arm_biquad_cascade_df2T_f32.c

00001 /* ----------------------------------------------------------------------  
00002 * Copyright (C) 2010 ARM Limited. All rights reserved.  
00003 *  
00004 * $Date:        29. November 2010  
00005 * $Revision:    V1.0.3  
00006 *  
00007 * Project:      CMSIS DSP Library  
00008 * Title:        arm_biquad_cascade_df2T_f32.c  
00009 *  
00010 * Description:  Processing function for the floating-point transposed  
00011 *               direct form II Biquad cascade filter. 
00012 *  
00013 * Target Processor: Cortex-M4/Cortex-M3
00014 *  
00015 * Version 1.0.3 2010/11/29 
00016 *    Re-organized the CMSIS folders and updated documentation.  
00017 *   
00018 * Version 1.0.2 2010/11/11  
00019 *    Documentation updated.   
00020 *  
00021 * Version 1.0.1 2010/10/05   
00022 *    Production release and review comments incorporated.  
00023 *  
00024 * Version 1.0.0 2010/09/20   
00025 *    Production release and review comments incorporated  
00026 *  
00027 * Version 0.0.7  2010/06/10   
00028 *    Misra-C changes done  
00029 * -------------------------------------------------------------------- */ 
00030  
00031 #include "arm_math.h" 
00032  
00033 /**  
00034  * @ingroup groupFilters  
00035  */ 
00036  
00037 /**  
00038  * @defgroup BiquadCascadeDF2T Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure  
00039  *  
00040  * This set of functions implements arbitrary order recursive (IIR) filters using a transposed direct form II structure.  
00041  * The filters are implemented as a cascade of second order Biquad sections.  
00042  * These functions provide a slight memory savings as compared to the direct form I Biquad filter functions. 
00043  * Only floating-point data is supported.  
00044  *  
00045  * This function operate on blocks of input and output data and each call to the function  
00046  * processes <code>blockSize</code> samples through the filter.  
00047  * <code>pSrc</code> points to the array of input data and  
00048  * <code>pDst</code> points to the array of output data.  
00049  * Both arrays contain <code>blockSize</code> values.  
00050  *  
00051  * \par Algorithm  
00052  * Each Biquad stage implements a second order filter using the difference equation:  
00053  * <pre>  
00054  *    y[n] = b0 * x[n] + d1  
00055  *    d1 = b1 * x[n] + a1 * y[n] + d2  
00056  *    d2 = b2 * x[n] + a2 * y[n]  
00057  * </pre>  
00058  * where d1 and d2 represent the two state values.  
00059  *  
00060  * \par  
00061  * A Biquad filter using a transposed Direct Form II structure is shown below.  
00062  * \image html BiquadDF2Transposed.gif "Single transposed Direct Form II Biquad"  
00063  * Coefficients <code>b0, b1, and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients.  
00064  * Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients.  
00065  * Pay careful attention to the sign of the feedback coefficients.  
00066  * Some design tools flip the sign of the feedback coefficients:  
00067  * <pre>  
00068  *    y[n] = b0 * x[n] + d1;  
00069  *    d1 = b1 * x[n] - a1 * y[n] + d2;  
00070  *    d2 = b2 * x[n] - a2 * y[n];  
00071  * </pre>  
00072  * In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library.  
00073  *  
00074  * \par  
00075  * Higher order filters are realized as a cascade of second order sections.  
00076  * <code>numStages</code> refers to the number of second order stages used.  
00077  * For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages.  
00078  * A 9th order filter would be realized with <code>numStages=5</code> second order stages with the  
00079  * coefficients for one of the stages configured as a first order filter (<code>b2=0</code> and <code>a2=0</code>).  
00080  *  
00081  * \par  
00082  * <code>pState</code> points to the state variable array.  
00083  * Each Biquad stage has 2 state variables <code>d1</code> and <code>d2</code>.  
00084  * The state variables are arranged in the <code>pState</code> array as:  
00085  * <pre>  
00086  *     {d11, d12, d21, d22, ...}  
00087  * </pre>  
00088  * where <code>d1x</code> refers to the state variables for the first Biquad and  
00089  * <code>d2x</code> refers to the state variables for the second Biquad.  
00090  * The state array has a total length of <code>2*numStages</code> values.  
