arm_biquad_cascade_df1_32x64_q31.c
476 lines
| 18.2 KiB
| text/x-c
|
CLexer
r71 | /* ---------------------------------------------------------------------- | |||
* Copyright (C) 2010 ARM Limited. All rights reserved. | ||||
* | ||||
* $Date: 15. July 2011 | ||||
* $Revision: V1.0.10 | ||||
* | ||||
* Project: CMSIS DSP Library | ||||
* Title: arm_biquad_cascade_df1_32x64_q31.c | ||||
* | ||||
* Description: High precision Q31 Biquad cascade filter processing function | ||||
* | ||||
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 | ||||
* | ||||
* Version 1.0.10 2011/7/15 | ||||
* Big Endian support added and Merged M0 and M3/M4 Source code. | ||||
* | ||||
* Version 1.0.3 2010/11/29 | ||||
* Re-organized the CMSIS folders and updated documentation. | ||||
* | ||||
* Version 1.0.2 2010/11/11 | ||||
* Documentation updated. | ||||
* | ||||
* Version 1.0.1 2010/10/05 | ||||
* Production release and review comments incorporated. | ||||
* | ||||
* Version 1.0.0 2010/09/20 | ||||
* Production release and review comments incorporated. | ||||
* | ||||
* Version 0.0.7 2010/06/10 | ||||
* Misra-C changes done | ||||
* -------------------------------------------------------------------- */ | ||||
#include "arm_math.h" | ||||
/** | ||||
* @ingroup groupFilters | ||||
*/ | ||||
/** | ||||
* @defgroup BiquadCascadeDF1_32x64 High Precision Q31 Biquad Cascade Filter | ||||
* | ||||
* This function implements a high precision Biquad cascade filter which operates on | ||||
* Q31 data values. The filter coefficients are in 1.31 format and the state variables | ||||
* are in 1.63 format. The double precision state variables reduce quantization noise | ||||
* in the filter and provide a cleaner output. | ||||
* These filters are particularly useful when implementing filters in which the | ||||
* singularities are close to the unit circle. This is common for low pass or high | ||||
* pass filters with very low cutoff frequencies. | ||||
* | ||||
* The function operates on blocks of input and output data | ||||
* and each call to the function processes <code>blockSize</code> samples through | ||||
* the filter. <code>pSrc</code> and <code>pDst</code> points to input and output arrays | ||||
* containing <code>blockSize</code> Q31 values. | ||||
* | ||||
* \par Algorithm | ||||
* Each Biquad stage implements a second order filter using the difference equation: | ||||
* <pre> | ||||
* y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | ||||
* </pre> | ||||
* A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage. | ||||
* \image html Biquad.gif "Single Biquad filter stage" | ||||
* Coefficients <code>b0, b1, and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients. | ||||
* Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> 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 | ||||
* <pre> | ||||
* y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2] | ||||
* </pre> | ||||
* In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library. | ||||
* | ||||
* \par | ||||
* Higher order filters are realized as a cascade of second order sections. | ||||
* <code>numStages</code> refers to the number of second order stages used. | ||||
* For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages. | ||||
* \image html BiquadCascade.gif "8th order filter using a cascade of Biquad stages" | ||||
