Diff: src/Cortex-M4-M3/FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c

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+++ b/src/Cortex-M4-M3/FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c	Thu Mar 10 15:07:50 2011 +0000
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+/* ----------------------------------------------------------------------  
+* Copyright (C) 2010 ARM Limited. All rights reserved.  
+*  
+* $Date:        29. November 2010  
+* $Revision: 	V1.0.3  
+*  
+* Project: 	    CMSIS DSP Library  
+* Title:	    arm_biquad_cascade_df1_32x64_q31.c  
+*  
+* Description:	High precision Q31 Biquad cascade filter processing function  
+*  
+* 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 BiquadCascadeDF1_32x64 High Precision Q31 Biquad Cascade Filter  
+ *  
+ * This function implements a high precision Biquad cascade filter which operates on  
+ * Q31 data values.  The filter coefficients are in 1.31 format and the state variables  
+ * are in 1.63 format.  The double precision state variables reduce quantization noise  
+ * in the filter and provide a cleaner output.  
+ * These filters are particularly useful when implementing filters in which the  
+ * singularities are close to the unit circle.  This is common for low pass or high  
+ * pass filters with very low cutoff frequencies.  
+ *  
+ * The function operates on blocks of input and output data  
+ * and each call to the function processes <code>blockSize</code> samples through  
+ * the filter. <code>pSrc</code> and <code>pDst</code> points to input and output arrays  
+ * containing <code>blockSize</code> Q31 values.  
+ *  
+ * \par Algorithm  
+ * Each Biquad stage implements a second order filter using the difference equation:  
+ * <pre>  
+ *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]  
+ * </pre>  
+ * A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage.  
+ * \image html Biquad.gif "Single Biquad filter stage"  
+ * 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 use the difference equation  
+ * <pre>  
+ *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2]  
+ * </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.  
+ * \image html BiquadCascade.gif "8th order filter using a cascade of Biquad 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  
+ * The <code>pState</code> points to state variables array .  
+ * Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</code> and each state variable in 1.63 format to improve precision.  
+ * The state variables are arranged in the array as:  
+ * <pre>  
+ *     {x[n-1], x[n-2], y[n-1], y[n-2]}  
+ * </pre>  
+ *  
+ * \par  
+ * The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.  
+ * The state array has a total length of <code>4*numStages</code> values of data in 1.63 format.  
+ * The state variables are updated after each block of data is processed; the coefficients are untouched.  
+ *  
+ * \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 Function  
+ * There is also an associated initialization function which performs the 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 filter instance structure use  
+ * <pre>  
+ *     arm_biquad_cas_df1_32x64_ins_q31 S1 = {numStages, pState, pCoeffs, postShift};  
+ * </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; <code>postShift</code> shift to be applied which is described in detail below.  
+ * \par Fixed-Point Behavior  
+ * Care must be taken while using Biquad Cascade 32x64 filter function.  
+ * Following issues must be considered:  
+ * - Scaling of coefficients  
+ * - Filter gain  
+ * - Overflow and saturation  
+ *  
+ * \par  
+ * Filter coefficients are represented as fractional values and  
+ * restricted to lie in the range <code>[-1 +1)</code>.  
+ * The processing function has an additional scaling parameter <code>postShift</code>  
+ * which allows the filter coefficients to exceed the range <code>[+1 -1)</code>.  
+ * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.  
+ * \image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator"  
+ * This essentially scales the filter coefficients by <code>2^postShift</code>.  
+ * For example, to realize the coefficients  
+ * <pre>  
+ *    {1.5, -0.8, 1.2, 1.6, -0.9}  
+ * </pre>  
+ * set the Coefficient array to:  
+ * <pre>  
+ *    {0.75, -0.4, 0.6, 0.8, -0.45}  
+ * </pre>  
+ * and set <code>postShift=1</code>  
+ *  
+ * \par  
+ * The second thing to keep in mind is the gain through the filter.  
+ * The frequency response of a Biquad filter is a function of its coefficients.  
+ * It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies.  
+ * 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.  
+ * 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.  
+ *  
+ * \par  
+ * The third item to consider is the overflow and saturation behavior of the fixed-point Q31 version.  
+ * This is described in the function specific documentation below.  
