arm_math.h

  /**
   * @param[in,out] *S           points to an instance of the high precision Q31 Biquad cascade filter structure.
   * @param[in]     numStages    number of 2nd order stages in the filter.
   * @param[in]     *pCoeffs     points to the filter coefficients.
   * @param[in]     *pState      points to the state buffer.
   * @param[in]     postShift    shift to be applied to the output. Varies according to the coefficients format
   * @return        none
   */

  void arm_biquad_cas_df1_32x64_init_q31(
  arm_biquad_cas_df1_32x64_ins_q31 * S,
  uint8_t numStages,
  q31_t * pCoeffs,
  q63_t * pState,
  uint8_t postShift);



  /**
   * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
   */

  typedef struct
  {
    uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
    float32_t *pState;         /**< points to the array of state coefficients.  The array is of length 2*numStages. */
    float32_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
  } arm_biquad_cascade_df2T_instance_f32;


  /**
   * @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);


  /**
   * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
   * @param[in,out] *S           points to an instance of the filter data structure.
   * @param[in]     numStages    number of 2nd order stages in the filter.
   * @param[in]     *pCoeffs     points to the filter coefficients.
   * @param[in]     *pState      points to the state buffer.
   * @return        none
   */

  void arm_biquad_cascade_df2T_init_f32(
  arm_biquad_cascade_df2T_instance_f32 * S,
  uint8_t numStages,
  float32_t * pCoeffs,
  float32_t * pState);



  /**
   * @brief Instance structure for the Q15 FIR lattice filter.
   */

  typedef struct
  {
    uint16_t numStages;                          /**< number of filter stages. */
    q15_t *pState;                               /**< points to the state variable array. The array is of length numStages. */
    q15_t *pCoeffs;                              /**< points to the coefficient array. The array is of length numStages. */
  } arm_fir_lattice_instance_q15;

  /**
   * @brief Instance structure for the Q31 FIR lattice filter.
   */

  typedef struct
  {
    uint16_t numStages;                          /**< number of filter stages. */
    q31_t *pState;                               /**< points to the state variable array. The array is of length numStages. */
    q31_t *pCoeffs;                              /**< points to the coefficient array. The array is of length numStages. */
  } arm_fir_lattice_instance_q31;

  /**
   * @brief Instance structure for the floating-point FIR lattice filter.
   */

  typedef struct
  {
    uint16_t numStages;                  /**< number of filter stages. */
    float32_t *pState;                   /**< points to the state variable array. The array is of length numStages. */
    float32_t *pCoeffs;                  /**< points to the coefficient array. The array is of length numStages. */
  } arm_fir_lattice_instance_f32;

  /**
   * @brief Initialization function for the Q15 FIR lattice filter.
   * @param[in] *S points to an instance of the Q15 FIR lattice structure.
   * @param[in] numStages  number of filter stages.
   * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages. 
   * @param[in] *pState points to the state buffer.  The array is of length numStages. 
   * @return none.
   */

  void arm_fir_lattice_init_q15(
  arm_fir_lattice_instance_q15 * S,
  uint16_t numStages,
  q15_t * pCoeffs,
  q15_t * pState);


  /**
   * @brief Processing function for the Q15 FIR lattice filter.
   * @param[in] *S points to an instance of the Q15 FIR lattice 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_fir_lattice_q15(
  const arm_fir_lattice_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Initialization function for the Q31 FIR lattice filter.
   * @param[in] *S points to an instance of the Q31 FIR lattice structure.
   * @param[in] numStages  number of filter stages.
   * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages.
   * @param[in] *pState points to the state buffer.   The array is of length numStages.
   * @return none.
   */

  void arm_fir_lattice_init_q31(
  arm_fir_lattice_instance_q31 * S,
  uint16_t numStages,
  q31_t * pCoeffs,
  q31_t * pState);


  /**
   * @brief Processing function for the Q31 FIR lattice filter.
   * @param[in]  *S        points to an instance of the Q31 FIR lattice 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_fir_lattice_q31(
  const arm_fir_lattice_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