* A 9th order filter would be realized with <code>numStages=5</code> second order stages with the coefficients for one of the stages configured as a first order filter (<code>b2=0</code> and <code>a2=0</code>). | ||||
* | ||||
* \par | ||||
* The <code>pState</code> points to state variables array . | ||||
* Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</code> and each state variable in 1.63 format to improve precision. | ||||
* The state variables are arranged in the array as: | ||||
* <pre> | ||||
* {x[n-1], x[n-2], y[n-1], y[n-2]} | ||||
* </pre> | ||||
* | ||||
* \par | ||||
* 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 <code>4*numStages</code> values of data in 1.63 format. | ||||
* The state variables are updated after each block of data is processed; the coefficients are untouched. | ||||
* | ||||
* \par 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. | ||||
* | ||||
* \par Init Function | ||||
* There is also an associated initialization function which performs the following operations: | ||||
* - Sets the values of the internal structure fields. | ||||
* - Zeros out the values in the state buffer. | ||||
* \par | ||||
* 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. | ||||
* For example, to statically initialize the filter instance structure use | ||||
* <pre> | ||||
* arm_biquad_cas_df1_32x64_ins_q31 S1 = {numStages, pState, pCoeffs, postShift}; | ||||
* </pre> | ||||
* where <code>numStages</code> is the number of Biquad stages in the filter; <code>pState</code> is the address of the state buffer; | ||||
* <code>pCoeffs</code> is the address of the coefficient buffer; <code>postShift</code> shift to be applied which is described in detail below. | ||||
* \par Fixed-Point Behavior | ||||
* Care must be taken while using Biquad Cascade 32x64 filter function. | ||||
* Following issues must be considered: | ||||
* - Scaling of coefficients | ||||
* - Filter gain | ||||
* - Overflow and saturation | ||||
* | ||||
* \par | ||||
* Filter coefficients are represented as fractional values and | ||||
* restricted to lie in the range <code>[-1 +1)</code>. | ||||
* The processing function has an additional scaling parameter <code>postShift</code> | ||||
* which allows the filter coefficients to exceed the range <code>[+1 -1)</code>. | ||||
* At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits. | ||||
* \image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator" | ||||
* This essentially scales the filter coefficients by <code>2^postShift</code>. | ||||
* For example, to realize the coefficients | ||||
* <pre> | ||||
* {1.5, -0.8, 1.2, 1.6, -0.9} | ||||
* </pre> | ||||
* set the Coefficient array to: | ||||
* <pre> | ||||
* {0.75, -0.4, 0.6, 0.8, -0.45} | ||||
* </pre> | ||||
* and set <code>postShift=1</code> | ||||
* | ||||
* \par | ||||
* The second thing to keep in mind is the gain through the filter. | ||||
* The frequency response of a Biquad filter is a function of its coefficients. | ||||
* It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies. | ||||
* This means that an input signal with amplitude < 1.0 may result in an output > 1.0 and these are saturated or overflowed based on the implementation of the filter. | ||||
* To avoid this behavior the filter needs to be scaled down such that its peak gain < 1.0 or the input signal must be scaled down so that the combination of input and filter are never overflowed. | ||||
