arm_biquad_cascade_df2T_f32.c
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| text/x-c
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CLexer
jeandet@pc-de-jeandet3.lab-lpp.local
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r16 | /* ---------------------------------------------------------------------- | ||
| * Copyright (C) 2010 ARM Limited. All rights reserved. | ||||
| * | ||||
| * $Date: 29. November 2010 | ||||
| * $Revision: V1.0.3 | ||||
| * | ||||
| * 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 | ||||
| * | ||||
| * Version 1.0.3 2010/11/29 | ||||
| * Re-organized the CMSIS folders and updated documentation. | ||||
| * | ||||
| * Version 1.0.2 2010/11/11 | ||||
| * Documentation updated. | ||||
| * | ||||
| * Version 1.0.1 2010/10/05 | ||||
| * Production release and review comments incorporated. | ||||
| * | ||||
| * Version 1.0.0 2010/09/20 | ||||
| * Production release and review comments incorporated | ||||
| * | ||||
| * Version 0.0.7 2010/06/10 | ||||
| * Misra-C changes done | ||||
| * -------------------------------------------------------------------- */ | ||||
| #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. | ||||
| * | ||||
| * \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. | ||||
| */ | ||||
| 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 acc0; /* Simulates the accumulator */ | ||||
| float32_t b0, b1, b2, a1, a2; /* Filter coefficients */ | ||||
| float32_t Xn; /* temporary input */ | ||||
| float32_t d1, d2; /* state variables */ | ||||
| uint32_t sample, stage = S->numStages; /* loop counters */ | ||||
| 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) | ||||
| { | ||||
| /* Read the first input */ | ||||
| Xn = *pIn++; | ||||
| /* y[n] = b0 * x[n] + d1 */ | ||||
| acc0 = (b0 * Xn) + d1; | ||||
| /* Store the result in the accumulator in the destination buffer. */ | ||||
| *pOut++ = acc0; | ||||
| /* Every time after the output is computed state should be updated. */ | ||||
| /* d1 = b1 * x[n] + a1 * y[n] + d2 */ | ||||
| d1 = ((b1 * Xn) + (a1 * acc0)) + d2; | ||||
| /* d2 = b2 * x[n] + a2 * y[n] */ | ||||
| d2 = (b2 * Xn) + (a2 * acc0); | ||||
| /* Read the second input */ | ||||
| Xn = *pIn++; | ||||
| /* y[n] = b0 * x[n] + d1 */ | ||||
| acc0 = (b0 * Xn) + d1; | ||||
| /* Store the result in the accumulator in the destination buffer. */ | ||||
| *pOut++ = acc0; | ||||
| /* Every time after the output is computed state should be updated. */ | ||||
| /* d1 = b1 * x[n] + a1 * y[n] + d2 */ | ||||
| d1 = ((b1 * Xn) + (a1 * acc0)) + d2; | ||||
| /* d2 = b2 * x[n] + a2 * y[n] */ | ||||
| d2 = (b2 * Xn) + (a2 * acc0); | ||||
| /* Read the third input */ | ||||
| Xn = *pIn++; | ||||
| /* y[n] = b0 * x[n] + d1 */ | ||||
| acc0 = (b0 * Xn) + d1; | ||||
| /* Store the result in the accumulator in the destination buffer. */ | ||||
| *pOut++ = acc0; | ||||
| /* Every time after the output is computed state should be updated. */ | ||||
| /* d1 = b1 * x[n] + a1 * y[n] + d2 */ | ||||
| d1 = ((b1 * Xn) + (a1 * acc0)) + d2; | ||||
| /* d2 = b2 * x[n] + a2 * y[n] */ | ||||
| d2 = (b2 * Xn) + (a2 * acc0); | ||||
| /* Read the fourth input */ | ||||
| Xn = *pIn++; | ||||
| /* y[n] = b0 * x[n] + d1 */ | ||||
| acc0 = (b0 * Xn) + d1; | ||||
| /* Store the result in the accumulator in the destination buffer. */ | ||||
| *pOut++ = acc0; | ||||
| /* Every time after the output is computed state should be updated. */ | ||||
| /* d1 = b1 * x[n] + a1 * y[n] + d2 */ | ||||
| d1 = (b1 * Xn) + (a1 * acc0) + d2; | ||||
| /* d2 = b2 * x[n] + a2 * y[n] */ | ||||
| d2 = (b2 * Xn) + (a2 * acc0); | ||||
| /* 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++; | ||||
| /* y[n] = b0 * x[n] + d1 */ | ||||
| acc0 = (b0 * Xn) + d1; | ||||
| /* Store the result in the accumulator in the destination buffer. */ | ||||
| *pOut++ = acc0; | ||||
| /* Every time after the output is computed state should be updated. */ | ||||
| /* d1 = b1 * x[n] + a1 * y[n] + d2 */ | ||||
| d1 = ((b1 * Xn) + (a1 * acc0)) + d2; | ||||
| /* d2 = b2 * x[n] + a2 * y[n] */ | ||||
| d2 = (b2 * Xn) + (a2 * acc0); | ||||
| /* 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); | ||||
| } | ||||
| /** | ||||
| * @} end of BiquadCascadeDF2T group | ||||
| */ | ||||