DSP/Source/FilteringFunctions/arm_biquad_cascade_df1_f32.c

/* ----------------------------------------------------------------------
 * Project:      CMSIS DSP Library
 * Title:        arm_biquad_cascade_df1_f32.c
 * Description:  Processing function for the floating-point Biquad cascade DirectFormI(DF1) filter
 *
 * $Date:        27. January 2017
 * $Revision:    V.1.5.1
 *
 * Target Processor: Cortex-M cores
 * -------------------------------------------------------------------- */
/*
 * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
 *
 * SPDX-License-Identifier: Apache-2.0
 *
 * Licensed under the Apache License, Version 2.0 (the License); you may
 * not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an AS IS BASIS, WITHOUT
 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

#include "arm_math.h"

/**
 * @ingroup groupFilters
 */

/**
 * @defgroup BiquadCascadeDF1 Biquad Cascade IIR Filters Using Direct Form I Structure
 *
 * This set of functions implements arbitrary order recursive (IIR) filters.
 * The filters are implemented as a cascade of second order Biquad sections.
 * The functions support Q15, Q31 and floating-point data types.
 * Fast version of Q15 and Q31 also supported on CortexM4 and Cortex-M3.
 *
 * The functions 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] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
 * </pre>
 * A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage.
 * \image html Biquad.gif "Single Biquad filter stage"
 * 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 use the difference equation
 * <pre>
 *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2]
 * </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.
 * \image html BiquadCascade.gif "8th order filter using a cascade of Biquad 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
 * The <code>pState</code> points to state variables array.
 * Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</code>.
 * The state variables are arranged in the <code>pState</code> array as:
 * <pre>
 *     {x[n-1], x[n-2], y[n-1], y[n-2]}
 * </pre>
 *
 * \par
 * The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.
 * The state array has a total length of <code>4*numStages</code> values.
 * The state variables are updated after each block of data is processed, the coefficients are untouched.
 *
 * \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.
 * There are separate instance structure declarations for each of the 3 supported data types.
 *
 * \par Init Functions
 * There is also an associated initialization function for each data type.
 * The initialization function performs following operations:
 * - Sets the values of the internal structure fields.
 * - Zeros out the values in the state buffer.
 * To do this manually without calling the init function, assign the follow subfields of the instance structure:
 * numStages, pCoeffs, pState. Also set all of the values in pState to zero.
 *
 * \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.
 * The code below statically initializes each of the 3 different data type filter instance structures
 * <pre>
 *     arm_biquad_casd_df1_inst_f32 S1 = {numStages, pState, pCoeffs};
 *     arm_biquad_casd_df1_inst_q15 S2 = {numStages, pState, pCoeffs, postShift};
 *     arm_biquad_casd_df1_inst_q31 S3 = {numStages, pState, pCoeffs, postShift};
 * </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; <code>postShift</code> shift to be applied.
 *
 * \par Fixed-Point Behavior
 * Care must be taken when using the Q15 and Q31 versions of the Biquad Cascade filter functions.
 * Following issues must be considered:
 * - Scaling of coefficients
 * - Filter gain
 * - Overflow and saturation
 *
 * \par
 * <b>Scaling of coefficients: </b>
 * Filter coefficients are represented as fractional values and
 * coefficients are restricted to lie in the range <code>[-1 +1)</code>.
 * The fixed-point functions have an additional scaling parameter <code>postShift</code>
 * which allow the filter coefficients to exceed the range <code>[+1 -1)</code>.
 * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
 * \image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator"
 * This essentially scales the filter coefficients by <code>2^postShift</code>.
 * For example, to realize the coefficients
 * <pre>
 *    {1.5, -0.8, 1.2, 1.6, -0.9}
 * </pre>
 * set the pCoeffs array to:
 * <pre>
 *    {0.75, -0.4, 0.6, 0.8, -0.45}
 * </pre>
 * and set <code>postShift=1</code>
 *
 * \par
 * <b>Filter gain: </b>
 * The frequency response of a Biquad filter is a function of its coefficients.
 * It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies.
 * This means that an input signal with amplitude < 1.0 may result in an output > 1.0 and these are saturated or overflowed based on the implementation of the filter.
 * To avoid this behavior the filter needs to be scaled down such that its peak gain < 1.0 or the input signal must be scaled down so that the combination of input and filter are never overflowed.
 *
 * \par
 * <b>Overflow and saturation: </b>
 * For Q15 and Q31 versions, it is described separately as part of the function specific documentation below.
 */

/**
 * @addtogroup BiquadCascadeDF1
 * @{
 */

/**
 * @param[in]  *S         points to an instance of the floating-point Biquad cascade 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 per call.
 * @return     none.
 *
 */

void arm_biquad_cascade_df1_f32(
  const arm_biquad_casd_df1_inst_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;                 /*  pState pointer            */
  float32_t *pCoeffs = S->pCoeffs;               /*  coefficient pointer       */
  float32_t acc;                                 /*  Simulates the accumulator */
  float32_t b0, b1, b2, a1, a2;                  /*  Filter coefficients       */
  float32_t Xn1, Xn2, Yn1, Yn2;                  /*  Filter pState variables   */
  float32_t Xn;                                  /*  temporary input           */
  uint32_t sample, stage = S->numStages;         /*  loop counters             */