/**
 * @brief Initialization function for the floating-point FIR lattice filter.
 * @param[in] *S points to an instance of the floating-point FIR lattice structure.
 * @param[in] numStages  number of filter stages.
 * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages.
 * @param[in] *pState points to the state buffer.  The array is of length numStages.
 * @return none.
 */

  void arm_fir_lattice_init_f32(
  arm_fir_lattice_instance_f32 * S,
  uint16_t numStages,
  float32_t * pCoeffs,
  float32_t * pState);

  /**
   * @brief Processing function for the floating-point FIR lattice filter.
   * @param[in]  *S        points to an instance of the floating-point FIR lattice 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_fir_lattice_f32(
  const arm_fir_lattice_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Instance structure for the Q15 IIR lattice filter.
   */
  typedef struct
  {
    uint16_t numStages;                         /**< number of stages in the filter. */
    q15_t *pState;                              /**< points to the state variable array. The array is of length numStages+blockSize. */
    q15_t *pkCoeffs;                            /**< points to the reflection coefficient array. The array is of length numStages. */
    q15_t *pvCoeffs;                            /**< points to the ladder coefficient array. The array is of length numStages+1. */
  } arm_iir_lattice_instance_q15;

  /**
   * @brief Instance structure for the Q31 IIR lattice filter.
   */
  typedef struct
  {
    uint16_t numStages;                         /**< number of stages in the filter. */
    q31_t *pState;                              /**< points to the state variable array. The array is of length numStages+blockSize. */
    q31_t *pkCoeffs;                            /**< points to the reflection coefficient array. The array is of length numStages. */
    q31_t *pvCoeffs;                            /**< points to the ladder coefficient array. The array is of length numStages+1. */
  } arm_iir_lattice_instance_q31;

  /**
   * @brief Instance structure for the floating-point IIR lattice filter.
   */
  typedef struct
  {
    uint16_t numStages;                         /**< number of stages in the filter. */
    float32_t *pState;                          /**< points to the state variable array. The array is of length numStages+blockSize. */
    float32_t *pkCoeffs;                        /**< points to the reflection coefficient array. The array is of length numStages. */
    float32_t *pvCoeffs;                        /**< points to the ladder coefficient array. The array is of length numStages+1. */
  } arm_iir_lattice_instance_f32;

  /**
   * @brief Processing function for the floating-point IIR lattice filter.
   * @param[in] *S points to an instance of the floating-point IIR lattice 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_iir_lattice_f32(
  const arm_iir_lattice_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Initialization function for the floating-point IIR lattice filter.
   * @param[in] *S points to an instance of the floating-point IIR lattice structure.
   * @param[in] numStages number of stages in the filter.
   * @param[in] *pkCoeffs points to the reflection coefficient buffer.  The array is of length numStages.
   * @param[in] *pvCoeffs points to the ladder coefficient buffer.  The array is of length numStages+1.
   * @param[in] *pState points to the state buffer.  The array is of length numStages+blockSize-1.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_iir_lattice_init_f32(
  arm_iir_lattice_instance_f32 * S,
  uint16_t numStages,
  float32_t * pkCoeffs,
  float32_t * pvCoeffs,
  float32_t * pState,
  uint32_t blockSize);


  /**
   * @brief Processing function for the Q31 IIR lattice filter.
   * @param[in] *S points to an instance of the Q31 IIR lattice 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_iir_lattice_q31(
  const arm_iir_lattice_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Initialization function for the Q31 IIR lattice filter.
   * @param[in] *S points to an instance of the Q31 IIR lattice structure.
   * @param[in] numStages number of stages in the filter.
   * @param[in] *pkCoeffs points to the reflection coefficient buffer.  The array is of length numStages.
   * @param[in] *pvCoeffs points to the ladder coefficient buffer.  The array is of length numStages+1.
   * @param[in] *pState points to the state buffer.  The array is of length numStages+blockSize.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_iir_lattice_init_q31(
  arm_iir_lattice_instance_q31 * S,
  uint16_t numStages,
  q31_t * pkCoeffs,
  q31_t * pvCoeffs,
  q31_t * pState,
  uint32_t blockSize);


