/* ---------------------------------------------------------------------- * 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_stereo_df2T_f32.c * * Description: Processing function for the floating-point transposed * direct form II Biquad cascade filter. 2 channels * * 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 BiquadCascadeDF2T Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure * * This set of functions implements arbitrary order recursive (IIR) filters using a transposed direct form II structure. * The filters are implemented as a cascade of second order Biquad sections. * These functions provide a slight memory savings as compared to the direct form I Biquad filter functions. * Only floating-point data is supported. * * This function 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] + d1       
*    d1 = b1 * x[n] + a1 * y[n] + d2       
*    d2 = b2 * x[n] + a2 * y[n]       
*
* where d1 and d2 represent the two state values. * * \par * A Biquad filter using a transposed Direct Form II structure is shown below. * \image html BiquadDF2Transposed.gif "Single transposed Direct Form II Biquad" * 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 flip the sign of the feedback coefficients: * 
       
*    y[n] = b0 * x[n] + d1;       
*    d1 = b1 * x[n] - a1 * y[n] + d2;       
*    d2 = b2 * x[n] - a2 * y[n];       
*
* 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. * 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 * pState points to the state variable array. * Each Biquad stage has 2 state variables d1 and d2. * The state variables are arranged in the pState array as: * 
       
*     {d11, d12, d21, d22, ...}       
*
* where d1x refers to the state variables for the first Biquad and * d2x refers to the state variables for the second Biquad. * The state array has a total length of 2*numStages values. * The state variables are updated after each block of data is processed; the coefficients are untouched. * * \par * The CMSIS library contains Biquad filters in both Direct Form I and transposed Direct Form II. * The advantage of the Direct Form I structure is that it is numerically more robust for fixed-point data types. * That is why the Direct Form I structure supports Q15 and Q31 data types. * The transposed Direct Form II structure, on the other hand, requires a wide dynamic range for the state variables d1 and d2. * Because of this, the CMSIS library only has a floating-point version of the Direct Form II Biquad. * The advantage of the Direct Form II Biquad is that it requires half the number of state variables, 2 rather than 4, per Biquad stage. * * \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 Functions * There is also an associated initialization function. * 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. * For example, to statically initialize the instance structure use * 
       
*     arm_biquad_cascade_df2T_instance_f32 S1 = {numStages, pState, pCoeffs};       
*