* | ||||
* \par | ||||
* The third item to consider is the overflow and saturation behavior of the fixed-point Q31 version. | ||||
* This is described in the function specific documentation below. | ||||
*/ | ||||
/** | ||||
* @addtogroup BiquadCascadeDF1_32x64 | ||||
* @{ | ||||
*/ | ||||
/** | ||||
* @details | ||||
* @param[in] *S points to an instance of the high precision Q31 Biquad cascade filter. | ||||
* @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. | ||||
* | ||||
* \par | ||||
* 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 bits and lie in the range [-0.25 +0.25). | ||||
* After all 5 multiply-accumulates are performed, the 2.62 accumulator is shifted by <code>postShift</code> bits and the result truncated to | ||||
* 1.31 format by discarding the low 32 bits. | ||||
* | ||||
* \par | ||||
* Two related functions are provided in the CMSIS DSP library. | ||||
* <code>arm_biquad_cascade_df1_q31()</code> implements a Biquad cascade with 32-bit coefficients and state variables with a Q63 accumulator. | ||||
* <code>arm_biquad_cascade_df1_fast_q31()</code> implements a Biquad cascade with 32-bit coefficients and state variables with a Q31 accumulator. | ||||
*/ | ||||
void arm_biquad_cas_df1_32x64_q31( | ||||
const arm_biquad_cas_df1_32x64_ins_q31 * S, | ||||
q31_t * pSrc, | ||||
q31_t * pDst, | ||||
uint32_t blockSize) | ||||
{ | ||||
q31_t *pIn = pSrc; /* input pointer initialization */ | ||||
q31_t *pOut = pDst; /* output pointer initialization */ | ||||
q63_t *pState = S->pState; /* state pointer initialization */ | ||||
q31_t *pCoeffs = S->pCoeffs; /* coeff pointer initialization */ | ||||
q63_t acc; /* accumulator */ | ||||
q63_t Xn1, Xn2, Yn1, Yn2; /* Filter state variables */ | ||||
q31_t b0, b1, b2, a1, a2; /* Filter coefficients */ | ||||
q63_t Xn; /* temporary input */ | ||||
int32_t shift = (int32_t) S->postShift + 1; /* Shift to be applied to the output */ | ||||
uint32_t sample, stage = S->numStages; /* loop counters */ | ||||
#ifndef ARM_MATH_CM0 | ||||
/* Run the below code for Cortex-M4 and Cortex-M3 */ | ||||
do | ||||
{ | ||||
/* Reading the coefficients */ | ||||
b0 = *pCoeffs++; | ||||
b1 = *pCoeffs++; | ||||
b2 = *pCoeffs++; | ||||
a1 = *pCoeffs++; | ||||
a2 = *pCoeffs++; | ||||
/* Reading the state values */ | ||||
Xn1 = pState[0]; | ||||
Xn2 = pState[1]; | ||||
Yn1 = pState[2]; | ||||
Yn2 = pState[3]; | ||||
/* Apply loop unrolling and compute 4 output values simultaneously. */ | ||||
/* The variable acc hold output value that is being computed and | ||||
* stored in the destination buffer | ||||
* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | ||||
*/ | ||||
sample = blockSize >> 2u; | ||||
/* First part of the processing with loop unrolling. Compute 4 outputs at a time. | ||||
** a second loop below computes the remaining 1 to 3 samples. */ | ||||
while(sample > 0u) | ||||
{ | ||||
/* Read the input */ | ||||
Xn = *pIn++; | ||||
/* The value is shifted to the MSB to perform 32x64 multiplication */ | ||||
Xn = Xn << 32; | ||||
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | ||||
/* acc = b0 * x[n] */ | ||||
acc = mult32x64(Xn, b0); | ||||
/* acc += b1 * x[n-1] */ | ||||
acc += mult32x64(Xn1, b1); | ||||
/* acc += b[2] * x[n-2] */ | ||||
acc += mult32x64(Xn2, b2); | ||||
/* acc += a1 * y[n-1] */ | ||||
