Diff: cmsis_dsp/FilteringFunctions/arm_biquad_cascade_df2T_f32.c

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+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision:     V1.1.0  
+*    
+* Project:         CMSIS DSP Library    
+* Title:        arm_biquad_cascade_df2T_f32.c    
+*    
+* Description:  Processing function for the floating-point transposed    
+*               direct form II Biquad cascade filter.   
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated    
+*    
+* Version 0.0.7  2010/06/10     
+*    Misra-C changes done    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**       
+ * @ingroup groupFilters       
+ */
+
+/**       
+ * @defgroup BiquadCascadeDF2T Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure       
+ *       
+ * This set of functions implements arbitrary order recursive (IIR) filters using a transposed direct form II structure.       
+ * The filters are implemented as a cascade of second order Biquad sections.       
+ * These functions provide a slight memory savings as compared to the direct form I Biquad filter functions.      
+ * Only floating-point data is supported.       
+ *       
+ * This function operate on blocks of input and output data and each call to the function       
+ * processes <code>blockSize</code> samples through the filter.       
+ * <code>pSrc</code> points to the array of input data and       
+ * <code>pDst</code> points to the array of output data.       
+ * Both arrays contain <code>blockSize</code> values.       
+ *       
+ * \par Algorithm       
+ * Each Biquad stage implements a second order filter using the difference equation:       
+ * <pre>       
+ *    y[n] = b0 * x[n] + d1       
+ *    d1 = b1 * x[n] + a1 * y[n] + d2       
+ *    d2 = b2 * x[n] + a2 * y[n]       
+ * </pre>       
+ * where d1 and d2 represent the two state values.       
+ *       
+ * \par       
+ * A Biquad filter using a transposed Direct Form II structure is shown below.       
+ * \image html BiquadDF2Transposed.gif "Single transposed Direct Form II Biquad"       
+ * Coefficients <code>b0, b1, and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients.       
+ * Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients.       
+ * Pay careful attention to the sign of the feedback coefficients.       
+ * Some design tools flip the sign of the feedback coefficients:       
+ * <pre>       
+ *    y[n] = b0 * x[n] + d1;       
+ *    d1 = b1 * x[n] - a1 * y[n] + d2;       
+ *    d2 = b2 * x[n] - a2 * y[n];       
+ * </pre>       
+ * In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library.       
+ *       
+ * \par       
+ * Higher order filters are realized as a cascade of second order sections.       
+ * <code>numStages</code> refers to the number of second order stages used.       
+ * For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages.       
+ * A 9th order filter would be realized with <code>numStages=5</code> second order stages with the       
+ * coefficients for one of the stages configured as a first order filter (<code>b2=0</code> and <code>a2=0</code>).       
+ *       
+ * \par       
+ * <code>pState</code> points to the state variable array.       
+ * Each Biquad stage has 2 state variables <code>d1</code> and <code>d2</code>.       
+ * The state variables are arranged in the <code>pState</code> array as:       
+ * <pre>       
+ *     {d11, d12, d21, d22, ...}       
+ * </pre>       
+ * where <code>d1x</code> refers to the state variables for the first Biquad and       
+ * <code>d2x</code> refers to the state variables for the second Biquad.       
+ * The state array has a total length of <code>2*numStages</code> values.       
+ * The state variables are updated after each block of data is processed; the coefficients are untouched.       
+ *       
+ * \par       
+ * The CMSIS library contains Biquad filters in both Direct Form I and transposed Direct Form II.    
+ * The advantage of the Direct Form I structure is that it is numerically more robust for fixed-point data types.    
+ * That is why the Direct Form I structure supports Q15 and Q31 data types.    
+ * The transposed Direct Form II structure, on the other hand, requires a wide dynamic range for the state variables <code>d1</code> and <code>d2</code>.    
+ * Because of this, the CMSIS library only has a floating-point version of the Direct Form II Biquad.    
+ * The advantage of the Direct Form II Biquad is that it requires half the number of state variables, 2 rather than 4, per Biquad stage.    
