Finite Impulse Response (FIR) Sparse Filters

Functions
void	arm_fir_sparse_f32 (arm_fir_sparse_instance_f32 *S, float32_t *pSrc, float32_t *pDst, float32_t *pScratchIn, uint32_t blockSize)
	Processing function for the floating-point sparse FIR filter. More...
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)
	Initialization function for the floating-point sparse FIR filter. More...
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)
	Initialization function for the Q15 sparse FIR filter. More...
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)
	Initialization function for the Q31 sparse FIR filter. More...
void	arm_fir_sparse_init_q7 (arm_fir_sparse_instance_q7 *S, uint16_t numTaps, q7_t *pCoeffs, q7_t *pState, int32_t *pTapDelay, uint16_t maxDelay, uint32_t blockSize)
	Initialization function for the Q7 sparse FIR filter. More...
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)
	Processing function for the Q15 sparse FIR filter. More...
void	arm_fir_sparse_q31 (arm_fir_sparse_instance_q31 *S, q31_t *pSrc, q31_t *pDst, q31_t *pScratchIn, uint32_t blockSize)
	Processing function for the Q31 sparse FIR filter. More...
void	arm_fir_sparse_q7 (arm_fir_sparse_instance_q7 *S, q7_t *pSrc, q7_t *pDst, q7_t *pScratchIn, q31_t *pScratchOut, uint32_t blockSize)
	Processing function for the Q7 sparse FIR filter. More...

Description

This group of functions implements sparse FIR filters. Sparse FIR filters are equivalent to standard FIR filters except that most of the coefficients are equal to zero. Sparse filters are used for simulating reflections in communications and audio applications.

There are separate functions for Q7, Q15, Q31, and floating-point data types. 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 points to input and output arrays respectively containing blockSize values.

Algorithm:

The sparse filter instant structure contains an array of tap indices pTapDelay which specifies the locations of the non-zero coefficients. This is in addition to the coefficient array b. The implementation essentially skips the multiplications by zero and leads to an efficient realization.

     y[n] = b[0] * x[n-pTapDelay[0]] + b[1] * x[n-pTapDelay[1]] + b[2] * x[n-pTapDelay[2]] + ...+ b[numTaps-1] * x[n-pTapDelay[numTaps-1]]
 

Sparse FIR filter. b[n] represents the filter coefficients

pCoeffs points to a coefficient array of size numTaps; pTapDelay points to an array of nonzero indices and is also of size numTaps; pState points to a state array of size maxDelay + blockSize, where maxDelay is the largest offset value that is ever used in the pTapDelay array. Some of the processing functions also require temporary working buffers.

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 and offset arrays may be shared among several instances while state variable arrays cannot be shared. There are separate instance structure declarations for each of the 4 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. To do this manually without calling the init function, assign the follow subfields of the instance structure: numTaps, pCoeffs, pTapDelay, maxDelay, stateIndex, pState. Also set all of the values in pState to zero.

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 4 different data type filter instance structures

arm_fir_sparse_instance_f32 S = {numTaps, 0, pState, pCoeffs, maxDelay, pTapDelay};
arm_fir_sparse_instance_q31 S = {numTaps, 0, pState, pCoeffs, maxDelay, pTapDelay};
arm_fir_sparse_instance_q15 S = {numTaps, 0, pState, pCoeffs, maxDelay, pTapDelay};
arm_fir_sparse_instance_q7 S =  {numTaps, 0, pState, pCoeffs, maxDelay, pTapDelay};
 

Fixed-Point Behavior

Care must be taken when using the fixed-point versions of the sparse FIR 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_fir_sparse_f32	(	arm_fir_sparse_instance_f32 *	S,
		float32_t *	pSrc,
		float32_t *	pDst,
		float32_t *	pScratchIn,
		uint32_t	blockSize
	)

Parameters

[in]	*S	points to an instance of the floating-point sparse FIR structure.
[in]	*pSrc	points to the block of input data.
[out]	*pDst	points to the block of output data
[in]	*pScratchIn	points to a temporary buffer of size blockSize.
[in]	blockSize	number of input samples to process per call.

Returns

none.

