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-/* ----------------------------------------------------------------------
- * Project: CMSIS DSP Library
- * Title: arm_biquad_cascade_df1_f32.c
- * Description: Processing function for the floating-point Biquad cascade DirectFormI(DF1) filter
- *
- * $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 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 <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] + 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>.
- * The state variables are arranged in the <code>pState</code> 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.
- * 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
- * <pre>
- * 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};
- * </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.
- *
- * \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
- * <b>Scaling of coefficients: </b>
- * Filter coefficients are represented as fractional values and
- * coefficients are restricted to lie in the range <code>[-1 +1)</code>.
- * The fixed-point functions have an additional scaling parameter <code>postShift</code>
- * which allow 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 pCoeffs array to:
- * <pre>
- * {0.75, -0.4, 0.6, 0.8, -0.45}
- * </pre>
- * and set <code>postShift=1</code>
- *
- * \par
- * <b>Filter gain: </b>
- * 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
- * <b>Overflow and saturation: </b>
- * 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 */
-
-
-#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 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 /* #if defined (ARM_MATH_DSP) */
-
-}
-
-
- /**
- * @} end of BiquadCascadeDF1 group
- */