+ *       
+ * \par Instance Structure       
+ * The coefficients and state variables for a filter are stored together in an instance data structure.       
+ * A separate instance structure must be defined for each filter.       
+ * Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.       
+ *       
+ * \par Init Functions       
+ * There is also an associated initialization function.      
+ * The initialization function performs following operations:       
+ * - Sets the values of the internal structure fields.       
+ * - Zeros out the values in the state buffer.       
+ *       
+ * \par       
+ * Use of the initialization function is optional.       
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.       
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.       
+ * Set the values in the state buffer to zeros before static initialization.       
+ * For example, to statically initialize the instance structure use       
+ * <pre>       
+ *     arm_biquad_cascade_df2T_instance_f32 S1 = {numStages, pState, pCoeffs};       
+ * </pre>       
+ * where <code>numStages</code> is the number of Biquad stages in the filter; <code>pState</code> is the address of the state buffer.       
+ * <code>pCoeffs</code> is the address of the coefficient buffer;        
+ *       
+ */
+
+/**       
+ * @addtogroup BiquadCascadeDF2T       
+ * @{       
+ */
+
+/**      
+ * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.      
+ * @param[in]  *S        points to an instance of the filter data structure.      
+ * @param[in]  *pSrc     points to the block of input data.      
+ * @param[out] *pDst     points to the block of output data      
+ * @param[in]  blockSize number of samples to process.      
+ * @return none.      
+ */
+
+void arm_biquad_cascade_df2T_f32(
+  const arm_biquad_cascade_df2T_instance_f32 * S,
+  float32_t * pSrc,
+  float32_t * pDst,
+  uint32_t blockSize)
+{
+
+  float32_t *pIn = pSrc;                         /*  source pointer            */
+  float32_t *pOut = pDst;                        /*  destination pointer       */
+  float32_t *pState = S->pState;                 /*  State pointer             */
+  float32_t *pCoeffs = S->pCoeffs;               /*  coefficient pointer       */
+  float32_t acc0;                                /*  accumulator               */
+  float32_t b0, b1, b2, a1, a2;                  /*  Filter coefficients       */
+  float32_t Xn;                                  /*  temporary input           */
+  float32_t d1, d2;                              /*  state variables           */
+  uint32_t sample, stage = S->numStages;         /*  loop counters             */
+
+#ifndef ARM_MATH_CM0
+
+  float32_t Xn1, Xn2;                            /*  Input State variables     */
+  float32_t acc1;                                /*  accumulator               */
+
+
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+  do
+  {
+    /* Reading the coefficients */
+    b0 = *pCoeffs++;
+    b1 = *pCoeffs++;
+    b2 = *pCoeffs++;
+    a1 = *pCoeffs++;
+    a2 = *pCoeffs++;
+
+    /*Reading the state values */
+    d1 = pState[0];
+    d2 = pState[1];
+
+    /* Apply loop unrolling and compute 4 output values simultaneously. */
+    sample = blockSize >> 2u;
+
+    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.       
