| /* ---------------------------------------------------------------------- |
| * Project: CMSIS DSP Library |
| * Title: arm_biquad_cascade_df1_f32.c |
| * Description: Processing function for the floating-point Biquad cascade DirectFormI(DF1) 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 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 available. |
| |
| 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 Function |
| 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 Scaling of coefficients |
| 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 Filter gain |
| 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 Overflow and saturation |
| For Q15 and Q31 versions, it is described separately as part of the function specific documentation below. |
| */ |
| |
| /** |
| @addtogroup BiquadCascadeDF1 |
| @{ |
| */ |
| |
| /** |
| @brief Processing function for the floating-point Biquad cascade filter. |
| @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 |
| @return none |
| */ |
| |
| #if defined(ARM_MATH_NEON) |
| void arm_biquad_cascade_df1_f32( |
| const arm_biquad_casd_df1_inst_f32 * S, |
| const float32_t * pSrc, |
| float32_t * pDst, |
| uint32_t blockSize) |
| { |
| |
| const float32_t *pIn = pSrc; /* source pointer */ |
| float32_t *pOut = pDst; /* destination pointer */ |
| float32_t *pState = S->pState; /* pState pointer */ |
| const float32_t *pCoeffs = S->pCoeffs; /* coefficient pointer */ |
| float32_t acc; /* Simulates the accumulator */ |
| |
| uint32_t sample, stage = S->numStages; /* loop counters */ |
| |
| float32x4_t Xn; |
| float32x2_t Yn; |
| float32x2_t a; |
| float32x4_t b; |
| |
| float32x4_t x,tmp; |
| float32x2_t t; |
| float32x2x2_t y; |
| |
| float32_t Xns; |
| |
| while (stage > 0U) |
| { |
| /* Reading the coefficients */ |
| Xn = vld1q_f32(pState); |
| Yn = vld1_f32(pState + 2); |
| |
| b = vld1q_f32(pCoeffs); |
| b = vrev64q_f32(b); |
| b = vcombine_f32(vget_high_f32(b), vget_low_f32(b)); |
| |
| a = vld1_f32(pCoeffs + 3); |
| a = vrev64_f32(a); |
| b[0] = 0.0; |
| pCoeffs += 5; |
| |
| /* Reading the pState values */ |
| |
| /* 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] |
| */ |
| |
| /* 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. */ |
| sample = blockSize >> 2U; |
| |
| while (sample > 0U) |
| { |
| /* Read the first 4 inputs */ |
| x = vld1q_f32(pIn); |
| |
| pIn += 4; |
| |
| tmp = vextq_f32(Xn, x, 1); |
| t = vmul_f32(vget_high_f32(b), vget_high_f32(tmp)); |
| t = vmla_f32(t, vget_low_f32(b), vget_low_f32(tmp)); |
| t = vmla_f32(t, a, Yn); |
| t = vpadd_f32(t, t); |
| Yn = vext_f32(Yn, t, 1); |
| |
| tmp = vextq_f32(Xn, x, 2); |
| t = vmul_f32(vget_high_f32(b), vget_high_f32(tmp)); |
| t = vmla_f32(t, vget_low_f32(b), vget_low_f32(tmp)); |
| t = vmla_f32(t, a, Yn); |
| t = vpadd_f32(t, t); |
| Yn = vext_f32(Yn, t, 1); |
| |
| y.val[0] = Yn; |
| |
| tmp = vextq_f32(Xn, x, 3); |
| t = vmul_f32(vget_high_f32(b), vget_high_f32(tmp)); |
| t = vmla_f32(t, vget_low_f32(b), vget_low_f32(tmp)); |
| t = vmla_f32(t, a, Yn); |
| t = vpadd_f32(t, t); |
| Yn = vext_f32(Yn, t, 1); |
| |
| Xn = x; |
| t = vmul_f32(vget_high_f32(b), vget_high_f32(Xn)); |
| t = vmla_f32(t, vget_low_f32(b), vget_low_f32(Xn)); |
| t = vmla_f32(t, a, Yn); |
| t = vpadd_f32(t, t); |
| Yn = vext_f32(Yn, t, 1); |
| |
| y.val[1] = Yn; |
| |
| tmp = vcombine_f32(y.val[0], y.val[1]); |
| |
| /* Store the 4 outputs and increment the pointer */ |
| vst1q_f32(pOut, tmp); |
| pOut += 4; |
| |
| /* Decrement the loop counter */ |
| sample--; |
| } |
| |
| /* If the block size 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 */ |
| Xns = *pIn++; |
| |
| /* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ |
| acc = (b[1] * Xn[2]) + (b[2] * Xn[3]) + (b[3] * Xns) + (a[0] * Yn[0]) + (a[1] * Yn[1]); |
| |
| /* 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 */ |
| Xn[2] = Xn[3]; |
| Xn[3] = Xns; |
| Yn[0] = Yn[1]; |
| Yn[1] = acc; |
| |
| /* Decrement the loop counter */ |
| sample--; |
| |
| } |
| |
| vst1q_f32(pState,vcombine_f32(vrev64_f32(vget_high_f32(Xn)),vrev64_f32(Yn))); |
| pState += 4; |
| /* Store the updated state variables back into the pState array */ |
| |
| /* 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--; |
| } |
| } |
| |
| #else |
| void arm_biquad_cascade_df1_f32( |
| const arm_biquad_casd_df1_inst_f32 * S, |
| const float32_t * pSrc, |
| float32_t * pDst, |
| uint32_t blockSize) |
| { |
| const float32_t *pIn = pSrc; /* Source pointer */ |
| float32_t *pOut = pDst; /* Destination pointer */ |
| float32_t *pState = S->pState; /* pState pointer */ |
| const float32_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */ |
| float32_t acc; /* 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 */ |
| |
| 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]; |
| |
| #if defined (ARM_MATH_LOOPUNROLL) |
| |
| /* Apply loop unrolling and compute 4 output values simultaneously. */ |
| /* 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] |
| */ |
| |
| /* Loop unrolling: Compute 4 outputs at a time */ |
| sample = blockSize >> 2U; |
| |
| 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 output in 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 output in 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 output in 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 output in 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 loop counter */ |
| sample--; |
| } |
| |
| /* Loop unrolling: Compute remaining outputs */ |
| sample = blockSize & 0x3U; |
| |
| #else |
| |
| /* Initialize blkCnt with number of samples */ |
| sample = blockSize; |
| |
| #endif /* #if defined (ARM_MATH_LOOPUNROLL) */ |
| |
| 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 output in 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 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 output pointer */ |
| pOut = pDst; |
| |
| /* decrement loop counter */ |
| stage--; |
| |
| } while (stage > 0U); |
| |
| } |
| |
| #endif /* #if defined(ARM_MATH_NEON) */ |
| /** |
| @} end of BiquadCascadeDF1 group |
| */ |