#if defined (ARM_MATH_DSP)

  /* 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 pState values */
    Xn1 = pState[0];
    Xn2 = pState[1];
    Yn1 = pState[2];
    Yn2 = pState[3];

    /* Apply loop unrolling and compute 4 output values simultaneously. */
    /*      The variable acc hold output values that are being computed:
     *
     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]
     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]
     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]
     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]
     */

    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)
    {
      /* Read the first input */
      Xn = *pIn++;

      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
      Yn2 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);

      /* Store the result in the accumulator in the destination buffer. */
      *pOut++ = Yn2;

      /* Every time after the output is computed state should be updated. */
      /* The states should be updated as:  */
      /* Xn2 = Xn1    */
      /* Xn1 = Xn     */
      /* Yn2 = Yn1    */
      /* Yn1 = acc   */

      /* Read the second input */
      Xn2 = *pIn++;

      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
      Yn1 = (b0 * Xn2) + (b1 * Xn) + (b2 * Xn1) + (a1 * Yn2) + (a2 * Yn1);

      /* Store the result in the accumulator in the destination buffer. */
      *pOut++ = Yn1;

      /* Every time after the output is computed state should be updated. */
      /* The states should be updated as:  */
      /* Xn2 = Xn1    */
      /* Xn1 = Xn     */
      /* Yn2 = Yn1    */
      /* Yn1 = acc   */

      /* Read the third input */
      Xn1 = *pIn++;

      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
      Yn2 = (b0 * Xn1) + (b1 * Xn2) + (b2 * Xn) + (a1 * Yn1) + (a2 * Yn2);

      /* Store the result in the accumulator in the destination buffer. */
      *pOut++ = Yn2;

      /* Every time after the output is computed state should be updated. */
      /* The states should be updated as: */
      /* Xn2 = Xn1    */
      /* Xn1 = Xn     */
      /* Yn2 = Yn1    */
      /* Yn1 = acc   */

      /* Read the forth input */
      Xn = *pIn++;

      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
      Yn1 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn2) + (a2 * Yn1);

      /* Store the result in the accumulator in the destination buffer. */
      *pOut++ = Yn1;

      /* Every time after the output is computed state should be updated. */
      /* The states should be updated as:  */
      /* Xn2 = Xn1    */
      /* Xn1 = Xn     */
      /* Yn2 = Yn1    */
      /* Yn1 = acc   */
      Xn2 = Xn1;
      Xn1 = Xn;

      /* 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++;

      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
      acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);

      /* Store the result in the accumulator in the destination buffer. */
      *pOut++ = acc;

      /* Every time after the output is computed state should be updated. */
      /* The states should be updated as:    */
      /* Xn2 = Xn1    */
      /* Xn1 = Xn     */
      /* Yn2 = Yn1    */
      /* Yn1 = acc   */
      Xn2 = Xn1;
      Xn1 = Xn;
      Yn2 = Yn1;
      Yn1 = acc;

      /* decrement the loop counter */
      sample--;

    }

    /*  Store the updated state variables back into the pState array */
    *pState++ = Xn1;
    *pState++ = Xn2;
    *pState++ = Yn1;
    *pState++ = Yn2;

    /*  The first stage goes from the input buffer to the output buffer. */
    /*  Subsequent numStages  occur in-place in the output buffer */
    pIn = pDst;

    /* Reset the output 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 pState values */
    Xn1 = pState[0];
    Xn2 = pState[1];
    Yn1 = pState[2];
    Yn2 = pState[3];

    /*      The variables acc holds the output value that is computed:
     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]
     */

    sample = blockSize;

    while (sample > 0U)
    {
      /* Read the input */
      Xn = *pIn++;

      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
      acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);

      /* Store the result in the accumulator in the destination buffer. */
      *pOut++ = acc;

      /* Every time after the output is computed state should be updated. */
      /* The states should be updated as:    */
      /* Xn2 = Xn1    */
      /* Xn1 = Xn     */
      /* Yn2 = Yn1    */
      /* Yn1 = acc   */
      Xn2 = Xn1;
      Xn1 = Xn;
      Yn2 = Yn1;
      Yn1 = acc;

      /* decrement the loop counter */
      sample--;
    }

    /*  Store the updated state variables back into the pState array */
    *pState++ = Xn1;
    *pState++ = Xn2;
    *pState++ = Yn1;
    *pState++ = Yn2;

    /*  The first stage goes from the input buffer to the output buffer. */
    /*  Subsequent numStages  occur in-place in the output buffer */
    pIn = pDst;

    /* Reset the output pointer */
    pOut = pDst;

    /* decrement the loop counter */
    stage--;

  } while (stage > 0U);

#endif /* #if defined (ARM_MATH_DSP) */

}


  /**
   * @} end of BiquadCascadeDF1 group
   */