| /* ---------------------------------------------------------------------- |
| * 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_df2T_f32.c |
| * |
| * Description: Processing function for the floating-point transposed |
| * direct form II Biquad cascade 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 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 <code>blockSize</code> samples through the filter. |
| * <code>pSrc</code> points to the array of input data and |
| * <code>pDst</code> points to the array of output data. |
| * Both arrays contain <code>blockSize</code> values. |
| * |
| * \par Algorithm |
| * Each Biquad stage implements a second order filter using the difference equation: |
| * <pre> |
| * y[n] = b0 * x[n] + d1 |
| * d1 = b1 * x[n] + a1 * y[n] + d2 |
| * d2 = b2 * x[n] + a2 * y[n] |
| * </pre> |
| * 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 <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 flip the sign of the feedback coefficients: |
| * <pre> |
| * y[n] = b0 * x[n] + d1; |
| * d1 = b1 * x[n] - a1 * y[n] + d2; |
| * d2 = b2 * x[n] - a2 * y[n]; |
| * </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. |
| * 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 |
| * <code>pState</code> points to the state variable array. |
| * Each Biquad stage has 2 state variables <code>d1</code> and <code>d2</code>. |
| * The state variables are arranged in the <code>pState</code> array as: |
| * <pre> |
| * {d11, d12, d21, d22, ...} |
| * </pre> |
| * where <code>d1x</code> refers to the state variables for the first Biquad and |
| * <code>d2x</code> refers to the state variables for the second Biquad. |
| * The state array has a total length of <code>2*numStages</code> 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 <code>d1</code> and <code>d2</code>. |
| * 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 |
| * <pre> |
| * arm_biquad_cascade_df2T_instance_f32 S1 = {numStages, pState, pCoeffs}; |
| * </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; |
| * |
| */ |
| |
| /** |
| * @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_df2T_f32( |
| const arm_biquad_cascade_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 acc1; /* accumulator */ |
| float32_t b0, b1, b2, a1, a2; /* Filter coefficients */ |
| float32_t Xn1; /* temporary input */ |
| float32_t d1, d2; /* state variables */ |
| uint32_t sample, stage = S->numStages; /* loop counters */ |
| |
| #if defined(ARM_MATH_CM7) |
| |
| float32_t Xn2, Xn3, Xn4, Xn5, Xn6, Xn7, Xn8; /* Input State variables */ |
| float32_t Xn9, Xn10, Xn11, Xn12, Xn13, Xn14, Xn15, Xn16; |
| float32_t acc2, acc3, acc4, acc5, acc6, acc7; /* Simulates the accumulator */ |
| float32_t acc8, acc9, acc10, acc11, acc12, acc13, acc14, acc15, acc16; |
| |
| do |
| { |
| /* Reading the coefficients */ |
| b0 = pCoeffs[0]; |
| b1 = pCoeffs[1]; |
| b2 = pCoeffs[2]; |
| a1 = pCoeffs[3]; |
| /* Apply loop unrolling and compute 16 output values simultaneously. */ |
| sample = blockSize >> 4u; |
| a2 = pCoeffs[4]; |
| |
| /*Reading the state values */ |
| d1 = pState[0]; |
| d2 = pState[1]; |
| |
| pCoeffs += 5u; |
| |
| |
| /* First part of the processing with loop unrolling. Compute 16 outputs at a time. |
