/* ---------------------------------------------------------------------- * Copyright (C) 2010 ARM Limited. All rights reserved. * * $Date: 15. July 2011 * $Revision: V1.0.10 * * 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 * * Version 1.0.10 2011/7/15 * Big Endian support added and Merged M0 and M3/M4 Source code. * * 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 blockSize samples through the filter. * pSrc points to the array of input data and * pDst points to the array of output data. * Both arrays contain blockSize values. * * \par Algorithm * Each Biquad stage implements a second order filter using the difference equation: * 
   
 *    y[n] = b0 * x[n] + d1   
 *    d1 = b1 * x[n] + a1 * y[n] + d2   
 *    d2 = b2 * x[n] + a2 * y[n]   
 *
* 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 b0, b1, and b2 multiply the input signal x[n] and are referred to as the feedforward coefficients. * Coefficients a1 and a2 multiply the output signal y[n] 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: * 
   
 *    y[n] = b0 * x[n] + d1;   
 *    d1 = b1 * x[n] - a1 * y[n] + d2;   
 *    d2 = b2 * x[n] - a2 * y[n];   
 *
* In this case the feedback coefficients a1 and a2 must be negated when used with the CMSIS DSP Library. * * \par * Higher order filters are realized as a cascade of second order sections. * numStages refers to the number of second order stages used. * For example, an 8th order filter would be realized with numStages=4 second order stages. * A 9th order filter would be realized with numStages=5 second order stages with the * coefficients for one of the stages configured as a first order filter (b2=0 and a2=0). * * \par * pState points to the state variable array. * Each Biquad stage has 2 state variables d1 and d2. * The state variables are arranged in the pState array as: * 
   
 *     {d11, d12, d21, d22, ...}   
 *
* where d1x refers to the state variables for the first Biquad and * d2x refers to the state variables for the second Biquad. * The state array has a total length of 2*numStages 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 d1 and d2. * 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 * 
   
 *     arm_biquad_cascade_df2T_instance_f32 S1 = {numStages, pState, pCoeffs};   
 *
* where numStages is the number of Biquad stages in the filter; pState is the address of the state buffer. * pCoeffs 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 */ #ifndef ARM_MATH_CM0 /* 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) { /* 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); #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 */ 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); #endif /* #ifndef ARM_MATH_CM0 */ } /** * @} end of BiquadCascadeDF2T group */