  /**
   * @brief Processing function for the Q15 IIR lattice filter.
   * @param[in] *S points to an instance of the Q15 IIR lattice 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_iir_lattice_q15(
  const arm_iir_lattice_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);


/**
 * @brief Initialization function for the Q15 IIR lattice filter.
 * @param[in] *S points to an instance of the fixed-point Q15 IIR lattice structure.
 * @param[in] numStages  number of stages in the filter.
 * @param[in] *pkCoeffs points to reflection coefficient buffer.  The array is of length numStages.
 * @param[in] *pvCoeffs points to ladder coefficient buffer.  The array is of length numStages+1.
 * @param[in] *pState points to state buffer.  The array is of length numStages+blockSize.
 * @param[in] blockSize number of samples to process per call.
 * @return none.
 */

  void arm_iir_lattice_init_q15(
  arm_iir_lattice_instance_q15 * S,
  uint16_t numStages,
  q15_t * pkCoeffs,
  q15_t * pvCoeffs,
  q15_t * pState,
  uint32_t blockSize);

  /**
   * @brief Instance structure for the floating-point LMS filter.
   */

  typedef struct
  {
    uint16_t numTaps;    /**< number of coefficients in the filter. */
    float32_t *pState;   /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    float32_t *pCoeffs;  /**< points to the coefficient array. The array is of length numTaps. */
    float32_t mu;        /**< step size that controls filter coefficient updates. */
  } arm_lms_instance_f32;

  /**
   * @brief Processing function for floating-point LMS filter.
   * @param[in]  *S points to an instance of the floating-point LMS filter structure.
   * @param[in]  *pSrc points to the block of input data.
   * @param[in]  *pRef points to the block of reference data.
   * @param[out] *pOut points to the block of output data.
   * @param[out] *pErr points to the block of error data.
   * @param[in]  blockSize number of samples to process.
   * @return     none.
   */

  void arm_lms_f32(
  const arm_lms_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pRef,
  float32_t * pOut,
  float32_t * pErr,
  uint32_t blockSize);

  /**
   * @brief Initialization function for floating-point LMS filter.
   * @param[in] *S points to an instance of the floating-point LMS filter structure.
   * @param[in] numTaps  number of filter coefficients.
   * @param[in] *pCoeffs points to the coefficient buffer.
   * @param[in] *pState points to state buffer.
   * @param[in] mu step size that controls filter coefficient updates.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_lms_init_f32(
  arm_lms_instance_f32 * S,
  uint16_t numTaps,
  float32_t * pCoeffs,
  float32_t * pState,
  float32_t mu,
  uint32_t blockSize);

  /**
   * @brief Instance structure for the Q15 LMS filter.
   */

  typedef struct
  {
    uint16_t numTaps;    /**< number of coefficients in the filter. */
    q15_t *pState;       /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    q15_t *pCoeffs;      /**< points to the coefficient array. The array is of length numTaps. */
    q15_t mu;            /**< step size that controls filter coefficient updates. */
    uint32_t postShift;  /**< bit shift applied to coefficients. */
  } arm_lms_instance_q15;


  /**
   * @brief Initialization function for the Q15 LMS filter.
   * @param[in] *S points to an instance of the Q15 LMS filter structure.
   * @param[in] numTaps  number of filter coefficients.
   * @param[in] *pCoeffs points to the coefficient buffer.
   * @param[in] *pState points to the state buffer.
   * @param[in] mu step size that controls filter coefficient updates.
   * @param[in] blockSize number of samples to process.
   * @param[in] postShift bit shift applied to coefficients.
   * @return    none.
   */

  void arm_lms_init_q15(
  arm_lms_instance_q15 * S,
  uint16_t numTaps,
  q15_t * pCoeffs,
  q15_t * pState,
  q15_t mu,
  uint32_t blockSize,
  uint32_t postShift);

  /**
   * @brief Processing function for Q15 LMS filter.
   * @param[in] *S points to an instance of the Q15 LMS filter structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[in] *pRef points to the block of reference data.
   * @param[out] *pOut points to the block of output data.
   * @param[out] *pErr points to the block of error data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_lms_q15(
  const arm_lms_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pRef,
  q15_t * pOut,
  q15_t * pErr,
  uint32_t blockSize);