| ** a second loop below computes the remaining 1 to 15 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 */ |
| Xn1 = pIn[0 ]; |
| Xn2 = pIn[1 ]; |
| |
| /* Sample 1. 5 cycles */ |
| Xn3 = pIn[2 ]; |
| acc1 = b0 * Xn1 + d1; |
| |
| Xn4 = pIn[3 ]; |
| d1 = b1 * Xn1 + d2; |
| |
| Xn5 = pIn[4 ]; |
| d2 = b2 * Xn1; |
| |
| Xn6 = pIn[5 ]; |
| d1 += a1 * acc1; |
| |
| Xn7 = pIn[6 ]; |
| d2 += a2 * acc1; |
| |
| /* Sample 2. 5 cycles */ |
| Xn8 = pIn[7 ]; |
| acc2 = b0 * Xn2 + d1; |
| |
| Xn9 = pIn[8 ]; |
| d1 = b1 * Xn2 + d2; |
| |
| Xn10 = pIn[9 ]; |
| d2 = b2 * Xn2; |
| |
| Xn11 = pIn[10]; |
| d1 += a1 * acc2; |
| |
| Xn12 = pIn[11]; |
| d2 += a2 * acc2; |
| |
| /* Sample 3. 5 cycles */ |
| Xn13 = pIn[12]; |
| acc3 = b0 * Xn3 + d1; |
| |
| Xn14 = pIn[13]; |
| d1 = b1 * Xn3 + d2; |
| |
| Xn15 = pIn[14]; |
| d2 = b2 * Xn3; |
| |
| Xn16 = pIn[15]; |
| d1 += a1 * acc3; |
| |
| pIn += 16; |
| d2 += a2 * acc3; |
| |
| /* Sample 4. 5 cycles */ |
| acc4 = b0 * Xn4 + d1; |
| d1 = b1 * Xn4 + d2; |
| d2 = b2 * Xn4; |
| d1 += a1 * acc4; |
| d2 += a2 * acc4; |
| |
| /* Sample 5. 5 cycles */ |
| acc5 = b0 * Xn5 + d1; |
| d1 = b1 * Xn5 + d2; |
| d2 = b2 * Xn5; |
| d1 += a1 * acc5; |
| d2 += a2 * acc5; |
| |
| /* Sample 6. 5 cycles */ |
| acc6 = b0 * Xn6 + d1; |
| d1 = b1 * Xn6 + d2; |
| d2 = b2 * Xn6; |
| d1 += a1 * acc6; |
| d2 += a2 * acc6; |
| |
| /* Sample 7. 5 cycles */ |
| acc7 = b0 * Xn7 + d1; |
| d1 = b1 * Xn7 + d2; |
| d2 = b2 * Xn7; |
| d1 += a1 * acc7; |
| d2 += a2 * acc7; |
| |
| /* Sample 8. 5 cycles */ |
| acc8 = b0 * Xn8 + d1; |
| d1 = b1 * Xn8 + d2; |
| d2 = b2 * Xn8; |
| d1 += a1 * acc8; |
| d2 += a2 * acc8; |
| |
| /* Sample 9. 5 cycles */ |
| acc9 = b0 * Xn9 + d1; |
| d1 = b1 * Xn9 + d2; |
| d2 = b2 * Xn9; |
| d1 += a1 * acc9; |
| d2 += a2 * acc9; |
| |
| /* Sample 10. 5 cycles */ |
| acc10 = b0 * Xn10 + d1; |
| d1 = b1 * Xn10 + d2; |
| d2 = b2 * Xn10; |
| d1 += a1 * acc10; |
| d2 += a2 * acc10; |
| |
| /* Sample 11. 5 cycles */ |
| acc11 = b0 * Xn11 + d1; |
| d1 = b1 * Xn11 + d2; |
| d2 = b2 * Xn11; |
| d1 += a1 * acc11; |
| d2 += a2 * acc11; |
| |
| /* Sample 12. 5 cycles */ |
| acc12 = b0 * Xn12 + d1; |
| d1 = b1 * Xn12 + d2; |
| d2 = b2 * Xn12; |
| d1 += a1 * acc12; |
| d2 += a2 * acc12; |
| |
| /* Sample 13. 5 cycles */ |
| acc13 = b0 * Xn13 + d1; |
| d1 = b1 * Xn13 + d2; |
| d2 = b2 * Xn13; |
| |
| pOut[0 ] = acc1 ; |
| d1 += a1 * acc13; |
| |
| pOut[1 ] = acc2 ; |
| d2 += a2 * acc13; |
| |
| /* Sample 14. 5 cycles */ |
| pOut[2 ] = acc3 ; |
| acc14 = b0 * Xn14 + d1; |
| |
| pOut[3 ] = acc4 ; |
| d1 = b1 * Xn14 + d2; |
| |
| pOut[4 ] = acc5 ; |
| d2 = b2 * Xn14; |
| |
| pOut[5 ] = acc6 ; |
| d1 += a1 * acc14; |
| |
| pOut[6 ] = acc7 ; |
| d2 += a2 * acc14; |
| |
| /* Sample 15. 5 cycles */ |
| pOut[7 ] = acc8 ; |
| pOut[8 ] = acc9 ; |
| acc15 = b0 * Xn15 + d1; |
| |
| pOut[9 ] = acc10; |
| d1 = b1 * Xn15 + d2; |
| |
| pOut[10] = acc11; |
| d2 = b2 * Xn15; |
| |
| pOut[11] = acc12; |
| d1 += a1 * acc15; |
| |
| pOut[12] = acc13; |
| d2 += a2 * acc15; |
| |
| /* Sample 16. 5 cycles */ |
| pOut[13] = acc14; |
| acc16 = b0 * Xn16 + d1; |
| |
| pOut[14] = acc15; |
| d1 = b1 * Xn16 + d2; |
| |
| pOut[15] = acc16; |