acc += mult32x64(Yn1, a1); | ||||
/* acc += a2 * y[n-2] */ | ||||
acc += mult32x64(Yn2, a2); | ||||
/* The result is converted to 1.63 , Yn2 variable is reused */ | ||||
Yn2 = acc << shift; | ||||
/* Store the output in the destination buffer in 1.31 format. */ | ||||
*pOut++ = (q31_t) (acc >> (32 - shift)); | ||||
/* Read the second input into Xn2, to reuse the value */ | ||||
Xn2 = *pIn++; | ||||
/* The value is shifted to the MSB to perform 32x64 multiplication */ | ||||
Xn2 = Xn2 << 32; | ||||
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | ||||
/* acc = b0 * x[n] */ | ||||
acc = mult32x64(Xn2, b0); | ||||
/* acc += b1 * x[n-1] */ | ||||
acc += mult32x64(Xn, b1); | ||||
/* acc += b[2] * x[n-2] */ | ||||
acc += mult32x64(Xn1, b2); | ||||
/* acc += a1 * y[n-1] */ | ||||
acc += mult32x64(Yn2, a1); | ||||
/* acc += a2 * y[n-2] */ | ||||
acc += mult32x64(Yn1, a2); | ||||
/* The result is converted to 1.63, Yn1 variable is reused */ | ||||
Yn1 = acc << shift; | ||||
/* The result is converted to 1.31 */ | ||||
/* Store the output in the destination buffer. */ | ||||
*pOut++ = (q31_t) (acc >> (32 - shift)); | ||||
/* Read the third input into Xn1, to reuse the value */ | ||||
Xn1 = *pIn++; | ||||
/* The value is shifted to the MSB to perform 32x64 multiplication */ | ||||
Xn1 = Xn1 << 32; | ||||
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | ||||
/* acc = b0 * x[n] */ | ||||
acc = mult32x64(Xn1, b0); | ||||
/* acc += b1 * x[n-1] */ | ||||
acc += mult32x64(Xn2, b1); | ||||
/* acc += b[2] * x[n-2] */ | ||||
acc += mult32x64(Xn, b2); | ||||
/* acc += a1 * y[n-1] */ | ||||
acc += mult32x64(Yn1, a1); | ||||
/* acc += a2 * y[n-2] */ | ||||
acc += mult32x64(Yn2, a2); | ||||
/* The result is converted to 1.63, Yn2 variable is reused */ | ||||
Yn2 = acc << shift; | ||||
/* Store the output in the destination buffer in 1.31 format. */ | ||||
*pOut++ = (q31_t) (acc >> (32 - shift)); | ||||
/* Read the fourth input into Xn, to reuse the value */ | ||||
Xn = *pIn++; | ||||
/* The value is shifted to the MSB to perform 32x64 multiplication */ | ||||
Xn = Xn << 32; | ||||
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | ||||
/* acc = b0 * x[n] */ | ||||
acc = mult32x64(Xn, b0); | ||||
/* acc += b1 * x[n-1] */ | ||||
acc += mult32x64(Xn1, b1); | ||||
/* acc += b[2] * x[n-2] */ | ||||
acc += mult32x64(Xn2, b2); | ||||
/* acc += a1 * y[n-1] */ | ||||
acc += mult32x64(Yn2, a1); | ||||
/* acc += a2 * y[n-2] */ | ||||
acc += mult32x64(Yn1, a2); | ||||
/* The result is converted to 1.63, Yn1 variable is reused */ | ||||
Yn1 = acc << shift; | ||||
/* Every time after the output is computed state should be updated. */ | ||||
/* The states should be updated as: */ | ||||
/* Xn2 = Xn1 */ | ||||
/* Xn1 = Xn */ | ||||
/* Yn2 = Yn1 */ | ||||
/* Yn1 = acc */ | ||||
Xn2 = Xn1; | ||||
Xn1 = Xn; | ||||
/* Store the output in the destination buffer in 1.31 format. */ | ||||
*pOut++ = (q31_t) (acc >> (32 - shift)); | ||||
/* decrement the loop counter */ | ||||
sample--; | ||||
} | ||||
/* If the blockSize is not a multiple of 4, compute any remaining output samples here. | ||||
** No loop unrolling is used. */ | ||||
sample = (blockSize & 0x3u); | ||||
while(sample > 0u) | ||||
{ | ||||
/* Read the input */ | ||||
Xn = *pIn++; | ||||
/* The value is shifted to the MSB to perform 32x64 multiplication */ | ||||
