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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 */
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