| d2 = b2 * Xn16; |
| |
| sample--; |
| d1 += a1 * acc16; |
| |
| pOut += 16; |
| d2 += a2 * acc16; |
| } |
| |
| sample = blockSize & 0xFu; |
| while(sample > 0u) { |
| Xn1 = *pIn; |
| acc1 = b0 * Xn1 + d1; |
| |
| pIn++; |
| d1 = b1 * Xn1 + d2; |
| |
| *pOut = acc1; |
| d2 = b2 * Xn1; |
| |
| pOut++; |
| d1 += a1 * acc1; |
| |
| sample--; |
| d2 += a2 * acc1; |
| } |
| |
| /* Store the updated state variables back into the state array */ |
| pState[0] = d1; |
| /* The current stage input is given as the output to the next stage */ |
| pIn = pDst; |
| |
| pState[1] = d2; |
| /* decrement the loop counter */ |
| stage--; |
| |
| pState += 2u; |
| |
| /*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 */ |
| d1 = pState[0]; |
| d2 = pState[1]; |
| |
| |
| sample = blockSize; |
| |
| while(sample > 0u) |
| { |
| /* Read the input */ |
| Xn1 = *pIn++; |
| |
| /* y[n] = b0 * x[n] + d1 */ |
| acc1 = (b0 * Xn1) + d1; |
| |
| /* Store the result in the accumulator in the destination buffer. */ |
| *pOut++ = acc1; |
| |
| /* Every time after the output is computed state should be updated. */ |
| /* d1 = b1 * x[n] + a1 * y[n] + d2 */ |
| d1 = ((b1 * Xn1) + (a1 * acc1)) + d2; |
| |
| /* d2 = b2 * x[n] + a2 * y[n] */ |
| d2 = (b2 * Xn1) + (a2 * acc1); |
| |
| /* decrement the loop counter */ |
| sample--; |
| } |
| |
| /* Store the updated state variables back into the state array */ |
| *pState++ = d1; |
| *pState++ = d2; |
| |
| /* 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 Xn2, Xn3, Xn4; /* Input State variables */ |
| float32_t acc2, acc3, acc4; /* accumulator */ |
| |
| |
| float32_t p0, p1, p2, p3, p4, A1; |
| |
| /* 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 */ |
| d1 = pState[0]; |
| d2 = pState[1]; |
| |
| /* 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 */ |
| Xn1 = pIn[0]; |
| Xn2 = pIn[1]; |
| Xn3 = pIn[2]; |
| Xn4 = pIn[3]; |
| pIn += 4; |
| |
| p0 = b0 * Xn1; |
| p1 = b1 * Xn1; |
| acc1 = p0 + d1; |
| p0 = b0 * Xn2; |
| p3 = a1 * acc1; |
| p2 = b2 * Xn1; |
| A1 = p1 + p3; |
| p4 = a2 * acc1; |
| d1 = A1 + d2; |
| d2 = p2 + p4; |
| |
| p1 = b1 * Xn2; |
| acc2 = p0 + d1; |
| p0 = b0 * Xn3; |
| p3 = a1 * acc2; |
| p2 = b2 * Xn2; |
| A1 = p1 + p3; |
| p4 = a2 * acc2; |
| d1 = A1 + d2; |
| d2 = p2 + p4; |
| |
| p1 = b1 * Xn3; |
| acc3 = p0 + d1; |
| p0 = b0 * Xn4; |
| p3 = a1 * acc3; |
| p2 = b2 * Xn3; |
| A1 = p1 + p3; |
| p4 = a2 * acc3; |
| d1 = A1 + d2; |
| d2 = p2 + p4; |
| |
| acc4 = p0 + d1; |
| p1 = b1 * Xn4; |
| p3 = a1 * acc4; |
| p2 = b2 * Xn4; |
| A1 = p1 + p3; |
| p4 = a2 * acc4; |
| d1 = A1 + d2; |
| d2 = p2 + p4; |
| |
| pOut[0] = acc1; |
| pOut[1] = acc2; |
| pOut[2] = acc3; |
| pOut[3] = acc4; |
| pOut += 4; |
| |
| sample--; |
| } |
| |
| sample = blockSize & 0x3u; |
| while(sample > 0u) { |
| Xn1 = *pIn++; |
| |
| p0 = b0 * Xn1; |
| p1 = b1 * Xn1; |
| acc1 = p0 + d1; |
| p3 = a1 * acc1; |
| p2 = b2 * Xn1; |
| A1 = p1 + p3; |
| p4 = a2 * acc1; |
| d1 = A1 + d2; |
| d2 = p2 + p4; |
| |
| *pOut++ = acc1; |
| |
| sample--; |
| } |
| |
| /* Store the updated state variables back into the state array */ |
| *pState++ = d1; |
| *pState++ = d2; |
| |
| /* 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 |
| */ |