  /**
   * @brief Instance structure for the Q31 LMS filter.
   */

  typedef struct
  {
    uint16_t numTaps;    /**< number of coefficients in the filter. */
    q31_t *pState;       /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    q31_t *pCoeffs;      /**< points to the coefficient array. The array is of length numTaps. */
    q31_t mu;            /**< step size that controls filter coefficient updates. */
    uint32_t postShift;  /**< bit shift applied to coefficients. */

  } arm_lms_instance_q31;

  /**
   * @brief Processing function for Q31 LMS filter.
   * @param[in]  *S points to an instance of the Q15 LMS filter structure.
   * @param[in]  *pSrc points to the block of input data.
   * @param[in]  *pRef points to the block of reference data.
   * @param[out] *pOut points to the block of output data.
   * @param[out] *pErr points to the block of error data.
   * @param[in]  blockSize number of samples to process.
   * @return     none.
   */

  void arm_lms_q31(
  const arm_lms_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pRef,
  q31_t * pOut,
  q31_t * pErr,
  uint32_t blockSize);

  /**
   * @brief Initialization function for Q31 LMS filter.
   * @param[in] *S points to an instance of the Q31 LMS filter structure.
   * @param[in] numTaps  number of filter coefficients.
   * @param[in] *pCoeffs points to coefficient buffer.
   * @param[in] *pState points to state buffer.
   * @param[in] mu step size that controls filter coefficient updates.
   * @param[in] blockSize number of samples to process.
   * @param[in] postShift bit shift applied to coefficients.
   * @return none.
   */

  void arm_lms_init_q31(
  arm_lms_instance_q31 * S,
  uint16_t numTaps,
  q31_t * pCoeffs,
  q31_t * pState,
  q31_t mu,
  uint32_t blockSize,
  uint32_t postShift);

  /**
   * @brief Instance structure for the floating-point normalized LMS filter.
   */

  typedef struct
  {
    uint16_t numTaps;     /**< number of coefficients in the filter. */
    float32_t *pState;    /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    float32_t *pCoeffs;   /**< points to the coefficient array. The array is of length numTaps. */
    float32_t mu;        /**< step size that control filter coefficient updates. */
    float32_t energy;    /**< saves previous frame energy. */
    float32_t x0;        /**< saves previous input sample. */
  } arm_lms_norm_instance_f32;

  /**
   * @brief Processing function for floating-point normalized LMS filter.
   * @param[in] *S points to an instance of the floating-point normalized LMS filter structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[in] *pRef points to the block of reference data.
   * @param[out] *pOut points to the block of output data.
   * @param[out] *pErr points to the block of error data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_lms_norm_f32(
  arm_lms_norm_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pRef,
  float32_t * pOut,
  float32_t * pErr,
  uint32_t blockSize);

  /**
   * @brief Initialization function for floating-point normalized LMS filter.
   * @param[in] *S points to an instance of the floating-point LMS filter structure.
   * @param[in] numTaps  number of filter coefficients.
   * @param[in] *pCoeffs points to coefficient buffer.
   * @param[in] *pState points to state buffer.
   * @param[in] mu step size that controls filter coefficient updates.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_lms_norm_init_f32(
  arm_lms_norm_instance_f32 * S,
  uint16_t numTaps,
  float32_t * pCoeffs,
  float32_t * pState,
  float32_t mu,
  uint32_t blockSize);


  /**
   * @brief Instance structure for the Q31 normalized LMS filter.
   */
  typedef struct
  {
    uint16_t numTaps;     /**< number of coefficients in the filter. */
    q31_t *pState;        /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    q31_t *pCoeffs;       /**< points to the coefficient array. The array is of length numTaps. */
    q31_t mu;             /**< step size that controls filter coefficient updates. */
    uint8_t postShift;    /**< bit shift applied to coefficients. */
    q31_t *recipTable;    /**< points to the reciprocal initial value table. */
    q31_t energy;         /**< saves previous frame energy. */
    q31_t x0;             /**< saves previous input sample. */
  } arm_lms_norm_instance_q31;

