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diff --git a/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c b/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c deleted file mode 100644 index a44d10d..0000000 --- a/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c +++ /dev/null @@ -1,561 +0,0 @@ -/* ---------------------------------------------------------------------- -* Copyright (C) 2010-2014 ARM Limited. All rights reserved. -* -* $Date: 19. October 2015 -* $Revision: V.1.4.5 a -* -* 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 -* -* Redistribution and use in source and binary forms, with or without -* modification, are permitted provided that the following conditions -* are met: -* - Redistributions of source code must retain the above copyright -* notice, this list of conditions and the following disclaimer. -* - Redistributions in binary form must reproduce the above copyright -* notice, this list of conditions and the following disclaimer in -* the documentation and/or other materials provided with the -* distribution. -* - Neither the name of ARM LIMITED nor the names of its contributors -* may be used to endorse or promote products derived from this -* software without specific prior written permission. -* -* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS -* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT -* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS -* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE -* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, -* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, -* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; -* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER -* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT -* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN -* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE -* POSSIBILITY OF SUCH DAMAGE. -* -------------------------------------------------------------------- */ - -#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. - * To do this manually without calling the init function, assign the follow subfields of the instance structure: - * numStages, pCoeffs, postShift, pState. Also set all of the values in pState to zero. - * - * \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 */ - q31_t Xn1, Xn2; /* Input Filter state variables */ - q63_t Yn1, Yn2; /* Output Filter state variables */ - q31_t b0, b1, b2, a1, a2; /* Filter coefficients */ - q31_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 */ - q31_t acc_l, acc_h; /* temporary output */ - uint32_t uShift = ((uint32_t) S->postShift + 1u); - uint32_t lShift = 32u - uShift; /* Shift to be applied to the output */ - - -#ifndef ARM_MATH_CM0_FAMILY - - /* 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 = (q31_t) (pState[0]); - Xn2 = (q31_t) (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++; - - /* 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 = (q63_t) Xn *b0; - - /* acc += b1 * x[n-1] */ - acc += (q63_t) Xn1 *b1; - - /* acc += b[2] * x[n-2] */ - acc += (q63_t) 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; - - /* Calc lower part of acc */ - acc_l = acc & 0xffffffff; - - /* Calc upper part of acc */ - acc_h = (acc >> 32) & 0xffffffff; - - /* Apply shift for lower part of acc and upper part of acc */ - acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift; - - /* Store the output in the destination buffer in 1.31 format. */ - *pOut = acc_h; - - /* Read the second input into Xn2, to reuse the value */ - Xn2 = *pIn++; - - /* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ - - /* acc += b1 * x[n-1] */ - acc = (q63_t) Xn *b1; - - /* acc = b0 * x[n] */ - acc += (q63_t) Xn2 *b0; - - /* acc += b[2] * x[n-2] */ - acc += (q63_t) 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; - - /* Calc lower part of acc */ - acc_l = acc & 0xffffffff; - - /* Calc upper part of acc */ - acc_h = (acc >> 32) & 0xffffffff; - - /* Apply shift for lower part of acc and upper part of acc */ - acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift; - - /* Read the third input into Xn1, to reuse the value */ - Xn1 = *pIn++; - - /* The result is converted to 1.31 */ - /* Store the output in the destination buffer. */ - *(pOut + 1u) = acc_h; - - /* 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 = (q63_t) Xn1 *b0; - - /* acc += b1 * x[n-1] */ - acc += (q63_t) Xn2 *b1; - - /* acc += b[2] * x[n-2] */ - acc += (q63_t) 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; - - /* Calc lower part of acc */ - acc_l = acc & 0xffffffff; - - /* Calc upper part of acc */ - acc_h = (acc >> 32) & 0xffffffff; - - /* Apply shift for lower part of acc and upper part of acc */ - acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift; - - /* Store the output in the destination buffer in 1.31 format. */ - *(pOut + 2u) = acc_h; - - /* Read the fourth input into Xn, to reuse the value */ - Xn = *pIn++; - - /* 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 = (q63_t) Xn *b0; - - /* acc += b1 * x[n-1] */ - acc += (q63_t) Xn1 *b1; - - /* acc += b[2] * x[n-2] */ - acc += (q63_t) 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; - - /* Calc lower part of acc */ - acc_l = acc & 0xffffffff; - - /* Calc upper part of acc */ - acc_h = (acc >> 32) & 0xffffffff; - - /* Apply shift for lower part of acc and upper part of acc */ - acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift; - - /* Store the output in the destination buffer in 1.31 format. */ - *(pOut + 3u) = acc_h; - - /* 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; - - /* update output pointer */ - pOut += 4u; - - /* 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++; - - /* 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 = (q63_t) Xn *b0; - /* acc += b1 * x[n-1] */ - acc += (q63_t) Xn1 *b1; - /* acc += b[2] * x[n-2] */ - acc += (q63_t) 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; - /* The result is converted to 1.63, Yn1 variable is reused */ - Yn1 = acc << shift; - - /* Calc lower part of acc */ - acc_l = acc & 0xffffffff; - - /* Calc upper part of acc */ - acc_h = (acc >> 32) & 0xffffffff; - - /* Apply shift for lower part of acc and upper part of acc */ - acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift; - - /* Store the output in the destination buffer in 1.31 format. */ - *pOut++ = acc_h; - /* 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 */ - /* Store the updated state variables back into the pState array */ - *pState++ = (q63_t) Xn1; - *pState++ = (q63_t) 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++; - - /* 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 = (q63_t) Xn *b0; - /* acc += b1 * x[n-1] */ - acc += (q63_t) Xn1 *b1; - /* acc += b[2] * x[n-2] */ - acc += (q63_t) 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; - - /* The result is converted to 1.63, Yn1 variable is reused */ - Yn1 = acc << shift; - - /* Calc lower part of acc */ - acc_l = acc & 0xffffffff; - - /* Calc upper part of acc */ - acc_h = (acc >> 32) & 0xffffffff; - - /* Apply shift for lower part of acc and upper part of acc */ - acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift; - - /* Store the output in the destination buffer in 1.31 format. */ - *pOut++ = acc_h; - - /* 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++ = (q63_t) Xn1; - *pState++ = (q63_t) Xn2; - *pState++ = Yn1; - *pState++ = Yn2; - - } while(--stage); - -#endif /* #ifndef ARM_MATH_CM0_FAMILY */ -} - - /** - * @} end of BiquadCascadeDF1_32x64 group - */ |