CMSIS DSP Library from CMSIS 2.0. See http://www.onarm.com/cmsis/ for full details
Dependents: K22F_DSP_Matrix_least_square BNO055-ELEC3810 1BNO055 ECE4180Project--Slave2 ... more
Finite Impulse Response (FIR) Interpolator
[Filtering Functions]
These functions combine an upsampler (zero stuffer) and an FIR filter. More...
Functions | |
void | arm_fir_interpolate_f32 (const arm_fir_interpolate_instance_f32 *S, float32_t *pSrc, float32_t *pDst, uint32_t blockSize) |
Processing function for the floating-point FIR interpolator. | |
arm_status | arm_fir_interpolate_init_f32 (arm_fir_interpolate_instance_f32 *S, uint8_t L, uint16_t numTaps, float32_t *pCoeffs, float32_t *pState, uint32_t blockSize) |
Initialization function for the floating-point FIR interpolator. | |
arm_status | arm_fir_interpolate_init_q15 (arm_fir_interpolate_instance_q15 *S, uint8_t L, uint16_t numTaps, q15_t *pCoeffs, q15_t *pState, uint32_t blockSize) |
Initialization function for the Q15 FIR interpolator. | |
arm_status | arm_fir_interpolate_init_q31 (arm_fir_interpolate_instance_q31 *S, uint8_t L, uint16_t numTaps, q31_t *pCoeffs, q31_t *pState, uint32_t blockSize) |
Initialization function for the Q31 FIR interpolator. | |
void | arm_fir_interpolate_q15 (const arm_fir_interpolate_instance_q15 *S, q15_t *pSrc, q15_t *pDst, uint32_t blockSize) |
Processing function for the Q15 FIR interpolator. | |
void | arm_fir_interpolate_q31 (const arm_fir_interpolate_instance_q31 *S, q31_t *pSrc, q31_t *pDst, uint32_t blockSize) |
Processing function for the Q31 FIR interpolator. |
Detailed Description
These functions combine an upsampler (zero stuffer) and an FIR filter.
They are used in multirate systems for increasing the sample rate of a signal without introducing high frequency images. Conceptually, the functions are equivalent to the block diagram below:
Components included in the FIR Interpolator functions
After upsampling by a factor of L
, the signal should be filtered by a lowpass filter with a normalized cutoff frequency of 1/L
in order to eliminate high frequency copies of the spectrum. The user of the function is responsible for providing the filter coefficients.
The FIR interpolator functions provided in the CMSIS DSP Library combine the upsampler and FIR filter in an efficient manner. The upsampler inserts L-1
zeros between each sample. Instead of multiplying by these zero values, the FIR filter is designed to skip them. This leads to an efficient implementation without any wasted effort. The functions operate on blocks of input and output data. pSrc
points to an array of blockSize
input values and pDst
points to an array of blockSize*L
output values.
The library provides separate functions for Q15, Q31, and floating-point data types.
- Algorithm:
- The functions use a polyphase filter structure:
y[n] = b[0] * x[n] + b[L] * x[n-1] + ... + b[L*(phaseLength-1)] * x[n-phaseLength+1] y[n+1] = b[1] * x[n] + b[L+1] * x[n-1] + ... + b[L*(phaseLength-1)+1] * x[n-phaseLength+1] ... y[n+(L-1)] = b[L-1] * x[n] + b[2*L-1] * x[n-1] + ....+ b[L*(phaseLength-1)+(L-1)] * x[n-phaseLength+1]
This approach is more efficient than straightforward upsample-then-filter algorithms. With this method the computation is reduced by a factor of1/L
when compared to using a standard FIR filter.
pCoeffs
points to a coefficient array of sizenumTaps
.numTaps
must be a multiple of the interpolation factorL
and this is checked by the initialization functions. Internally, the function divides the FIR filter's impulse response into shorter filters of lengthphaseLength=numTaps/L
. Coefficients are stored in time reversed order.
{b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
pState
points to a state array of sizeblockSize + phaseLength - 1
. Samples in the state buffer are stored in the order:
{x[n-phaseLength+1], x[n-phaseLength], x[n-phaseLength-1], x[n-phaseLength-2]....x[0], x[1], ..., x[blockSize-1]}
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 array should be allocated separately. 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.
- Checks to make sure that the length of the filter is a multiple of the interpolation factor.
- 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. The code below statically initializes each of the 3 different data type filter instance structures
arm_fir_interpolate_instance_f32 S = {L, phaseLength, pCoeffs, pState}; arm_fir_interpolate_instance_q31 S = {L, phaseLength, pCoeffs, pState}; arm_fir_interpolate_instance_q15 S = {L, phaseLength, pCoeffs, pState};
whereL
is the interpolation factor;phaseLength=numTaps/L
is the length of each of the shorter FIR filters used internally,pCoeffs
is the address of the coefficient buffer;pState
is the address of the state buffer. Be sure to set the values in the state buffer to zeros when doing static initialization.
- Fixed-Point Behavior
- Care must be taken when using the fixed-point versions of the FIR interpolate 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_interpolate_f32 | ( | const arm_fir_interpolate_instance_f32 * | S, |
float32_t * | pSrc, | ||
float32_t * | pDst, | ||
uint32_t | blockSize | ||
) |
Processing function for the floating-point FIR interpolator.