  /**
   * @brief Processing function for Q31 normalized LMS filter.
   * @param[in] *S points to an instance of the Q31 normalized LMS filter structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[in] *pRef points to the block of reference data.
   * @param[out] *pOut points to the block of output data.
   * @param[out] *pErr points to the block of error data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_lms_norm_q31(
  arm_lms_norm_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pRef,
  q31_t * pOut,
  q31_t * pErr,
  uint32_t blockSize);

  /**
   * @brief Initialization function for Q31 normalized LMS filter.
   * @param[in] *S points to an instance of the Q31 normalized LMS filter structure.
   * @param[in] numTaps  number of filter coefficients.
   * @param[in] *pCoeffs points to coefficient buffer.
   * @param[in] *pState points to state buffer.
   * @param[in] mu step size that controls filter coefficient updates.
   * @param[in] blockSize number of samples to process.
   * @param[in] postShift bit shift applied to coefficients.
   * @return none.
   */

  void arm_lms_norm_init_q31(
  arm_lms_norm_instance_q31 * S,
  uint16_t numTaps,
  q31_t * pCoeffs,
  q31_t * pState,
  q31_t mu,
  uint32_t blockSize,
  uint8_t postShift);

  /**
   * @brief Instance structure for the Q15 normalized LMS filter.
   */

  typedef struct
  {
    uint16_t numTaps;    /**< Number of coefficients in the filter. */
    q15_t *pState;        /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    q15_t *pCoeffs;       /**< points to the coefficient array. The array is of length numTaps. */
    q15_t mu;            /**< step size that controls filter coefficient updates. */
    uint8_t postShift;   /**< bit shift applied to coefficients. */
    q15_t *recipTable;   /**< Points to the reciprocal initial value table. */
    q15_t energy;        /**< saves previous frame energy. */
    q15_t x0;            /**< saves previous input sample. */
  } arm_lms_norm_instance_q15;

  /**
   * @brief Processing function for Q15 normalized LMS filter.
   * @param[in] *S points to an instance of the Q15 normalized LMS filter structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[in] *pRef points to the block of reference data.
   * @param[out] *pOut points to the block of output data.
   * @param[out] *pErr points to the block of error data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_lms_norm_q15(
  arm_lms_norm_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pRef,
  q15_t * pOut,
  q15_t * pErr,
  uint32_t blockSize);


  /**
   * @brief Initialization function for Q15 normalized LMS filter.
   * @param[in] *S points to an instance of the Q15 normalized LMS filter structure.
   * @param[in] numTaps  number of filter coefficients.
   * @param[in] *pCoeffs points to coefficient buffer.
   * @param[in] *pState points to state buffer.
   * @param[in] mu step size that controls filter coefficient updates.
   * @param[in] blockSize number of samples to process.
   * @param[in] postShift bit shift applied to coefficients.
   * @return none.
   */

  void arm_lms_norm_init_q15(
  arm_lms_norm_instance_q15 * S,
  uint16_t numTaps,
  q15_t * pCoeffs,
  q15_t * pState,
  q15_t mu,
  uint32_t blockSize,
  uint8_t postShift);

  /**
   * @brief Correlation of floating-point sequences.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   * @return none.
   */

  void arm_correlate_f32(
  float32_t * pSrcA,
  uint32_t srcALen,
  float32_t * pSrcB,
  uint32_t srcBLen,
  float32_t * pDst);


   /**   
   * @brief Correlation of Q15 sequences   
   * @param[in] *pSrcA points to the first input sequence.   
   * @param[in] srcALen length of the first input sequence.   
   * @param[in] *pSrcB points to the second input sequence.   
   * @param[in] srcBLen length of the second input sequence.   
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.   
   * @param[in]  *pScratch points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
   * @return none.   
   */
  void arm_correlate_opt_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst,
  q15_t * pScratch);


  /**
   * @brief Correlation of Q15 sequences.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   * @return none.
   */

  void arm_correlate_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst);

