arm_biquad_cascade_df1_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_df1_f32.c  
00009 *  
00010 * Description:  Processing function for the  
00011 *               floating-point Biquad cascade DirectFormI(DF1) 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 0.0.5  2010/04/26   
00028 *    incorporated review comments and updated with latest CMSIS layer  
00029 *  
00030 * Version 0.0.3  2010/03/10   
00031 *    Initial version  
00032 * -------------------------------------------------------------------- */ 
00033  
00034 #include "arm_math.h" 
00035  
00036 /**  
00037  * @ingroup groupFilters  
00038  */ 
00039  
00040 /**  
00041  * @defgroup BiquadCascadeDF1 Biquad Cascade IIR Filters Using Direct Form I Structure  
00042  *  
00043  * This set of functions implements arbitrary order recursive (IIR) filters.  
00044  * The filters are implemented as a cascade of second order Biquad sections.  
00045  * The functions support Q15, Q31 and floating-point data types. Fast version of Q15 and Q31 also supported.  
00046  *  
00047  * The functions operate on blocks of input and output data and each call to the function  
00048  * processes <code>blockSize</code> samples through the filter.  
00049  * <code>pSrc</code> points to the array of input data and  
00050  * <code>pDst</code> points to the array of output data.  
00051  * Both arrays contain <code>blockSize</code> values.  
00052  *  
00053  * \par Algorithm  
00054  * Each Biquad stage implements a second order filter using the difference equation:  
00055  * <pre>  
00056  *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]  
00057  * </pre>  
00058  * A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage.  
00059  * \image html Biquad.gif "Single Biquad filter stage"  
00060  * Coefficients <code>b0, b1 and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients.  
00061  * Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients.  
00062  * Pay careful attention to the sign of the feedback coefficients.  
00063  * Some design tools use the difference equation  
00064  * <pre>  
00065  *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2]  
00066  * </pre>  
00067  * In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library.  
00068  *  
00069  * \par  
00070  * Higher order filters are realized as a cascade of second order sections.  
00071  * <code>numStages</code> refers to the number of second order stages used.  
00072  * For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages.  
00073  * \image html BiquadCascade.gif "8th order filter using a cascade of Biquad stages"  
00074  * 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>).  
00075  *  
00076  * \par  
00077  * The <code>pState</code> points to state variables array.  
00078  * Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</code>.  
00079  * The state variables are arranged in the <code>pState</code> array as:  
00080  * <pre>  
00081  *     {x[n-1], x[n-2], y[n-1], y[n-2]}  
00082  * </pre>  
00083  *  
00084  * \par  
00085  * The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.  
00086  * The state array has a total length of <code>4*numStages</code> values.  
00087  * The state variables are updated after each block of data is processed, the coefficients are untouched.  
00088  *  
00089  * \par Instance Structure  
00090  * The coefficients and state variables for a filter are stored together in an instance data structure.  
00091  * A separate instance structure must be defined for each filter.  
00092  * Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.  
00093  * There are separate instance structure declarations for each of the 3 supported data types.  
00094  *  
00095  * \par Init Functions  
00096  * There is also an associated initialization function for each data type.  
00097  * The initialization function performs following operations:  
00098  * - Sets the values of the internal structure fields.  
00099  * - Zeros out the values in the state buffer.  
00100  *  
00101  * \par  
00102  * Use of the initialization function is optional.  
00103  * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.  
00104  * To place an instance structure into a const data section, the instance structure must be manually initialized.  
00105  * Set the values in the state buffer to zeros before static initialization.  
00106  * The code below statically initializes each of the 3 different data type filter instance structures  
00107  * <pre>  
00108  *     arm_biquad_casd_df1_inst_f32 S1 = {numStages, pState, pCoeffs};  
00109  *     arm_biquad_casd_df1_inst_q15 S2 = {numStages, pState, pCoeffs, postShift};  
00110  *     arm_biquad_casd_df1_inst_q31 S3 = {numStages, pState, pCoeffs, postShift};  
00111  * </pre>  
00112  * where <code>numStages</code> is the number of Biquad stages in the filter; <code>pState</code> is the address of the state buffer;  
00113  * <code>pCoeffs</code> is the address of the coefficient buffer; <code>postShift</code> shift to be applied.  
00114  *  
00115  * \par Fixed-Point Behavior  
00116  * Care must be taken when using the Q15 and Q31 versions of the Biquad Cascade filter functions.  