* 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; * */ /** * @addtogroup BiquadCascadeDF2T * @{ */ /** * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter. * @param[in] *S points to an instance of the filter data 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. * @return none. */ LOW_OPTIMIZATION_ENTER void arm_biquad_cascade_stereo_df2T_f32( const arm_biquad_cascade_stereo_df2T_instance_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; /* State pointer */ float32_t *pCoeffs = S->pCoeffs; /* coefficient pointer */ float32_t acc1a, acc1b; /* accumulator */ float32_t b0, b1, b2, a1, a2; /* Filter coefficients */ float32_t Xn1a, Xn1b; /* temporary input */ float32_t d1a, d2a, d1b, d2b; /* state variables */ uint32_t sample, stage = S->numStages; /* loop counters */ #if defined(ARM_MATH_CM7) float32_t Xn2a, Xn3a, Xn4a, Xn5a, Xn6a, Xn7a, Xn8a; /* Input State variables */ float32_t Xn2b, Xn3b, Xn4b, Xn5b, Xn6b, Xn7b, Xn8b; /* Input State variables */ float32_t acc2a, acc3a, acc4a, acc5a, acc6a, acc7a, acc8a; /* Simulates the accumulator */ float32_t acc2b, acc3b, acc4b, acc5b, acc6b, acc7b, acc8b; /* Simulates the accumulator */ do { /* Reading the coefficients */ b0 = pCoeffs[0]; b1 = pCoeffs[1]; b2 = pCoeffs[2]; a1 = pCoeffs[3]; /* Apply loop unrolling and compute 8 output values simultaneously. */ sample = blockSize >> 3u; a2 = pCoeffs[4]; /*Reading the state values */ d1a = pState[0]; d2a = pState[1]; d1b = pState[2]; d2b = pState[3]; pCoeffs += 5u; /* First part of the processing with loop unrolling. Compute 8 outputs at a time. ** a second loop below computes the remaining 1 to 7 samples. */ while(sample > 0u) { /* y[n] = b0 * x[n] + d1 */ /* d1 = b1 * x[n] + a1 * y[n] + d2 */ /* d2 = b2 * x[n] + a2 * y[n] */ /* Read the first 2 inputs. 2 cycles */ Xn1a = pIn[0 ]; Xn1b = pIn[1 ]; /* Sample 1. 5 cycles */ Xn2a = pIn[2 ]; acc1a = b0 * Xn1a + d1a; Xn2b = pIn[3 ]; d1a = b1 * Xn1a + d2a; Xn3a = pIn[4 ]; d2a = b2 * Xn1a; Xn3b = pIn[5 ]; d1a += a1 * acc1a; Xn4a = pIn[6 ]; d2a += a2 * acc1a; /* Sample 2. 5 cycles */ Xn4b = pIn[7 ]; acc1b = b0 * Xn1b + d1b; Xn5a = pIn[8 ]; d1b = b1 * Xn1b + d2b; Xn5b = pIn[9 ]; d2b = b2 * Xn1b; Xn6a = pIn[10]; d1b += a1 * acc1b; Xn6b = pIn[11]; d2b += a2 * acc1b; /* Sample 3. 5 cycles */ Xn7a = pIn[12]; acc2a = b0 * Xn2a + d1a; Xn7b = pIn[13]; d1a = b1 * Xn2a + d2a; Xn8a = pIn[14]; d2a = b2 * Xn2a; Xn8b = pIn[15]; d1a += a1 * acc2a; pIn += 16; d2a += a2 * acc2a; /* Sample 4. 5 cycles */ acc2b = b0 * Xn2b + d1b; d1b = b1 * Xn2b + d2b; d2b = b2 * Xn2b; d1b += a1 * acc2b; d2b += a2 * acc2b; /* Sample 5. 5 cycles */ acc3a = b0 * Xn3a + d1a; d1a = b1 * Xn3a + d2a; d2a = b2 * Xn3a; d1a += a1 * acc3a; d2a += a2 * acc3a; /* Sample 6. 5 cycles */ acc3b = b0 * Xn3b + d1b; d1b = b1 * Xn3b + d2b; d2b = b2 * Xn3b; d1b += a1 * acc3b; d2b += a2 * acc3b; /* Sample 7. 5 cycles */ acc4a = b0 * Xn4a + d1a; d1a = b1 * Xn4a + d2a; d2a = b2 * Xn4a; d1a += a1 * acc4a; d2a += a2 * acc4a; /* Sample 8. 5 cycles */ acc4b = b0 * Xn4b + d1b; d1b = b1 * Xn4b + d2b; d2b = b2 * Xn4b; d1b += a1 * acc4b; d2b += a2 * acc4b; /* Sample 9. 5 cycles */ acc5a = b0 * Xn5a + d1a; d1a = b1 * Xn5a + d2a; d2a = b2 * Xn5a; d1a += a1 * acc5a; d2a += a2 * acc5a; /* Sample 10. 5 cycles */ acc5b = b0 * Xn5b + d1b; d1b = b1 * Xn5b + d2b; d2b = b2 * Xn5b; d1b += a1 * acc5b; d2b += a2 * acc5b; /* Sample 11. 