  /**
   * @brief Correlation of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   * @return none.
   */

  void arm_correlate_fast_q15(
             q15_t * pSrcA,
            uint32_t srcALen,
             q15_t * pSrcB,
            uint32_t srcBLen,
            q15_t * pDst);



  /**
   * @brief Correlation of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   * @param[in]  *pScratch points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
   * @return none.
   */

  void arm_correlate_fast_opt_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst,
  q15_t * pScratch);

  /**
   * @brief Correlation of Q31 sequences.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   * @return none.
   */

  void arm_correlate_q31(
  q31_t * pSrcA,
  uint32_t srcALen,
  q31_t * pSrcB,
  uint32_t srcBLen,
  q31_t * pDst);

  /**
   * @brief Correlation of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   * @return none.
   */

  void arm_correlate_fast_q31(
  q31_t * pSrcA,
  uint32_t srcALen,
  q31_t * pSrcB,
  uint32_t srcBLen,
  q31_t * pDst);



 /**   
   * @brief Correlation of Q7 sequences.   
   * @param[in] *pSrcA points to the first input sequence.   
   * @param[in] srcALen length of the first input sequence.   
   * @param[in] *pSrcB points to the second input sequence.   
   * @param[in] srcBLen length of the second input sequence.   
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.   
   * @param[in]  *pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.   
   * @param[in]  *pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).   
   * @return none.   
   */

  void arm_correlate_opt_q7(
  q7_t * pSrcA,
  uint32_t srcALen,
  q7_t * pSrcB,
  uint32_t srcBLen,
  q7_t * pDst,
  q15_t * pScratch1,
  q15_t * pScratch2);


  /**
   * @brief Correlation of Q7 sequences.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   * @return none.
   */

  void arm_correlate_q7(
  q7_t * pSrcA,
  uint32_t srcALen,
  q7_t * pSrcB,
  uint32_t srcBLen,
  q7_t * pDst);


  /**
   * @brief Instance structure for the floating-point sparse FIR filter.
   */
  typedef struct
  {
    uint16_t numTaps;             /**< number of coefficients in the filter. */
    uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
    float32_t *pState;            /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
    float32_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
    uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
    int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
  } arm_fir_sparse_instance_f32;

  /**
   * @brief Instance structure for the Q31 sparse FIR filter.
   */

  typedef struct
  {
    uint16_t numTaps;             /**< number of coefficients in the filter. */
    uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
    q31_t *pState;                /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
    q31_t *pCoeffs;               /**< points to the coefficient array. The array is of length numTaps.*/
    uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
    int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
  } arm_fir_sparse_instance_q31;

  /**
   * @brief Instance structure for the Q15 sparse FIR filter.
   */

  typedef struct
  {
    uint16_t numTaps;             /**< number of coefficients in the filter. */
    uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
    q15_t *pState;                /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
    q15_t *pCoeffs;               /**< points to the coefficient array. The array is of length numTaps.*/
    uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
    int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
  } arm_fir_sparse_instance_q15;

  /**
   * @brief Instance structure for the Q7 sparse FIR filter.
   */

  typedef struct
  {
    uint16_t numTaps;             /**< number of coefficients in the filter. */
    uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
    q7_t *pState;                 /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
    q7_t *pCoeffs;                /**< points to the coefficient array. The array is of length numTaps.*/
    uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
    int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
  } arm_fir_sparse_instance_q7;

  /**
   * @brief Processing function for the floating-point sparse FIR filter.
   * @param[in]  *S          points to an instance of the floating-point sparse FIR structure.
   * @param[in]  *pSrc       points to the block of input data.
   * @param[out] *pDst       points to the block of output data
   * @param[in]  *pScratchIn points to a temporary buffer of size blockSize.
   * @param[in]  blockSize   number of input samples to process per call.
   * @return none.
   */

  void arm_fir_sparse_f32(
  arm_fir_sparse_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  float32_t * pScratchIn,
  uint32_t blockSize);