00117  * Following issues must be considered:  
00118  * - Scaling of coefficients  
00119  * - Filter gain  
00120  * - Overflow and saturation  
00121  *  
00122  * \par  
00123  * <b>Scaling of coefficients: </b>  
00124  * Filter coefficients are represented as fractional values and  
00125  * coefficients are restricted to lie in the range <code>[-1 +1)</code>.  
00126  * The fixed-point functions have an additional scaling parameter <code>postShift</code>  
00127  * which allow the filter coefficients to exceed the range <code>[+1 -1)</code>.  
00128  * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.  
00129  * \image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator"  
00130  * This essentially scales the filter coefficients by <code>2^postShift</code>.  
00131  * For example, to realize the coefficients  
00132  * <pre>  
00133  *    {1.5, -0.8, 1.2, 1.6, -0.9}  
00134  * </pre>  
00135  * set the pCoeffs array to:  
00136  * <pre>  
00137  *    {0.75, -0.4, 0.6, 0.8, -0.45}  
00138  * </pre>  
00139  * and set <code>postShift=1</code>  
00140  *  
00141  * \par  
00142  * <b>Filter gain: </b>  
00143  * The frequency response of a Biquad filter is a function of its coefficients.  
00144  * It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies.  
00145  * 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.  
00146  * 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.  
00147  *  
00148  * \par  
00149  * <b>Overflow and saturation: </b>  
00150  * For Q15 and Q31 versions, it is described separately as part of the function specific documentation below.  
00151  */ 
00152  
00153 /**  
00154  * @addtogroup BiquadCascadeDF1  
00155  * @{  
00156  */ 
00157  
00158 /**  
00159  * @param[in]  *S         points to an instance of the floating-point Biquad cascade structure.  
00160  * @param[in]  *pSrc      points to the block of input data.  
00161  * @param[out] *pDst      points to the block of output data.  
00162  * @param[in]  blockSize  number of samples to process per call.  
00163  * @return     none.  
00164  *  
00165  */ 
00166  
00167 void arm_biquad_cascade_df1_f32( 
00168   const arm_biquad_casd_df1_inst_f32 * S, 
00169   float32_t * pSrc, 
00170   float32_t * pDst, 
00171   uint32_t blockSize) 
00172 { 
00173   float32_t *pIn = pSrc;                         /*  source pointer            */ 
00174   float32_t *pOut = pDst;                        /*  destination pointer       */ 
00175   float32_t *pState = S->pState;                 /*  pState pointer            */ 
00176   float32_t *pCoeffs = S->pCoeffs;               /*  coefficient pointer       */ 
00177   float32_t acc;                                 /*  Simulates the accumulator */ 
00178   float32_t b0, b1, b2, a1, a2;                  /*  Filter coefficients       */ 
00179   float32_t Xn1, Xn2, Yn1, Yn2;                  /*  Filter pState variables   */ 
00180   float32_t Xn;                                  /*  temporary input           */ 
00181   uint32_t sample, stage = S->numStages;         /*  loop counters             */ 
00182  
00183  
00184   do 
00185   { 
00186     /* Reading the coefficients */ 
00187     b0 = *pCoeffs++; 
00188     b1 = *pCoeffs++; 
00189     b2 = *pCoeffs++; 
00190     a1 = *pCoeffs++; 
00191     a2 = *pCoeffs++; 
00192  
00193     /* Reading the pState values */ 
00194     Xn1 = pState[0]; 
00195     Xn2 = pState[1]; 
00196     Yn1 = pState[2]; 
00197     Yn2 = pState[3]; 
00198  
00199     /* Apply loop unrolling and compute 4 output values simultaneously. */ 
00200     /*      The variable acc hold output values that are being computed:  
00201      *  
00202      *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]  
00203      *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]  
00204      *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]  
00205      *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]  
00206      */ 
00207  
00208     sample = blockSize >> 2u; 
00209  
00210     /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.  
