# Infinite Impulse Response (IIR) Lattice Filters
[Filtering Functions]

## Functions

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)
void | arm_iir_lattice_f32 (const arm_iir_lattice_instance_f32 *S, float32_t *pSrc, float32_t *pDst, uint32_t blockSize)
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)
void | arm_iir_lattice_q31 (const arm_iir_lattice_instance_q31 *S, q31_t *pSrc, q31_t *pDst, uint32_t blockSize)
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)
void | arm_iir_lattice_q15 (const arm_iir_lattice_instance_q15 *S, q15_t *pSrc, q15_t *pDst, uint32_t blockSize)

## Detailed Description

This set of functions implements lattice filters for Q15, Q31 and floating-point data types. Lattice filters are used in a variety of adaptive filter applications. The filter structure has feedforward and feedback components and the net impulse response is infinite length. The functions operate on blocks of input and output data and each call to the function processes `blockSize` samples through the filter. `pSrc` and `pDst` point to input and output arrays containing `blockSize` values.

Algorithm:

  Infinite Impulse Response Lattice filter

          fN(n)   =  x(n)
          fm-1(n) = fm(n) - km * gm-1(n-1)   for m = N, N-1, ...1
          gm(n)   = km * fm-1(n) + gm-1(n-1) for m = N, N-1, ...1
          y(n)    = vN * gN(n) + vN-1 * gN-1(n) + ...+ v0 * g0(n)

  `pkCoeffs` points to array of reflection coefficients of size `numStages`. Reflection coefficients are stored in time-reversed order.

          {kN, kN-1, ....k1}

  `pvCoeffs` points to the array of ladder coefficients of size `(numStages+1)`. Ladder coefficients are stored in time-reversed order.

          {vN, vN-1, ...v0}

  `pState` points to a state array of size `numStages + blockSize`. The state variables shown in the figure above (the g values) are stored in the `pState` array. The state variables are updated after each block of data is processed; the coefficients are untouched.

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.

Initialization Functions
  There is also an associated initialization function for each data type. The initialization function performs the following operations:
  - Sets the values of the internal structure fields.
  - Zeros out the values in the state buffer.

  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 and then manually initialize the instance structure as follows:

      arm_iir_lattice_instance_f32 S = {numStages, pState, pkCoeffs, pvCoeffs};
      arm_iir_lattice_instance_q31 S = {numStages, pState, pkCoeffs, pvCoeffs};
      arm_iir_lattice_instance_q15 S = {numStages, pState, pkCoeffs, pvCoeffs};

  where `numStages` is the number of stages in the filter; `pState` points to the state buffer array; `pkCoeffs` points to array of the reflection coefficients; `pvCoeffs` points to the array of ladder coefficients.

Fixed-Point Behavior
  Care must be taken when using the fixed-point versions of the IIR lattice filter functions. In particular, the overflow and saturation behavior of the accumulator used in each function must be considered. Refer to the function specific documentation below for usage guidelines.

## Function Documentation

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
| ) |  |

Initialization function for the floating-point IIR lattice filter.

Parameters:

  [in] | *S | points to an instance of the floating-point IIR lattice structure.
  [in] | numStages | number of stages in the filter.
  [in] | *pkCoeffs | points to the reflection coefficient buffer. The array is of length numStages.
  [in] | *pvCoeffs | points to the ladder coefficient buffer. The array is of length numStages+1.
  [in] | *pState | points to the state buffer. The array is of length numStages+blockSize.
  [in] | blockSize | number of samples to process.

Returns:
  none.

Definition at line 55 of file arm_iir_lattice_init_f32.c.

void arm_iir_lattice_f32 | ( | const arm_iir_lattice_instance_f32 * | S,
|  | float32_t * | pSrc,
|  | float32_t * | pDst,
|  | uint32_t | blockSize
| ) |  |

Processing function for the floating-point IIR lattice filter.

Parameters:

  [in] | *S | points to an instance of the floating-point IIR lattice structure.
  [in] | *pSrc | points to the block of input data.
  [out] | *pDst | points to the block of output data.
  [in] | blockSize | number of samples to process.

Returns:
  none.

Definition at line 120 of file arm_iir_lattice_f32.c.

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
| ) |  |

Initialization function for the Q31 IIR lattice filter.

Parameters:

  [in] | *S | points to an instance of the Q31 IIR lattice structure.
  [in] | numStages | number of stages in the filter.
  [in] | *pkCoeffs | points to the reflection coefficient buffer. The array is of length numStages.
  [in] | *pvCoeffs | points to the ladder coefficient buffer. The array is of length numStages+1.
  [in] | *pState | points to the state buffer. The array is of length numStages+blockSize.
  [in] | blockSize | number of samples to process.

Returns:
  none.

Definition at line 55 of file arm_iir_lattice_init_q31.c.

void arm_iir_lattice_q31 | ( | const arm_iir_lattice_instance_q31 * | S,
|  | q31_t * | pSrc,
|  | q31_t * | pDst,
|  | uint32_t | blockSize
| ) |  |

Processing function for the Q31 IIR lattice filter.

Parameters:

  [in] | *S | points to an instance of the Q31 IIR lattice structure.
  [in] | *pSrc | points to the block of input data.
  [out] | *pDst | points to the block of output data.
  [in] | blockSize | number of samples to process.

Returns:
  none.

Scaling and Overflow Behavior:

  The function is implemented using an internal 64-bit accumulator. The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit. Thus, if the accumulator result overflows it wraps around rather than clip. In order to avoid overflows completely the input signal must be scaled down by 2*log2(numStages) bits. After all multiply-accumulates are performed, the 2.62 accumulator is saturated to 1.32 format and then truncated to 1.31 format.

Definition at line 62 of file arm_iir_lattice_q31.c.

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
| ) |  |

Initialization function for the Q15 IIR lattice filter.

Parameters:

  [in] | *S | points to an instance of the Q15 IIR lattice structure.
  [in] | numStages | number of stages in the filter.
  [in] | *pkCoeffs | points to reflection coefficient buffer. The array is of length numStages.
  [in] | *pvCoeffs | points to ladder coefficient buffer. The array is of length numStages+1.
  [in] | *pState | points to state buffer. The array is of length numStages+blockSize.
  [in] | blockSize | number of samples to process per call.

Returns:
  none.

Definition at line 55 of file arm_iir_lattice_init_q15.c.

void arm_iir_lattice_q15 | ( | const arm_iir_lattice_instance_q15 * | S,
|  | q15_t * | pSrc,
|  | q15_t * | pDst,
|  | uint32_t | blockSize
| ) |  |

Processing function for the Q15 IIR lattice filter.

Parameters:

  [in] | *S | points to an instance of the Q15 IIR lattice structure.
  [in] | *pSrc | points to the block of input data.
  [out] | *pDst | points to the block of output data.
  [in] | blockSize | number of samples to process.

Returns:
  none.

Scaling and Overflow Behavior:

  The function is implemented using a 64-bit internal accumulator. Both coefficients and state variables are represented in 1.15 format and multiplications yield a 2.30 result. The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format. There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved. After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits. Lastly, the accumulator is saturated to yield a result in 1.15 format.

Definition at line 63 of file arm_iir_lattice_q15.c.

All Data Structures Files Functions Variables Typedefs Enumerations Enumerator Defines