123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359 |
- /* ----------------------------------------------------------------------
- * Copyright (C) 2010-2013 ARM Limited. All rights reserved.
- *
- * $Date: 17. January 2013
- *
- * 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 */
-
- #ifndef ARM_MATH_CM0_FAMILY_FAMILY
-
- 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);
-
- #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 */
- 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);
-
- #endif /* #ifndef ARM_MATH_CM0_FAMILY */
-
- }
- LOW_OPTIMIZATION_EXIT
-
- /**
- * @} end of BiquadCascadeDF2T group
- */
|