  /**
   * @brief  Initialization function for the floating-point sparse FIR filter.
   * @param[in,out] *S         points to an instance of the floating-point sparse FIR structure.
   * @param[in]     numTaps    number of nonzero coefficients in the filter.
   * @param[in]     *pCoeffs   points to the array of filter coefficients.
   * @param[in]     *pState    points to the state buffer.
   * @param[in]     *pTapDelay points to the array of offset times.
   * @param[in]     maxDelay   maximum offset time supported.
   * @param[in]     blockSize  number of samples that will be processed per block.
   * @return none
   */

  void arm_fir_sparse_init_f32(
  arm_fir_sparse_instance_f32 * S,
  uint16_t numTaps,
  float32_t * pCoeffs,
  float32_t * pState,
  int32_t * pTapDelay,
  uint16_t maxDelay,
  uint32_t blockSize);

  /**
   * @brief Processing function for the Q31 sparse FIR filter.
   * @param[in]  *S          points to an instance of the Q31 sparse FIR structure.
   * @param[in]  *pSrc       points to the block of input data.
   * @param[out] *pDst       points to the block of output data
   * @param[in]  *pScratchIn points to a temporary buffer of size blockSize.
   * @param[in]  blockSize   number of input samples to process per call.
   * @return none.
   */

  void arm_fir_sparse_q31(
  arm_fir_sparse_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  q31_t * pScratchIn,
  uint32_t blockSize);

  /**
   * @brief  Initialization function for the Q31 sparse FIR filter.
   * @param[in,out] *S         points to an instance of the Q31 sparse FIR structure.
   * @param[in]     numTaps    number of nonzero coefficients in the filter.
   * @param[in]     *pCoeffs   points to the array of filter coefficients.
   * @param[in]     *pState    points to the state buffer.
   * @param[in]     *pTapDelay points to the array of offset times.
   * @param[in]     maxDelay   maximum offset time supported.
   * @param[in]     blockSize  number of samples that will be processed per block.
   * @return none
   */

  void arm_fir_sparse_init_q31(
  arm_fir_sparse_instance_q31 * S,
  uint16_t numTaps,
  q31_t * pCoeffs,
  q31_t * pState,
  int32_t * pTapDelay,
  uint16_t maxDelay,
  uint32_t blockSize);

  /**
   * @brief Processing function for the Q15 sparse FIR filter.
   * @param[in]  *S           points to an instance of the Q15 sparse FIR structure.
   * @param[in]  *pSrc        points to the block of input data.
   * @param[out] *pDst        points to the block of output data
   * @param[in]  *pScratchIn  points to a temporary buffer of size blockSize.
   * @param[in]  *pScratchOut points to a temporary buffer of size blockSize.
   * @param[in]  blockSize    number of input samples to process per call.
   * @return none.
   */

  void arm_fir_sparse_q15(
  arm_fir_sparse_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  q15_t * pScratchIn,
  q31_t * pScratchOut,
  uint32_t blockSize);


  /**
   * @brief  Initialization function for the Q15 sparse FIR filter.
   * @param[in,out] *S         points to an instance of the Q15 sparse FIR structure.
   * @param[in]     numTaps    number of nonzero coefficients in the filter.
   * @param[in]     *pCoeffs   points to the array of filter coefficients.
   * @param[in]     *pState    points to the state buffer.
   * @param[in]     *pTapDelay points to the array of offset times.
   * @param[in]     maxDelay   maximum offset time supported.
   * @param[in]     blockSize  number of samples that will be processed per block.
   * @return none
   */

  void arm_fir_sparse_init_q15(
  arm_fir_sparse_instance_q15 * S,
  uint16_t numTaps,
  q15_t * pCoeffs,
  q15_t * pState,
  int32_t * pTapDelay,
  uint16_t maxDelay,
  uint32_t blockSize);

  /**
   * @brief Processing function for the Q7 sparse FIR filter.
   * @param[in]  *S           points to an instance of the Q7 sparse FIR structure.
   * @param[in]  *pSrc        points to the block of input data.
   * @param[out] *pDst        points to the block of output data
   * @param[in]  *pScratchIn  points to a temporary buffer of size blockSize.
   * @param[in]  *pScratchOut points to a temporary buffer of size blockSize.
   * @param[in]  blockSize    number of input samples to process per call.