00211      ** a second loop below computes the remaining 1 to 3 samples. */ 
00212     while(sample > 0u) 
00213     { 
00214       /* Read the first input */ 
00215       Xn = *pIn++; 
00216  
00217       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ 
00218       Yn2 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2); 
00219  
00220       /* Store the result in the accumulator in the destination buffer. */ 
00221       *pOut++ = Yn2; 
00222  
00223       /* Every time after the output is computed state should be updated. */ 
00224       /* The states should be updated as:  */ 
00225       /* Xn2 = Xn1    */ 
00226       /* Xn1 = Xn     */ 
00227       /* Yn2 = Yn1    */ 
00228       /* Yn1 = acc   */ 
00229  
00230       /* Read the second input */ 
00231       Xn2 = *pIn++; 
00232  
00233       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ 
00234       Yn1 = (b0 * Xn2) + (b1 * Xn) + (b2 * Xn1) + (a1 * Yn2) + (a2 * Yn1); 
00235  
00236       /* Store the result in the accumulator in the destination buffer. */ 
00237       *pOut++ = Yn1; 
00238  
00239       /* Every time after the output is computed state should be updated. */ 
00240       /* The states should be updated as:  */ 
00241       /* Xn2 = Xn1    */ 
00242       /* Xn1 = Xn     */ 
00243       /* Yn2 = Yn1    */ 
00244       /* Yn1 = acc   */ 
00245  
00246       /* Read the third input */ 
00247       Xn1 = *pIn++; 
00248  
00249       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ 
00250       Yn2 = (b0 * Xn1) + (b1 * Xn2) + (b2 * Xn) + (a1 * Yn1) + (a2 * Yn2); 
00251  
00252       /* Store the result in the accumulator in the destination buffer. */ 
00253       *pOut++ = Yn2; 
00254  
00255       /* Every time after the output is computed state should be updated. */ 
00256       /* The states should be updated as: */ 
00257       /* Xn2 = Xn1    */ 
00258       /* Xn1 = Xn     */ 
00259       /* Yn2 = Yn1    */ 
00260       /* Yn1 = acc   */ 
00261  
00262       /* Read the forth input */ 
00263       Xn = *pIn++; 
00264  
00265       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ 
00266       Yn1 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn2) + (a2 * Yn1); 
00267  
00268       /* Store the result in the accumulator in the destination buffer. */ 
00269       *pOut++ = Yn1; 
00270  
00271       /* Every time after the output is computed state should be updated. */ 
00272       /* The states should be updated as:  */ 
00273       /* Xn2 = Xn1    */ 
00274       /* Xn1 = Xn     */ 
00275       /* Yn2 = Yn1    */ 
00276       /* Yn1 = acc   */ 
00277       Xn2 = Xn1; 
00278       Xn1 = Xn; 
00279  
00280       /* decrement the loop counter */ 
00281       sample--; 
00282  
00283     } 
00284  
00285     /* If the blockSize is not a multiple of 4, compute any remaining output samples here.  
00286      ** No loop unrolling is used. */ 
00287     sample = blockSize & 0x3u; 
00288  
00289     while(sample > 0u) 
00290     { 
00291       /* Read the input */ 
00292       Xn = *pIn++; 
00293  
00294       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ 
00295       acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2); 
00296  
00297       /* Store the result in the accumulator in the destination buffer. */ 
00298       *pOut++ = acc; 
00299  
00300       /* Every time after the output is computed state should be updated. */ 
00301       /* The states should be updated as:    */ 
00302       /* Xn2 = Xn1    */ 
00303       /* Xn1 = Xn     */ 
00304       /* Yn2 = Yn1    */ 
00305       /* Yn1 = acc   */ 
00306       Xn2 = Xn1; 
00307       Xn1 = Xn; 
00308       Yn2 = Yn1; 
00309       Yn1 = acc; 
00310  
00311       /* decrement the loop counter */ 
00312       sample--; 
00313  
00314     } 
00315  
00316     /*  Store the updated state variables back into the pState array */ 
00317     *pState++ = Xn1; 
00318     *pState++ = Xn2; 
00319     *pState++ = Yn1; 
00320     *pState++ = Yn2; 
00321  
00322     /*  The first stage goes from the input wire to the output wire. */ 
00323     /*  Subsequent numStages occur in-place in the output wire */ 
00324     pIn = pDst; 
00325  
00326     /* Reset the output pointer */ 
00327     pOut = pDst; 
00328  
00329     /* decrement the loop counter */ 
00330     stage--; 
00331  
00332   } while(stage > 0u); 
00333  
00334 } 
00335  
00336  
00337   /**  
00338    * @} end of BiquadCascadeDF1 group  
00339    */