References arm_circularRead_f32(), arm_circularWrite_f32(), blockSize, arm_fir_sparse_instance_f32::maxDelay, arm_fir_sparse_instance_f32::numTaps, arm_fir_sparse_instance_f32::pCoeffs, arm_fir_sparse_instance_f32::pState, arm_fir_sparse_instance_f32::pTapDelay, and arm_fir_sparse_instance_f32::stateIndex.

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
	)

Parameters

[in,out]	*S	points to an instance of the floating-point sparse FIR structure.
[in]	numTaps	number of nonzero coefficients in the filter.
[in]	*pCoeffs	points to the array of filter coefficients.
[in]	*pState	points to the state buffer.
[in]	*pTapDelay	points to the array of offset times.
[in]	maxDelay	maximum offset time supported.
[in]	blockSize	number of samples that will be processed per block.

Returns

none

Description:

pCoeffs holds the filter coefficients and has length numTaps. pState holds the filter's state variables and must be of length maxDelay + blockSize, where maxDelay is the maximum number of delay line values. blockSize is the number of samples processed by the arm_fir_sparse_f32() function.

References arm_fir_sparse_instance_f32::maxDelay, arm_fir_sparse_instance_f32::numTaps, arm_fir_sparse_instance_f32::pCoeffs, arm_fir_sparse_instance_f32::pState, arm_fir_sparse_instance_f32::pTapDelay, and arm_fir_sparse_instance_f32::stateIndex.

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
	)

Parameters

[in,out]	*S	points to an instance of the Q15 sparse FIR structure.
[in]	numTaps	number of nonzero coefficients in the filter.
[in]	*pCoeffs	points to the array of filter coefficients.
[in]	*pState	points to the state buffer.
[in]	*pTapDelay	points to the array of offset times.
[in]	maxDelay	maximum offset time supported.
[in]	blockSize	number of samples that will be processed per block.

Returns

none

Description:

pCoeffs holds the filter coefficients and has length numTaps. pState holds the filter's state variables and must be of length maxDelay + blockSize, where maxDelay is the maximum number of delay line values. blockSize is the number of words processed by arm_fir_sparse_q15() function.

References arm_fir_sparse_instance_q15::maxDelay, arm_fir_sparse_instance_q15::numTaps, arm_fir_sparse_instance_q15::pCoeffs, arm_fir_sparse_instance_q15::pState, arm_fir_sparse_instance_q15::pTapDelay, and arm_fir_sparse_instance_q15::stateIndex.

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
	)

Parameters

[in,out]	*S	points to an instance of the Q31 sparse FIR structure.
[in]	numTaps	number of nonzero coefficients in the filter.
[in]	*pCoeffs	points to the array of filter coefficients.
[in]	*pState	points to the state buffer.
[in]	*pTapDelay	points to the array of offset times.
[in]	maxDelay	maximum offset time supported.
[in]	blockSize	number of samples that will be processed per block.

Returns

none

Description:

pCoeffs holds the filter coefficients and has length numTaps. pState holds the filter's state variables and must be of length maxDelay + blockSize, where maxDelay is the maximum number of delay line values. blockSize is the number of words processed by arm_fir_sparse_q31() function.

References arm_fir_sparse_instance_q31::maxDelay, arm_fir_sparse_instance_q31::numTaps, arm_fir_sparse_instance_q31::pCoeffs, arm_fir_sparse_instance_q31::pState, arm_fir_sparse_instance_q31::pTapDelay, and arm_fir_sparse_instance_q31::stateIndex.

void arm_fir_sparse_init_q7	(	arm_fir_sparse_instance_q7 *	S,
		uint16_t	numTaps,
		q7_t *	pCoeffs,
		q7_t *	pState,
		int32_t *	pTapDelay,
		uint16_t	maxDelay,
		uint32_t	blockSize
	)

Parameters

[in,out]	*S	points to an instance of the Q7 sparse FIR structure.
[in]	numTaps	number of nonzero coefficients in the filter.
[in]	*pCoeffs	points to the array of filter coefficients.
[in]	*pState	points to the state buffer.
[in]	*pTapDelay	points to the array of offset times.
[in]	maxDelay	maximum offset time supported.
[in]	blockSize	number of samples that will be processed per block.