+     ** a second loop below computes the remaining 1 to 3 samples. */
+    while(sample > 0u)
+    {
+
+      /* y[n] = b0 * x[n] + d1 */
+      /* d1 = b1 * x[n] + a1 * y[n] + d2 */
+      /* d2 = b2 * x[n] + a2 * y[n] */
+
+      /* Read the first input */
+      Xn1 = *pIn++;
+
+      /* y[n] = b0 * x[n] + d1 */
+      acc0 = (b0 * Xn1) + d1;
+
+      /* d1 = b1 * x[n] + d2 */
+      d1 = (b1 * Xn1) + d2;
+
+      /* d2 = b2 * x[n] */
+      d2 = (b2 * Xn1);
+
+      /* Read the second input */
+      Xn2 = *pIn++;
+
+      /* d1 = b1 * x[n] + a1 * y[n] */
+      d1 = (a1 * acc0) + d1;
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = acc0;
+
+      d2 = (a2 * acc0) + d2;
+
+      /* y[n] = b0 * x[n] + d1 */
+      acc1 = (b0 * Xn2) + d1;
+
+      /* Read the third input */
+      Xn1 = *pIn++;
+
+      d1 = (b1 * Xn2) + d2;
+
+      d2 = (b2 * Xn2);
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = acc1;
+
+      d1 = (a1 * acc1) + d1;
+
+      d2 = (a2 * acc1) + d2;
+
+      /* y[n] = b0 * x[n] + d1 */
+      acc0 = (b0 * Xn1) + d1;
+
+      d1 = (b1 * Xn1) + d2;
+
+      d2 = (b2 * Xn1);
+
+      /* Read the fourth input */
+      Xn2 = *pIn++;
+
+      d1 = (a1 * acc0) + d1;
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = acc0;
+
+      d2 = (a2 * acc0) + d2;
+
+      /* y[n] = b0 * x[n] + d1 */
+      acc1 = (b0 * Xn2) + d1;
+
+      d1 = (b1 * Xn2) + d2;
+
+      d2 = (b2 * Xn2);
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = acc1;
+
+      d1 = (a1 * acc1) + d1;
+
+      d2 = (a2 * acc1) + d2;
+
+      /* decrement the loop counter */
+      sample--;
+
+    }
+
+    /* If the blockSize is not a multiple of 4, compute any remaining output samples here.       
+     ** No loop unrolling is used. */
+    sample = blockSize & 0x3u;
+
+    while(sample > 0u)
+    {
+      /* Read the input */
+      Xn = *pIn++;
+
+      /* y[n] = b0 * x[n] + d1 */
+      acc0 = (b0 * Xn) + d1;
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = acc0;
+
+      /* Every time after the output is computed state should be updated. */
+      /* d1 = b1 * x[n] + a1 * y[n] + d2 */
+      d1 = ((b1 * Xn) + (a1 * acc0)) + d2;
+
+      /* d2 = b2 * x[n] + a2 * y[n] */
+      d2 = (b2 * Xn) + (a2 * acc0);
+
+      /* decrement the loop counter */
+      sample--;
+    }
+
+    /* Store the updated state variables back into the state array */
+    *pState++ = d1;
+    *pState++ = d2;
+
+    /* The current stage input is given as the output to the next stage */
+    pIn = pDst;
+
+    /*Reset the output working pointer */
+    pOut = pDst;
+
+    /* decrement the loop counter */
+    stage--;
+
+  } while(stage > 0u);
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  do
+  {
+    /* Reading the coefficients */
+    b0 = *pCoeffs++;
+    b1 = *pCoeffs++;
+    b2 = *pCoeffs++;
+    a1 = *pCoeffs++;
+    a2 = *pCoeffs++;
+
+    /*Reading the state values */
+    d1 = pState[0];
+    d2 = pState[1];
+
+
+    sample = blockSize;
+
+    while(sample > 0u)
+    {
+      /* Read the input */
+      Xn = *pIn++;
+
+      /* y[n] = b0 * x[n] + d1 */
+      acc0 = (b0 * Xn) + d1;
+
+      /* Store the result in the accumulator in the destination buffer. */
+      *pOut++ = acc0;
+
+      /* Every time after the output is computed state should be updated. */
+      /* d1 = b1 * x[n] + a1 * y[n] + d2 */
+      d1 = ((b1 * Xn) + (a1 * acc0)) + d2;
+
+      /* d2 = b2 * x[n] + a2 * y[n] */
+      d2 = (b2 * Xn) + (a2 * acc0);
+
+      /* decrement the loop counter */
+      sample--;
+    }
+
+    /* Store the updated state variables back into the state array */
+    *pState++ = d1;
+    *pState++ = d2;
+
+    /* The current stage input is given as the output to the next stage */
+    pIn = pDst;
+
+    /*Reset the output working pointer */
+    pOut = pDst;
+
+    /* decrement the loop counter */
+    stage--;
+
+  } while(stage > 0u);
+
+#endif /*  #ifndef ARM_MATH_CM0         */
+
+}
+
+
+  /**       
+   * @} end of BiquadCascadeDF2T group       
+   */