| /* ---------------------------------------------------------------------- |
| * Project: CMSIS DSP Library |
| * Title: arm_biquad_cascade_df1_32x64_q31.c |
| * Description: High precision Q31 Biquad cascade filter processing function |
| * |
| * $Date: 27. January 2017 |
| * $Revision: V.1.5.1 |
| * |
| * Target Processor: Cortex-M cores |
| * -------------------------------------------------------------------- */ |
| /* |
| * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved. |
| * |
| * SPDX-License-Identifier: Apache-2.0 |
| * |
| * Licensed under the Apache License, Version 2.0 (the License); you may |
| * not use this file except in compliance with the License. |
| * You may obtain a copy of the License at |
| * |
| * www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an AS IS BASIS, WITHOUT |
| * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| |
| #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 */ |
| |
| |
| #if defined (ARM_MATH_DSP) |
| |
| /* 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 /* #if defined (ARM_MATH_DSP) */ |
| } |
| |
| /** |
| * @} end of BiquadCascadeDF1_32x64 group |
| */ |