Xn = Xn << 32; | ||||
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | ||||
/* acc = b0 * x[n] */ | ||||
acc = mult32x64(Xn, b0); | ||||
/* acc += b1 * x[n-1] */ | ||||
acc += mult32x64(Xn1, b1); | ||||
/* acc += b[2] * x[n-2] */ | ||||
acc += mult32x64(Xn2, b2); | ||||
/* acc += a1 * y[n-1] */ | ||||
acc += mult32x64(Yn1, a1); | ||||
/* acc += a2 * y[n-2] */ | ||||
acc += mult32x64(Yn2, a2); | ||||
/* Every time after the output is computed state should be updated. */ | ||||
/* The states should be updated as: */ | ||||
/* Xn2 = Xn1 */ | ||||
/* Xn1 = Xn */ | ||||
/* Yn2 = Yn1 */ | ||||
/* Yn1 = acc */ | ||||
Xn2 = Xn1; | ||||
Xn1 = Xn; | ||||
Yn2 = Yn1; | ||||
Yn1 = acc << shift; | ||||
/* Store the output in the destination buffer in 1.31 format. */ | ||||
*pOut++ = (q31_t) (acc >> (32 - shift)); | ||||
/* decrement the loop counter */ | ||||
sample--; | ||||
} | ||||
/* The first stage output is given as input to the second stage. */ | ||||
pIn = pDst; | ||||
/* Reset to destination buffer working pointer */ | ||||
pOut = pDst; | ||||
/* Store the updated state variables back into the pState array */ | ||||
*pState++ = Xn1; | ||||
*pState++ = Xn2; | ||||
*pState++ = Yn1; | ||||
*pState++ = Yn2; | ||||
} while(--stage); | ||||
#else | ||||
/* Run the below code for Cortex-M0 */ | ||||
do | ||||
{ | ||||
/* Reading the coefficients */ | ||||
b0 = *pCoeffs++; | ||||
b1 = *pCoeffs++; | ||||
b2 = *pCoeffs++; | ||||
a1 = *pCoeffs++; | ||||
a2 = *pCoeffs++; | ||||
/* Reading the state values */ | ||||
Xn1 = pState[0]; | ||||
Xn2 = pState[1]; | ||||
Yn1 = pState[2]; | ||||
Yn2 = pState[3]; | ||||
/* The variable acc hold output value that is being computed and | ||||
* stored in the destination buffer | ||||
* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | ||||
*/ | ||||
sample = blockSize; | ||||
while(sample > 0u) | ||||
{ | ||||
/* Read the input */ | ||||
Xn = *pIn++; | ||||
/* The value is shifted to the MSB to perform 32x64 multiplication */ | ||||
Xn = Xn << 32; | ||||
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | ||||
/* acc = b0 * x[n] */ | ||||
acc = mult32x64(Xn, b0); | ||||
/* acc += b1 * x[n-1] */ | ||||
acc += mult32x64(Xn1, b1); | ||||
/* acc += b[2] * x[n-2] */ | ||||
acc += mult32x64(Xn2, b2); | ||||
/* acc += a1 * y[n-1] */ | ||||
acc += mult32x64(Yn1, a1); | ||||
/* acc += a2 * y[n-2] */ | ||||
acc += mult32x64(Yn2, a2); | ||||
/* Every time after the output is computed state should be updated. */ | ||||
/* The states should be updated as: */ | ||||
/* Xn2 = Xn1 */ | ||||
/* Xn1 = Xn */ | ||||
/* Yn2 = Yn1 */ | ||||
/* Yn1 = acc */ | ||||
Xn2 = Xn1; | ||||
Xn1 = Xn; | ||||
Yn2 = Yn1; | ||||
Yn1 = acc << shift; | ||||
/* Store the output in the destination buffer in 1.31 format. */ | ||||
*pOut++ = (q31_t) (acc >> (32 - shift)); | ||||
/* decrement the loop counter */ | ||||
sample--; | ||||
} | ||||
/* The first stage output is given as input to the second stage. */ | ||||
pIn = pDst; | ||||
/* Reset to destination buffer working pointer */ | ||||
pOut = pDst; | ||||
/* Store the updated state variables back into the pState array */ | ||||
*pState++ = Xn1; | ||||
*pState++ = Xn2; | ||||
*pState++ = Yn1; | ||||
*pState++ = Yn2; | ||||
} while(--stage); | ||||
#endif /* #ifndef ARM_MATH_CM0 */ | ||||
} | ||||
/** | ||||
* @} end of BiquadCascadeDF1_32x64 group | ||||
*/ | ||||