From 76177aa280494bb36d7a0bcbda1078d4db717020 Mon Sep 17 00:00:00 2001 From: Ali Labbene Date: Mon, 9 Dec 2019 11:25:19 +0100 Subject: Official ARM version: v4.5 --- .../arm_biquad_cascade_df1_f32.c | 425 +++++++++++++++++++++ 1 file changed, 425 insertions(+) create mode 100644 DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_f32.c (limited to 'DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_f32.c') diff --git a/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_f32.c b/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_f32.c new file mode 100644 index 0000000..83e9f76 --- /dev/null +++ b/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_f32.c @@ -0,0 +1,425 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010-2014 ARM Limited. All rights reserved. +* +* $Date: 19. March 2015 +* $Revision: V.1.4.5 +* +* Project: CMSIS DSP Library +* Title: arm_biquad_cascade_df1_f32.c +* +* Description: Processing function for the +* floating-point Biquad cascade DirectFormI(DF1) filter. +* +* 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 Biquad Cascade IIR Filters Using Direct Form I Structure + * + * 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. + * + * \par Algorithm + * Each Biquad stage implements a second order filter using the difference equation: + * 
    
+ *     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. + * \image html Biquad.gif "Single Biquad filter stage" + * Coefficients 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. + * + * \par + * Higher order filters are realized as a cascade of second order sections. + * 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. + * \image html BiquadCascade.gif "8th order filter using a cascade of Biquad stages" + * A 9th order filter would be realized with numStages=5 second order stages with the coefficients for one of the stages configured as a first order filter (b2=0 and a2=0). + * + * \par + * The 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]}    
+ *
+ * + * \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 4*numStages values. + * 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. + * There are separate instance structure declarations for each of the 3 supported data types. + * + * \par Init Functions + * There is also an associated initialization function for each data type. + * The initialization function performs 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, 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. + * The code below statically initializes each of the 3 different data type filter instance structures + * 
    
+ *     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. + * + * \par Fixed-Point Behavior + * Care must be taken when using the Q15 and Q31 versions of the Biquad Cascade filter functions. + * Following issues must be considered: + * - Scaling of coefficients + * - Filter gain + * - Overflow and saturation + * + * \par + * Scaling of coefficients: + * Filter coefficients are represented as fractional values and + * coefficients are restricted to lie in the range [-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. + * \image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator" + * This essentially scales the filter coefficients by 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 + * + * \par + * Filter gain: + * 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 + * Overflow and saturation: + * For Q15 and Q31 versions, it is described separately as part of the function specific documentation below. + */ + +/** + * @addtogroup BiquadCascadeDF1 + * @{ + */ + +/** + * @param[in] *S points to an instance of the floating-point Biquad cascade structure. + * @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 per call. + * @return none. + * + */ + +void arm_biquad_cascade_df1_f32( + const arm_biquad_casd_df1_inst_f32 * S, + float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize) +{ + float32_t *pIn = pSrc; /* source pointer */ + float32_t *pOut = pDst; /* destination pointer */ + float32_t *pState = S->pState; /* pState pointer */ + float32_t *pCoeffs = S->pCoeffs; /* coefficient pointer */ + float32_t acc; /* Simulates the accumulator */ + float32_t b0, b1, b2, a1, a2; /* Filter coefficients */ + float32_t Xn1, Xn2, Yn1, Yn2; /* Filter pState variables */ + float32_t Xn; /* temporary input */ + uint32_t sample, stage = S->numStages; /* loop counters */ + + +#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 pState 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 values that are being computed: + * + * acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] + * acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] + * acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] + * 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 first input */ + Xn = *pIn++; + + /* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ + Yn2 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2); + + /* Store the result in the accumulator in the destination buffer. */ + *pOut++ = Yn2; + + /* 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 */ + + /* Read the second input */ + Xn2 = *pIn++; + + /* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ + Yn1 = (b0 * Xn2) + (b1 * Xn) + (b2 * Xn1) + (a1 * Yn2) + (a2 * Yn1); + + /* Store the result in the accumulator in the destination buffer. */ + *pOut++ = Yn1; + + /* 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 */ + + /* Read the third input */ + Xn1 = *pIn++; + + /* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ + Yn2 = (b0 * Xn1) + (b1 * Xn2) + (b2 * Xn) + (a1 * Yn1) + (a2 * Yn2); + + /* Store the result in the accumulator in the destination buffer. */ + *pOut++ = Yn2; + + /* 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 */ + + /* Read the forth input */ + Xn = *pIn++; + + /* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ + Yn1 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn2) + (a2 * Yn1); + + /* Store the result in the accumulator in the destination buffer. */ + *pOut++ = Yn1; + + /* 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; + + /* 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 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2); + + /* Store the result in the accumulator in the destination buffer. */ + *pOut++ = acc; + + /* 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; + + /* decrement the loop counter */ + sample--; + + } + + /* Store the updated state variables back into the pState array */ + *pState++ = Xn1; + *pState++ = Xn2; + *pState++ = Yn1; + *pState++ = Yn2; + + /* The first stage goes from the input buffer to the output buffer. */ + /* Subsequent numStages occur in-place in the output buffer */ + pIn = pDst; + + /* Reset the output pointer */ + pOut = pDst; + + /* decrement the loop counter */ + stage--; + + } while(stage > 0u); + +#else + + /* Run the below code for Cortex-M0 */ + + do + { + /* Reading the coefficients */ + b0 = *pCoeffs++; + b1 = *pCoeffs++; + b2 = *pCoeffs++; + a1 = *pCoeffs++; + a2 = *pCoeffs++; + + /* Reading the pState values */ + Xn1 = pState[0]; + Xn2 = pState[1]; + Yn1 = pState[2]; + Yn2 = pState[3]; + + /* The variables acc holds the output value that is computed: + * 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 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2); + + /* Store the result in the accumulator in the destination buffer. */ + *pOut++ = acc; + + /* 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; + + /* decrement the loop counter */ + sample--; + } + + /* Store the updated state variables back into the pState array */ + *pState++ = Xn1; + *pState++ = Xn2; + *pState++ = Yn1; + *pState++ = Yn2; + + /* The first stage goes from the input buffer to the output buffer. */ + /* Subsequent numStages occur in-place in the output buffer */ + pIn = pDst; + + /* Reset the output pointer */ + pOut = pDst; + + /* decrement the loop counter */ + stage--; + + } while(stage > 0u); + +#endif /* #ifndef ARM_MATH_CM0_FAMILY */ + +} + + + /** + * @} end of BiquadCascadeDF1 group + */ -- cgit