00091  * The state variables are updated after each block of data is processed; the coefficients are untouched.  
00092  *  
00093  * \par  
00094  * The CMSIS library contains Biquad filters in both Direct Form I and transposed Direct Form II.  
00095  * The advantage of the Direct Form I structure is that it is numerically more robust for fixed-point data types.  
00096  * That is why the Direct Form I structure supports Q15 and Q31 data types.  
00097  * 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>.  
00098  * Because of this, the CMSIS library only has a floating-point version of the Direct Form II Biquad.  
00099  * 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.  
00100  *  
00101  * \par Instance Structure  
00102  * The coefficients and state variables for a filter are stored together in an instance data structure.  
00103  * A separate instance structure must be defined for each filter.  
00104  * Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.  
00105  *  
00106  * \par Init Functions  
00107  * There is also an associated initialization function. 
00108  * The initialization function performs following operations:  
00109  * - Sets the values of the internal structure fields.  
00110  * - Zeros out the values in the state buffer.  
00111  *  
00112  * \par  
00113  * Use of the initialization function is optional.  
00114  * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.  
00115  * To place an instance structure into a const data section, the instance structure must be manually initialized.  
00116  * Set the values in the state buffer to zeros before static initialization.  
00117  * For example, to statically initialize the instance structure use  
00118  * <pre>  
00119  *     arm_biquad_cascade_df2T_instance_f32 S1 = {numStages, pState, pCoeffs};  
00120  * </pre>  
00121  * where <code>numStages</code> is the number of Biquad stages in the filter; <code>pState</code> is the address of the state buffer.  
00122  * <code>pCoeffs</code> is the address of the coefficient buffer;   
00123  *  
00124  */ 
00125  
00126 /**  
00127  * @addtogroup BiquadCascadeDF2T  
00128  * @{  
00129  */ 
00130  
00131 /** 
00132  * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter. 
00133  * @param[in]  *S        points to an instance of the filter data structure. 
00134  * @param[in]  *pSrc     points to the block of input data. 
00135  * @param[out] *pDst     points to the block of output data 
00136  * @param[in]  blockSize number of samples to process. 
00137  * @return none. 
00138  */ 
00139  
00140 void arm_biquad_cascade_df2T_f32( 
00141   const arm_biquad_cascade_df2T_instance_f32 * S, 
00142   float32_t * pSrc, 
00143   float32_t * pDst, 
00144   uint32_t blockSize) 
00145 { 
00146  
00147   float32_t *pIn = pSrc;                         /*  source pointer            */ 
00148   float32_t *pOut = pDst;                        /*  destination pointer       */ 
00149   float32_t *pState = S->pState;                 /*  State pointer            */ 
00150   float32_t *pCoeffs = S->pCoeffs;               /*  coefficient pointer       */ 
00151   float32_t acc0;                                /*  Simulates the accumulator */ 
00152   float32_t b0, b1, b2, a1, a2;                  /*  Filter coefficients       */ 
00153   float32_t Xn;                                  /*  temporary input           */ 
00154   float32_t d1, d2;                              /*  state variables          */ 
00155   uint32_t sample, stage = S->numStages;         /*  loop counters             */ 
00156  
00157  
00158   do 
00159   { 
00160     /* Reading the coefficients */ 
00161     b0 = *pCoeffs++; 
00162     b1 = *pCoeffs++; 
00163     b2 = *pCoeffs++; 
00164     a1 = *pCoeffs++; 
00165     a2 = *pCoeffs++; 
00166  
00167     /*Reading the state values */ 
00168     d1 = pState[0]; 
00169     d2 = pState[1]; 
00170  
00171     /* Apply loop unrolling and compute 4 output values simultaneously. */ 
00172     sample = blockSize >> 2u; 
00173  
00174     /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.  
