+++ /dev/null
-/* ----------------------------------------------------------------------
-* Copyright (C) 2010-2013 ARM Limited. All rights reserved.
-*
-* $Date: 17. January 2013
-* $Revision: V1.4.1
-*
-* 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
- */
projects / qmk_firmware.git / blobdiff