| /* ---------------------------------------------------------------------- |
| * Project: CMSIS DSP Library |
| * Title: arm_biquad_cascade_df2T_f64.c |
| * Description: Processing function for floating-point transposed direct form II Biquad cascade filter |
| * |
| * $Date: 18. March 2019 |
| * $Revision: V1.6.0 |
| * |
| * Target Processor: Cortex-M cores |
| * -------------------------------------------------------------------- */ |
| /* |
| * Copyright (C) 2010-2019 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 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_f64 S1 = {numStages, pState, pCoeffs}; |
| 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_f64( |
| const arm_biquad_cascade_df2T_instance_f64 * S, |
| float64_t * pSrc, |
| float64_t * pDst, |
| uint32_t blockSize) |
| { |
| |
| float64_t *pIn = pSrc; /* Source pointer */ |
| float64_t *pOut = pDst; /* Destination pointer */ |
| float64_t *pState = S->pState; /* State pointer */ |
| float64_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */ |
| float64_t acc1; /* Accumulator */ |
| float64_t b0, b1, b2, a1, a2; /* Filter coefficients */ |
| float64_t Xn1; /* Temporary input */ |
| float64_t d1, d2; /* State variables */ |
| uint32_t sample, stage = S->numStages; /* Loop counters */ |
| |
| |
| do |
| { |
| /* Reading the coefficients */ |
| b0 = pCoeffs[0]; |
| b1 = pCoeffs[1]; |
| b2 = pCoeffs[2]; |
| a1 = pCoeffs[3]; |
| a2 = pCoeffs[4]; |
| |
| /* Reading the state values */ |
| d1 = pState[0]; |
| d2 = pState[1]; |
| |
| pCoeffs += 5U; |
| |
| #if defined (ARM_MATH_LOOPUNROLL) |
| |
| /* Loop unrolling: Compute 16 outputs at a time */ |
| sample = blockSize >> 4U; |
| |
| while (sample > 0U) { |
| |
| /* y[n] = b0 * x[n] + d1 */ |
| /* d1 = b1 * x[n] + a1 * y[n] + d2 */ |
| /* d2 = b2 * x[n] + a2 * y[n] */ |
| |
| /* 1 */ |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| |
| /* 2 */ |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| /* 3 */ |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| /* 4 */ |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| /* 5 */ |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| /* 6 */ |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| /* 7 */ |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| /* 8 */ |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| /* 9 */ |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| /* 10 */ |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| /* 11 */ |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| /* 12 */ |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| /* 13 */ |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| /* 14 */ |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| /* 15 */ |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| /* 16 */ |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| /* decrement loop counter */ |
| sample--; |
| } |
| |
| /* Loop unrolling: Compute remaining outputs */ |
| sample = blockSize & 0xFU; |
| |
| #else |
| |
| /* Initialize blkCnt with number of samples */ |
| sample = blockSize; |
| |
| #endif /* #if defined (ARM_MATH_LOOPUNROLL) */ |
| |
| while (sample > 0U) { |
| Xn1 = *pIn++; |
| |
| acc1 = b0 * Xn1 + d1; |
| |
| d1 = b1 * Xn1 + d2; |
| d1 += a1 * acc1; |
| |
| d2 = b2 * Xn1; |
| d2 += a2 * acc1; |
| |
| *pOut++ = acc1; |
| |
| /* decrement loop counter */ |
| sample--; |
| } |
| |
| /* Store the updated state variables back into the state array */ |
| pState[0] = d1; |
| pState[1] = d2; |
| |
| pState += 2U; |
| |
| /* The current stage input is given as the output to the next stage */ |
| pIn = pDst; |
| |
| /* Reset the output working pointer */ |
| pOut = pDst; |
| |
| /* decrement loop counter */ |
| stage--; |
| |
| } while (stage > 0U); |
| |
| } |
| LOW_OPTIMIZATION_EXIT |
| |
| /** |
| @} end of BiquadCascadeDF2T group |
| */ |