- Parameters:
-
[in] *S points to an instance of the floating-point FIR interpolator structure. [in] *pSrc points to the block of input data. [out] *pDst points to the block of output data. [in] blockSize number of input samples to process per call.
- Returns:
- none.
Definition at line 132 of file arm_fir_interpolate_f32.c.
arm_status arm_fir_interpolate_init_f32 | ( | arm_fir_interpolate_instance_f32 * | S, |
uint8_t | L, | ||
uint16_t | numTaps, | ||
float32_t * | pCoeffs, | ||
float32_t * | pState, | ||
uint32_t | blockSize | ||
) |
Initialization function for the floating-point FIR interpolator.
- Parameters:
-
[in,out] *S points to an instance of the floating-point FIR interpolator structure. [in] L upsample factor. [in] numTaps number of filter coefficients in the filter. [in] *pCoeffs points to the filter coefficient buffer. [in] *pState points to the state buffer. [in] blockSize number of input samples to process per call.
- Returns:
- The function returns ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_LENGTH_ERROR if the filter length
numTaps
is not a multiple of the interpolation factorL
.
Description:
pCoeffs
points to the array of filter coefficients stored in time reversed order:{b[numTaps-1], b[numTaps-2], b[numTaps-2], ..., b[1], b[0]}
The length of the filternumTaps
must be a multiple of the interpolation factorL
.
pState
points to the array of state variables.pState
is of length(numTaps/L)+blockSize-1
words whereblockSize
is the number of input samples processed by each call toarm_fir_interpolate_f32()
.
Definition at line 65 of file arm_fir_interpolate_init_f32.c.
arm_status arm_fir_interpolate_init_q15 | ( | arm_fir_interpolate_instance_q15 * | S, |
uint8_t | L, | ||
uint16_t | numTaps, | ||
q15_t * | pCoeffs, | ||
q15_t * | pState, | ||
uint32_t | blockSize | ||
) |
Initialization function for the Q15 FIR interpolator.
- Parameters:
-
[in,out] *S points to an instance of the Q15 FIR interpolator structure. [in] L upsample factor. [in] numTaps number of filter coefficients in the filter. [in] *pCoeffs points to the filter coefficient buffer. [in] *pState points to the state buffer. [in] blockSize number of input samples to process per call.
- Returns:
- The function returns ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_LENGTH_ERROR if the filter length
numTaps
is not a multiple of the interpolation factorL
.
Description:
pCoeffs
points to the array of filter coefficients stored in time reversed order:{b[numTaps-1], b[numTaps-2], b[numTaps-2], ..., b[1], b[0]}
The length of the filternumTaps
must be a multiple of the interpolation factorL
.
pState
points to the array of state variables.pState
is of length(numTaps/L)+blockSize-1
words whereblockSize
is the number of input samples processed by each call toarm_fir_interpolate_q15()
.
Definition at line 65 of file arm_fir_interpolate_init_q15.c.
arm_status arm_fir_interpolate_init_q31 | ( | arm_fir_interpolate_instance_q31 * | S, |
uint8_t | L, | ||
uint16_t | numTaps, | ||
q31_t * | pCoeffs, | ||
q31_t * | pState, | ||
uint32_t | blockSize | ||
) |
Initialization function for the Q31 FIR interpolator.
- Parameters:
-
[in,out] *S points to an instance of the Q31 FIR interpolator structure. [in] L upsample factor. [in] numTaps number of filter coefficients in the filter. [in] *pCoeffs points to the filter coefficient buffer. [in] *pState points to the state buffer. [in] blockSize number of input samples to process per call.
- Returns:
- The function returns ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_LENGTH_ERROR if the filter length
numTaps
is not a multiple of the interpolation factorL
.
Description:
pCoeffs
points to the array of filter coefficients stored in time reversed order:{b[numTaps-1], b[numTaps-2], b[numTaps-2], ..., b[1], b[0]}
The length of the filternumTaps
must be a multiple of the interpolation factorL
.
pState
points to the array of state variables.pState
is of length(numTaps/L)+blockSize-1
words whereblockSize
is the number of input samples processed by each call toarm_fir_interpolate_q31()
.
Definition at line 66 of file arm_fir_interpolate_init_q31.c.
void arm_fir_interpolate_q15 | ( | const arm_fir_interpolate_instance_q15 * | S, |
q15_t * | pSrc, | ||
q15_t * | pDst, | ||
uint32_t | blockSize | ||
) |
Processing function for the Q15 FIR interpolator.
- Parameters:
-
[in] *S points to an instance of the Q15 FIR interpolator structure. [in] *pSrc points to the block of input data. [out] *pDst points to the block of output data. [in] blockSize number of input samples to process per call.
- 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 59 of file arm_fir_interpolate_q15.c.
void arm_fir_interpolate_q31 | ( | const arm_fir_interpolate_instance_q31 * | S, |
q31_t * | pSrc, | ||
q31_t * | pDst, | ||
uint32_t | blockSize | ||
) |
Processing function for the Q31 FIR interpolator.
- Parameters:
-
[in] *S points to an instance of the Q31 FIR interpolator structure. [in] *pSrc points to the block of input data. [out] *pDst points to the block of output data. [in] blockSize number of input samples to process per call.
- 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
1/(numTaps/L)
. sincenumTaps/L
additions occur per output sample. After all multiply-accumulates are performed, the 2.62 accumulator is truncated to 1.32 format and then saturated to 1.31 format.
Definition at line 60 of file arm_fir_interpolate_q31.c.
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