * @return result filter output
+ * @brief  FIR low pass filter
+ */
+int32_t LPF_Calc2(int32_t newdata);
+int32_t Noise2(void);
+/**
+ * Initialize third LPF<br>
+ * Set all data to an initial value<br>
+ * @param initial value to preload into MACQ
+ * @param size depth of the filter, 2 to 16
+ * @return none
+ * @brief  Initialize third LPF
+ */
+void LPF_Init3(int32_t initial, int32_t size);
+
+/**
+ * Third LPF, calculate one filter output<br>
+ * Called at sampling rate
+ * @param newdata new ADC data
+ * @return result filter output
+ * @brief  FIR low pass filter
+ */
+int32_t LPF_Calc3(int32_t newdata);
+int32_t Noise3(void);
+
+/**
+ * Initialize fourth LPF<br>
+ * Set all data to an initial value<br>
+ * @param initial value to preload into MACQ
+ * @param size depth of the filter, 2 to 16
+ * @return none
+ * @brief  Initialize third LPF
+ */
+void LPF_Init4(int32_t initial, int32_t size);
+
+/**
+ * Fourth LPF, calculate one filter output<br>
+ * Called at sampling rate
+ * @param newdata new ADC data
+ * @return result filter output
+ * @brief  FIR low pass filter
+ */
+int32_t LPF_Calc4(int32_t newdata);
+int32_t Noise4(void);
+
+/**
+ * Initialize fifth LPF<br>
+ * Set all data to an initial value<br>
+ * @param initial value to preload into MACQ
+ * @param size depth of the filter, 2 to 16
+ * @return none
+ * @brief  Initialize fifth LPF
+ */
+void LPF_Init5(int32_t initial, int32_t size);
+
+/**
+ * fifth LPF, calculate one filter output<br>
+ * Called at sampling rate
+ * @param newdata new ADC data
+ * @return result filter output
+ * @brief  FIR low pass filter
+ */
+int32_t LPF_Calc5(int32_t newdata);
+int32_t Noise5(void);
+/**
+ * Initialize Sixth LPF<br>
+ * Set all data to an initial value<br>
+ * @param initial value to preload into MACQ
+ * @param size depth of the filter, 2 to 16
+ * @return none
+ * @brief  Initialize Sixth LPF
+ */
+void LPF_Init6(int32_t initial, int32_t size);
+
+/**
+ * Sixth LPF, calculate one filter output<br>
+ * Called at sampling rate
+ * @param newdata new ADC data
+ * @return result filter output
+ * @brief  FIR low pass filter
+ */
+int32_t LPF_Calc6(int32_t newdata);
+int32_t Noise6(void);
+
+/**
+ * Initialize Seventh LPF<br>
+ * Set all data to an initial value<br>
+ * @param initial value to preload into MACQ
+ * @param size depth of the filter, 2 to 16
+ * @return none
+ * @brief  Initialize Seventh LPF
+ */
+void LPF_Init7(int32_t initial, int32_t size);
+
+/**
+ * Seventh LPF, calculate one filter output<br>
+ * Called at sampling rate
+ * @param newdata new ADC data
+ * @return result filter output
+ * @brief  FIR low pass filter
+ */
+int32_t LPF_Calc7(int32_t newdata);
+int32_t Noise7(void);
+
+/**
+ * 3-wide non recursive Median filter <br>
+ * Called with new data at sampling rate
+ * @param newdata new ADC data
+ * @return result filter output
+ * @brief  Median filter
+ */
+int32_t Median(int32_t newdata);
+
+/**
+ * 5-wide non recursive Median filter <br>
+ * Called with new data at sampling rate
+ * @param newdata new ADC data
+ * @return result filter output
+ * @brief  Median filter
+ */
+int32_t Median5(int32_t newdata);
+
+/**
+ * 5-wide non recursive Median filter, second independent instance<br>
+ * Uses separate internal arrays from Median5 — safe to call simultaneously.
+ * @param newdata new ADC data
+ * @return result filter output
+ * @brief  Median filter (second instance)
+ */
+int32_t Median5_2(int32_t newdata);
+
+/**
+ * 7-wide non recursive Median filter <br>
+ * Called with new data at sampling rate
+ * @param newdata new ADC data
+ * @return result filter output
+ * @brief  Median filter
+ */
+int32_t Median7(int32_t newdata);
+
+/**
+ * 60-Hz notch high-Q, alpha=0.99, IIR filter, assuming fs=1000 Hz.<br>
+ * y(n) = (256x(n) -503x(n-1) + 256x(n-2) + 498y(n-1)-251y(n-2))/256 (2k sampling)<br>
+ * y(n) = (256x(n) -476x(n-1) + 256x(n-2) + 471y(n-1)-251y(n-2))/256 (1k sampling)
+ * @param data new ADC data
+ * @return result filter output
+ * @brief  60-Hz notch high-Q, IIR filter
+ */
+ int32_t Filter(int32_t data);
+
+/**
+ * Independent second instance of the 60-Hz notch IIR filter<br>
+ * Identical coefficients to Filter(), but separate internal state.<br>
+ * Use for a second simultaneous signal (e.g. left IR sensor).
+ * @param data new ADC data
+ * @return result filter output
+ * @brief  60-Hz notch high-Q, IIR filter (second instance)
+ */
+ int32_t Filter2(int32_t data);