00175      ** a second loop below computes the remaining 1 to 3 samples. */ 
00176     while(sample > 0u) 
00177     { 
00178       /* Read the first input */ 
00179       Xn = *pIn++; 
00180  
00181       /* y[n] = b0 * x[n] + d1 */ 
00182       acc0 = (b0 * Xn) + d1; 
00183  
00184       /* Store the result in the accumulator in the destination buffer. */ 
00185       *pOut++ = acc0; 
00186  
00187       /* Every time after the output is computed state should be updated. */ 
00188       /* d1 = b1 * x[n] + a1 * y[n] + d2 */ 
00189       d1 = ((b1 * Xn) + (a1 * acc0)) + d2; 
00190  
00191       /* d2 = b2 * x[n] + a2 * y[n] */ 
00192       d2 = (b2 * Xn) + (a2 * acc0); 
00193  
00194       /* Read the second input */ 
00195       Xn = *pIn++; 
00196  
00197       /* y[n] = b0 * x[n] + d1 */ 
00198       acc0 = (b0 * Xn) + d1; 
00199  
00200       /* Store the result in the accumulator in the destination buffer. */ 
00201       *pOut++ = acc0; 
00202  
00203       /* Every time after the output is computed state should be updated. */ 
00204       /* d1 = b1 * x[n] + a1 * y[n] + d2 */ 
00205       d1 = ((b1 * Xn) + (a1 * acc0)) + d2; 
00206  
00207       /* d2 = b2 * x[n] + a2 * y[n] */ 
00208       d2 = (b2 * Xn) + (a2 * acc0); 
00209  
00210       /* Read the third input */ 
00211       Xn = *pIn++; 
00212  
00213       /* y[n] = b0 * x[n] + d1 */ 
00214       acc0 = (b0 * Xn) + d1; 
00215  
00216       /* Store the result in the accumulator in the destination buffer. */ 
00217       *pOut++ = acc0; 
00218  
00219       /* Every time after the output is computed state should be updated. */ 
00220       /* d1 = b1 * x[n] + a1 * y[n] + d2 */ 
00221       d1 = ((b1 * Xn) + (a1 * acc0)) + d2; 
00222  
00223       /* d2 = b2 * x[n] + a2 * y[n] */ 
00224       d2 = (b2 * Xn) + (a2 * acc0); 
00225  
00226       /* Read the fourth input */ 
00227       Xn = *pIn++; 
00228  
00229       /* y[n] = b0 * x[n] + d1 */ 
00230       acc0 = (b0 * Xn) + d1; 
00231  
00232       /* Store the result in the accumulator in the destination buffer. */ 
00233       *pOut++ = acc0; 
00234  
00235       /* Every time after the output is computed state should be updated. */ 
00236       /* d1 = b1 * x[n] + a1 * y[n] + d2 */ 
00237       d1 = (b1 * Xn) + (a1 * acc0) + d2; 
00238  
00239       /* d2 = b2 * x[n] + a2 * y[n] */ 
00240       d2 = (b2 * Xn) + (a2 * acc0); 
00241  
00242       /* decrement the loop counter */ 
00243       sample--; 
00244  
00245     } 
00246  
00247     /* If the blockSize is not a multiple of 4, compute any remaining output samples here.  
00248      ** No loop unrolling is used. */ 
00249     sample = blockSize & 0x3u; 
00250  
00251     while(sample > 0u) 
00252     { 
00253       /* Read the input */ 
00254       Xn = *pIn++; 
00255  
00256       /* y[n] = b0 * x[n] + d1 */ 
00257       acc0 = (b0 * Xn) + d1; 
00258  
00259       /* Store the result in the accumulator in the destination buffer. */ 
00260       *pOut++ = acc0; 
00261  
00262       /* Every time after the output is computed state should be updated. */ 
00263       /* d1 = b1 * x[n] + a1 * y[n] + d2 */ 
00264       d1 = ((b1 * Xn) + (a1 * acc0)) + d2; 
00265  
00266       /* d2 = b2 * x[n] + a2 * y[n] */ 
00267       d2 = (b2 * Xn) + (a2 * acc0); 
00268  
00269       /* decrement the loop counter */ 
00270       sample--; 
00271     } 
00272  
00273     /* Store the updated state variables back into the state array */ 
00274     *pState++ = d1; 
00275     *pState++ = d2; 
00276  
00277     /* The current stage input is given as the output to the next stage */ 
00278     pIn = pDst; 
00279  
00280     /*Reset the output working pointer */ 
00281     pOut = pDst; 
00282  
00283     /* decrement the loop counter */ 
00284     stage--; 
00285  
00286   } while(stage > 0u); 
00287  
00288  
00289 } 
00290  
00291  
00292   /**  
00293    * @} end of BiquadCascadeDF2T group  
00294    */