Returns

none

Description:

pCoeffs holds the filter coefficients and has length numTaps. pState holds the filter's state variables and must be of length maxDelay + blockSize, where maxDelay is the maximum number of delay line values. blockSize is the number of samples processed by the arm_fir_sparse_q7() function.

References arm_fir_sparse_instance_q7::maxDelay, arm_fir_sparse_instance_q7::numTaps, arm_fir_sparse_instance_q7::pCoeffs, arm_fir_sparse_instance_q7::pState, arm_fir_sparse_instance_q7::pTapDelay, and arm_fir_sparse_instance_q7::stateIndex.

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
	)

Parameters

[in]	*S	points to an instance of the Q15 sparse FIR structure.
[in]	*pSrc	points to the block of input data.
[out]	*pDst	points to the block of output data
[in]	*pScratchIn	points to a temporary buffer of size blockSize.
[in]	*pScratchOut	points to a temporary buffer of size blockSize.
[in]	blockSize	number of input samples to process per call.

Returns

none.

Scaling and Overflow Behavior:

The function is implemented using an internal 32-bit accumulator. The 1.15 x 1.15 multiplications yield a 2.30 result and these are added to a 2.30 accumulator. Thus the full precision of the multiplications is maintained but there is only a single guard bit in the accumulator. If the accumulator result overflows it will wrap around rather than saturate. After all multiply-accumulates are performed, the 2.30 accumulator is truncated to 2.15 format and then saturated to 1.15 format. In order to avoid overflows the input signal or coefficients must be scaled down by log2(numTaps) bits.

References __PKHBT, __SIMD32, arm_circularRead_q15(), arm_circularWrite_q15(), blockSize, arm_fir_sparse_instance_q15::maxDelay, arm_fir_sparse_instance_q15::numTaps, arm_fir_sparse_instance_q15::pCoeffs, arm_fir_sparse_instance_q15::pState, arm_fir_sparse_instance_q15::pTapDelay, and arm_fir_sparse_instance_q15::stateIndex.

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

Parameters

[in]	*S	points to an instance of the Q31 sparse FIR structure.
[in]	*pSrc	points to the block of input data.
[out]	*pDst	points to the block of output data
[in]	*pScratchIn	points to a temporary buffer of size blockSize.
[in]	blockSize	number of input samples to process per call.

Returns

none.

Scaling and Overflow Behavior:

The function is implemented using an internal 32-bit accumulator. The 1.31 x 1.31 multiplications are truncated to 2.30 format. This leads to loss of precision on the intermediate multiplications and provides only a single guard bit. If the accumulator result overflows, it wraps around rather than saturate. In order to avoid overflows the input signal or coefficients must be scaled down by log2(numTaps) bits.

References arm_circularRead_f32(), arm_circularWrite_f32(), blockSize, arm_fir_sparse_instance_q31::maxDelay, arm_fir_sparse_instance_q31::numTaps, arm_fir_sparse_instance_q31::pCoeffs, arm_fir_sparse_instance_q31::pState, arm_fir_sparse_instance_q31::pTapDelay, and arm_fir_sparse_instance_q31::stateIndex.

void arm_fir_sparse_q7	(	arm_fir_sparse_instance_q7 *	S,
		q7_t *	pSrc,
		q7_t *	pDst,
		q7_t *	pScratchIn,
		q31_t *	pScratchOut,
		uint32_t	blockSize
	)

Parameters

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

Returns

none.

Scaling and Overflow Behavior:

The function is implemented using a 32-bit internal accumulator. Both coefficients and state variables are represented in 1.7 format and multiplications yield a 2.14 result. The 2.14 intermediate results are accumulated in a 32-bit accumulator in 18.14 format. There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved. The accumulator is then converted to 18.7 format by discarding the low 7 bits. Finally, the result is truncated to 1.7 format.

References __PACKq7, __SIMD32, arm_circularRead_q7(), arm_circularWrite_q7(), blockSize, arm_fir_sparse_instance_q7::maxDelay, arm_fir_sparse_instance_q7::numTaps, arm_fir_sparse_instance_q7::pCoeffs, arm_fir_sparse_instance_q7::pState, arm_fir_sparse_instance_q7::pTapDelay, and arm_fir_sparse_instance_q7::stateIndex.