5 cycles */ acc6a = b0 * Xn6a + d1a; d1a = b1 * Xn6a + d2a; d2a = b2 * Xn6a; d1a += a1 * acc6a; d2a += a2 * acc6a; /* Sample 12. 5 cycles */ acc6b = b0 * Xn6b + d1b; d1b = b1 * Xn6b + d2b; d2b = b2 * Xn6b; d1b += a1 * acc6b; d2b += a2 * acc6b; /* Sample 13. 5 cycles */ acc7a = b0 * Xn7a + d1a; d1a = b1 * Xn7a + d2a; pOut[0 ] = acc1a ; d2a = b2 * Xn7a; pOut[1 ] = acc1b ; d1a += a1 * acc7a; pOut[2 ] = acc2a ; d2a += a2 * acc7a; /* Sample 14. 5 cycles */ pOut[3 ] = acc2b ; acc7b = b0 * Xn7b + d1b; pOut[4 ] = acc3a ; d1b = b1 * Xn7b + d2b; pOut[5 ] = acc3b ; d2b = b2 * Xn7b; pOut[6 ] = acc4a ; d1b += a1 * acc7b; pOut[7 ] = acc4b ; d2b += a2 * acc7b; /* Sample 15. 5 cycles */ pOut[8 ] = acc5a ; acc8a = b0 * Xn8a + d1a; pOut[9 ] = acc5b; d1a = b1 * Xn8a + d2a; pOut[10] = acc6a; d2a = b2 * Xn8a; pOut[11] = acc6b; d1a += a1 * acc8a; pOut[12] = acc7a; d2a += a2 * acc8a; /* Sample 16. 5 cycles */ pOut[13] = acc7b; acc8b = b0 * Xn8b + d1b; pOut[14] = acc8a; d1b = b1 * Xn8b + d2b; pOut[15] = acc8b; d2b = b2 * Xn8b; sample--; d1b += a1 * acc8b; pOut += 16; d2b += a2 * acc8b; } sample = blockSize & 0x7u; while(sample > 0u) { /* Read the input */ Xn1a = *pIn++; //Channel a Xn1b = *pIn++; //Channel b /* y[n] = b0 * x[n] + d1 */ acc1a = (b0 * Xn1a) + d1a; acc1b = (b0 * Xn1b) + d1b; /* Store the result in the accumulator in the destination buffer. */ *pOut++ = acc1a; *pOut++ = acc1b; /* Every time after the output is computed state should be updated. */ /* d1 = b1 * x[n] + a1 * y[n] + d2 */ d1a = ((b1 * Xn1a) + (a1 * acc1a)) + d2a; d1b = ((b1 * Xn1b) + (a1 * acc1b)) + d2b; /* d2 = b2 * x[n] + a2 * y[n] */ d2a = (b2 * Xn1a) + (a2 * acc1a); d2b = (b2 * Xn1b) + (a2 * acc1b); sample--; } /* Store the updated state variables back into the state array */ pState[0] = d1a; pState[1] = d2a; pState[2] = d1b; pState[3] = d2b; /* The current stage input is given as the output to the next stage */ pIn = pDst; /* decrement the loop counter */ stage--; pState += 4u; /*Reset the output working pointer */ pOut = pDst; } while(stage > 0u); #elif defined(ARM_MATH_CM0_FAMILY) /* 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 */ d1a = pState[0]; d2a = pState[1]; d1b = pState[2]; d2b = pState[3]; sample = blockSize; while(sample > 0u) { /* Read the input */ Xn1a = *pIn++; //Channel a Xn1b = *pIn++; //Channel b /* y[n] = b0 * x[n] + d1 */ acc1a = (b0 * Xn1a) + d1a; acc1b = (b0 * Xn1b) + d1b; /* Store the result in the accumulator in the destination buffer. */ *pOut++ = acc1a; *pOut++ = acc1b; /* Every time after the output is computed state should be updated. */ /* d1 = b1 * x[n] + a1 * y[n] + d2 */ d1a = ((b1 * Xn1a) + (a1 * acc1a)) + d2a; d1b = ((b1 * Xn1b) + (a1 * acc1b)) + d2b; /* d2 = b2 * x[n] + a2 * y[n] */ d2a = (b2 * Xn1a) + (a2 * acc1a); d2b = (b2 * Xn1b) + (a2 * acc1b); /* decrement the loop counter */ sample--; } /* Store the updated state variables back into the state array */ *pState++ = d1a; *pState++ = d2a; *pState++ = d1b; *pState++ = d2b; /* The current stage input is given as the output to the next stage */ pIn = pDst; /*Reset the output working pointer */ pOut = pDst; /* decrement the loop counter */ stage--; } while(stage > 0u); #else float32_t Xn2a, Xn3a, Xn4a; /* Input State variables */ float32_t Xn2b, Xn3b, Xn4b; /* Input State variables */ float32_t acc2a, acc3a, acc4a; /* accumulator */ float32_t acc2b, acc3b, acc4b; /* accumulator */ float32_t p0a, p1a, p2a, p3a, p4a, A1a; float32_t p0b, p1b, p2b, p3b, p4b, A1b; /* 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 */ d1a = pState[0]; d2a = pState[1]; d1b = pState[2]; d2b = pState[3]; /* Apply loop unrolling and compute 4 output values simultaneously. */ 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) { /* y[n] = b0 * x[n] + d1 */ /* d1 = b1 * x[n] + a1 * y[n] + d2 */ /* d2 = b2 * x[n] + a2 * y[n] */ /* Read the four inputs */ Xn1a = pIn[0]; Xn1b = pIn[1]; Xn2a = pIn[2]; Xn2b = pIn[3]; Xn3a = pIn[4]; Xn3b = pIn[5]; Xn4a = pIn[6]; Xn4b = pIn[7]; pIn += 8; p0a = b0 * Xn1a; p0b = b0 * Xn1b; p1a = b1 * Xn1a; p1b = b1 * Xn1b; acc1a = p0a + d1a; acc1b = p0b + d1b; p0a = b0 * Xn2a; p0b = b0 * Xn2b; p3a = a1 * acc1a; p3b = a1 * acc1b; p2a = b2 * Xn1a; p2b = b2 * Xn1b; A1a = p1a + p3a; A1b = p1b + p3b; p4a = a2 * acc1a; p4b = a2 * acc1b; d1a = A1a + d2a; d1b = A1b + d2b; d2a = p2a + p4a; d2b = p2b + p4b; p1a = b1 * Xn2a; p1b = b1 * Xn2b; acc2a = p0a + d1a; acc2b = p0b + d1b; p0a = b0 * Xn3a; p0b = b0 * Xn3b; p3a = a1 * acc2a; p3b = a1 * acc2b; p2a = b2 * Xn2a; p2b = b2 * Xn2b; A1a = p1a + p3a; A1b = p1b + p3b; p4a = a2 * acc2a; p4b = a2 * acc2b; d1a = A1a + d2a; d1b = A1b + d2b; d2a = p2a + p4a; d2b = p2b + p4b; p1a = b1 * Xn3a; p1b = b1 * Xn3b; acc3a = p0a + d1a; acc3b = p0b + d1b; p0a = b0 * Xn4a; p0b = b0 * Xn4b; p3a = a1 * acc3a; p3b = a1 * acc3b; p2a = b2 * Xn3a; p2b = b2 * Xn3b; A1a = p1a + p3a; A1b = p1b + p3b; p4a = a2 * acc3a; p4b = a2 * acc3b; d1a = A1a + d2a; d1b = A1b + d2b; d2a = p2a + p4a; d2b = p2b + p4b; acc4a = p0a + d1a; acc4b = p0b + d1b; p1a = b1 * Xn4a; p1b = b1 * Xn4b; p3a = a1 * acc4a; p3b = a1 * acc4b; p2a = b2 * Xn4a; p2b = b2 * Xn4b; A1a = p1a + p3a; A1b = p1b + p3b; p4a = a2 * acc4a; p4b = a2 * acc4b; d1a = A1a + d2a; d1b = A1b + d2b; d2a = p2a + p4a; d2b = p2b + p4b; pOut[0] = acc1a; pOut[1] = acc1b; pOut[2] = acc2a; pOut[3] = acc2b; pOut[4] = acc3a; pOut[5] = acc3b; pOut[6] = acc4a; pOut[7] = acc4b; pOut += 8; sample--; } sample = blockSize & 0x3u; while(sample > 0u) { Xn1a = *pIn++; Xn1b = *pIn++; p0a = b0 * Xn1a; p0b = b0 * Xn1b; p1a = b1 * Xn1a; p1b = b1 * Xn1b; acc1a = p0a + d1a; acc1b = p0b + d1b; p3a = a1 * acc1a; p3b = a1 * acc1b; p2a = b2 * Xn1a; p2b = b2 * Xn1b; A1a = p1a + p3a; A1b = p1b + p3b; p4a = a2 * acc1a; p4b = a2 * acc1b; d1a = A1a + d2a; d1b = A1b + d2b; d2a = p2a + p4a; d2b = p2b + p4b; *pOut++ = acc1a; *pOut++ = acc1b; sample--; } /* Store the updated state variables back into the state array */ *pState++ = d1a; *pState++ = d2a; *pState++ = d1b; *pState++ = d2b; /* The current stage input is given as the output to the next stage */ pIn = pDst; /*Reset the output working pointer */ pOut = pDst; /* decrement the loop counter */ stage--; } while(stage > 0u); #endif } LOW_OPTIMIZATION_EXIT /** * @} end of BiquadCascadeDF2T group */