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 blockSize samples through the filter. pSrc points to the array of input data and pDst points to the array of output data. Both arrays contain blockSize values.
y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage.
Single Biquad filter stage
b0, b1 and b2 multiply the input signal x[n] and are referred to as the feedforward coefficients. Coefficients a1 and a2 multiply the output signal y[n] 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
y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2]
In this case the feedback coefficients a1 and a2 must be negated when used with the CMSIS DSP Library.numStages refers to the number of second order stages used. For example, an 8th order filter would be realized with numStages=4 second order stages.
8th order filter using a cascade of Biquad stages
numStages=5 second order stages with the coefficients for one of the stages configured as a first order filter (b2=0 and a2=0).pState points to state variables array. Each Biquad stage has 4 state variables x[n-1], x[n-2], y[n-1], and y[n-2]. The state variables are arranged in the pState array as:
{x[n-1], x[n-2], y[n-1], y[n-2]}
4*numStages values. The state variables are updated after each block of data is processed, the coefficients are untouched.
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};
where numStages is the number of Biquad stages in the filter; pState is the address of the state buffer; pCoeffs is the address of the coefficient buffer; postShift shift to be applied.[-1 +1). The fixed-point functions have an additional scaling parameter postShift which allow the filter coefficients to exceed the range [+1 -1). At the output of the filter's accumulator is a shift register which shifts the result by postShift bits.
Fixed-point Biquad with shift by postShift bits after accumulator
2^postShift. For example, to realize the coefficients
{1.5, -0.8, 1.2, 1.6, -0.9}
set the pCoeffs array to:
{0.75, -0.4, 0.6, 0.8, -0.45}
and set postShift=1| void arm_biquad_cascade_df1_init_f32 | ( | arm_biquad_casd_df1_inst_f32 * | S, |
| uint8_t | numStages, | ||
| float32_t * | pCoeffs, | ||
| float32_t * | pState | ||
| ) |
Initialization function for the floating-point Biquad cascade filter.
| [in,out] | *S | points to an instance of the floating-point Biquad cascade structure. |
| [in] | numStages | number of 2nd order stages in the filter. |
| [in] | *pCoeffs | points to the filter coefficients array. |
| [in] | *pState | points to the state array. |
Coefficient and State Ordering:
pCoeffs in the following order:
{b10, b11, b12, a11, a12, b20, b21, b22, a21, a22, ...}
b1x and a1x are the coefficients for the first stage, b2x and a2x are the coefficients for the second stage, and so on. The pCoeffs array contains a total of 5*numStages values.pState is a pointer to state array. Each Biquad stage has 4 state variables x[n-1], x[n-2], y[n-1], and y[n-2]. The state variables are arranged in the pState array as:
{x[n-1], x[n-2], y[n-1], y[n-2]}
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 4*numStages values. The state variables are updated after each block of data is processed; the coefficients are untouched. Definition at line 83 of file arm_biquad_cascade_df1_init_f32.c.
| void arm_biquad_cascade_df1_f32 | ( | const arm_biquad_casd_df1_inst_f32 * | S, |
| float32_t * | pSrc, | ||
| float32_t * | pDst, | ||
| uint32_t | blockSize | ||
| ) |
Processing function for the floating-point Biquad cascade filter.
| [in] | *S | points to an instance of the floating-point Biquad cascade 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 per call. |
Definition at line 171 of file arm_biquad_cascade_df1_f32.c.
| void arm_biquad_cascade_df1_init_q31 | ( | arm_biquad_casd_df1_inst_q31 * | S, |
| uint8_t | numStages, | ||
| q31_t * | pCoeffs, | ||
| q31_t * | pState, | ||
| int8_t | postShift | ||
| ) |
Initialization function for the Q31 Biquad cascade filter.
| [in,out] | *S | points to an instance of the Q31 Biquad cascade structure. |
| [in] | numStages | number of 2nd order stages in the filter. |
| [in] | *pCoeffs | points to the filter coefficients buffer. |
| [in] | *pState | points to the state buffer. |
| [in] | postShift | Shift to be applied after the accumulator. Varies according to the coefficients format |
Coefficient and State Ordering:
pCoeffs in the following order:
{b10, b11, b12, a11, a12, b20, b21, b22, a21, a22, ...}
where b1x and a1x are the coefficients for the first stage, b2x and a2x are the coefficients for the second stage, and so on. The pCoeffs array contains a total of 5*numStages values.pState points to state variables array. Each Biquad stage has 4 state variables x[n-1], x[n-2], y[n-1], and y[n-2]. The state variables are arranged in the pState array as:
{x[n-1], x[n-2], y[n-1], y[n-2]}
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 4*numStages values. The state variables are updated after each block of data is processed; the coefficients are untouched. Definition at line 81 of file arm_biquad_cascade_df1_init_q31.c.
| void arm_biquad_cascade_df1_q31 | ( | const arm_biquad_casd_df1_inst_q31 * | S, |
| q31_t * | pSrc, | ||
| q31_t * | pDst, | ||
| uint32_t | blockSize | ||
| ) |
Processing function for the Q31 Biquad cascade filter.
| [in] | *S | points to an instance of the Q31 Biquad cascade 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 per call. |
Scaling and Overflow Behavior:
postShift bits and the result truncated to 1.31 format by discarding the low 32 bits.arm_biquad_cascade_df1_fast_q31() for a faster but less precise implementation of this filter for Cortex-M3 and Cortex-M4. Definition at line 69 of file arm_biquad_cascade_df1_q31.c.
| void arm_biquad_cascade_df1_fast_q31 | ( | const arm_biquad_casd_df1_inst_q31 * | S, |
| q31_t * | pSrc, | ||
| q31_t * | pDst, | ||
| uint32_t | blockSize | ||
| ) |
Fast but less precise processing function for the Q31 Biquad cascade filter for Cortex-M3 and Cortex-M4.
| [in] | *S | points to an instance of the Q31 Biquad cascade 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 per call. |
Scaling and Overflow Behavior:
arm_biquad_cascade_df1_q31() for a slower implementation of this function which uses 64-bit accumulation to provide higher precision. Both the slow and the fast versions use the same instance structure. Use the function arm_biquad_cascade_df1_init_q31() to initialize the filter structure. Definition at line 70 of file arm_biquad_cascade_df1_fast_q31.c.
| void arm_biquad_cascade_df1_init_q15 | ( | arm_biquad_casd_df1_inst_q15 * | S, |
| uint8_t | numStages, | ||
| q15_t * | pCoeffs, | ||
| q15_t * | pState, | ||
| int8_t | postShift | ||
| ) |
Initialization function for the Q15 Biquad cascade filter.
| [in,out] | *S | points to an instance of the Q15 Biquad cascade structure. |
| [in] | numStages | number of 2nd order stages in the filter. |
| [in] | *pCoeffs | points to the filter coefficients. |
| [in] | *pState | points to the state buffer. |
| [in] | postShift | Shift to be applied to the accumulator result. Varies according to the coefficients format |
Coefficient and State Ordering:
pCoeffs in the following order:
{b10, 0, b11, b12, a11, a12, b20, 0, b21, b22, a21, a22, ...}
where b1x and a1x are the coefficients for the first stage, b2x and a2x are the coefficients for the second stage, and so on. The pCoeffs array contains a total of 6*numStages values. The zero coefficient between b1 and b2 facilities use of 16-bit SIMD instructions on the Cortex-M4.pState. Each Biquad stage has 4 state variables x[n-1], x[n-2], y[n-1], and y[n-2]. The state variables are arranged in the pState array as:
{x[n-1], x[n-2], y[n-1], y[n-2]}
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 4*numStages values. The state variables are updated after each block of data is processed; the coefficients are untouched. Definition at line 81 of file arm_biquad_cascade_df1_init_q15.c.
| void arm_biquad_cascade_df1_q15 | ( | const arm_biquad_casd_df1_inst_q15 * | S, |
| q15_t * | pSrc, | ||
| q15_t * | pDst, | ||
| uint32_t | blockSize | ||
| ) |
Processing function for the Q15 Biquad cascade filter.
| [in] | *S | points to an instance of the Q15 Biquad cascade structure. |
| [in] | *pSrc | points to the block of input data. |
| [out] | *pDst | points to the location where the output result is written. |
| [in] | blockSize | number of samples to process per call. |
Scaling and Overflow Behavior:
postShift bits to truncate the result to 1.15 format by discarding the low 16 bits. Finally, the result is saturated to 1.15 format.arm_biquad_cascade_df1_fast_q15() for a faster but less precise implementation of this filter for Cortex-M3 and Cortex-M4. Definition at line 70 of file arm_biquad_cascade_df1_q15.c.
| void arm_biquad_cascade_df1_fast_q15 | ( | const arm_biquad_casd_df1_inst_q15 * | S, |
| q15_t * | pSrc, | ||
| q15_t * | pDst, | ||
| uint32_t | blockSize | ||
| ) |
Fast but less precise processing function for the Q15 Biquad cascade filter for Cortex-M3 and Cortex-M4.
| [in] | *S | points to an instance of the Q15 Biquad cascade 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 per call. |
Scaling and Overflow Behavior:
postShift bits and the result truncated to 1.15 format by discarding the low 16 bits.arm_biquad_cascade_df1_q15() for a slower implementation of this function which uses 64-bit accumulation to avoid wrap around distortion. Both the slow and the fast versions use the same instance structure. Use the function arm_biquad_cascade_df1_init_q15() to initialize the filter structure. Definition at line 69 of file arm_biquad_cascade_df1_fast_q15.c.
1.7.2