+ */ 
+ 
+/**  
+ * @addtogroup BiquadCascadeDF1_32x64  
+ * @{  
+ */ 
+ 
+/**  
+ * @details  
+  
+ * @param[in]  *S points to an instance of the high precision Q31 Biquad cascade filter.  
+ * @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.  
+ *  
+ * \par  
+ * The function is implemented using an internal 64-bit accumulator.  
+ * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.  
+ * Thus, if the accumulator result overflows it wraps around rather than clip.  
+ * In order to avoid overflows completely the input signal must be scaled down by 2 bits and lie in the range [-0.25 +0.25).  
+ * After all 5 multiply-accumulates are performed, the 2.62 accumulator is shifted by <code>postShift</code> bits and the result truncated to  
+ * 1.31 format by discarding the low 32 bits.  
+ *  
+ * \par  
+ * Two related functions are provided in the CMSIS DSP library.  
+ * <code>arm_biquad_cascade_df1_q31()</code> implements a Biquad cascade with 32-bit coefficients and state variables with a Q63 accumulator.  
+ * <code>arm_biquad_cascade_df1_fast_q31()</code> implements a Biquad cascade with 32-bit coefficients and state variables with a Q31 accumulator.  
+ */ 
+ 
+void arm_biquad_cas_df1_32x64_q31( 
+  const arm_biquad_cas_df1_32x64_ins_q31 * S, 
+  q31_t * pSrc, 
+  q31_t * pDst, 
+  uint32_t blockSize) 
+{ 
+  q31_t *pIn = pSrc;                             /*  input pointer initialization  */ 
+  q31_t *pOut = pDst;                            /*  output pointer initialization */ 
+  q63_t *pState = S->pState;                     /*  state pointer initialization  */ 
+  q31_t *pCoeffs = S->pCoeffs;                   /*  coeff pointer initialization  */ 
+  q63_t acc;                                     /*  accumulator                   */ 
+  q63_t Xn1, Xn2, Yn1, Yn2;                      /*  Filter state variables        */ 
+  q31_t b0, b1, b2, a1, a2;                      /*  Filter coefficients           */ 
+  q63_t Xn;                                      /*  temporary input               */ 
+  int32_t shift = (int32_t) S->postShift + 1;    /*  Shift to be applied to the output */ 
+  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 */ 
+    Xn1 = pState[0]; 
+    Xn2 = pState[1]; 
+    Yn1 = pState[2]; 
+    Yn2 = pState[3]; 
+ 
+    /* Apply loop unrolling and compute 4 output values simultaneously. */ 
+    /* The variable acc hold output value that is being computed and  
+     * stored in the destination buffer  
+     * acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]  
+     */ 
+ 
+    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 input */ 
+      Xn = *pIn++; 
+ 
+      /* The value is shifted to the MSB to perform 32x64 multiplication */ 
+      Xn = Xn << 32; 
+ 
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ 
+ 
+      /* acc =  b0 * x[n] */ 
+      acc = mult32x64(Xn, b0); 
+      /* acc +=  b1 * x[n-1] */ 
+      acc += mult32x64(Xn1, b1); 
+      /* acc +=  b[2] * x[n-2] */ 
+      acc += mult32x64(Xn2, b2); 
+      /* acc +=  a1 * y[n-1] */ 
+      acc += mult32x64(Yn1, a1); 
+      /* acc +=  a2 * y[n-2] */ 
+      acc += mult32x64(Yn2, a2); 
+ 
+      /* The result is converted to 1.63 , Yn2 variable is reused */ 
+      Yn2 = acc << shift; 
+ 
+      /* Store the output in the destination buffer in 1.31 format. */ 
+      *pOut++ = (q31_t) (acc >> (32 - shift)); 
+ 
+      /* Read the second input into Xn2, to reuse the value */ 
+      Xn2 = *pIn++; 
+ 
+      /* The value is shifted to the MSB to perform 32x64 multiplication */ 
+      Xn2 = Xn2 << 32; 
+ 
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ 
+ 
+      /* acc =  b0 * x[n] */ 
+      acc = mult32x64(Xn2, b0); 
+      /* acc +=  b1 * x[n-1] */ 
+      acc += mult32x64(Xn, b1); 
+      /* acc +=  b[2] * x[n-2] */ 
+      acc += mult32x64(Xn1, b2); 
+      /* acc +=  a1 * y[n-1] */ 
+      acc += mult32x64(Yn2, a1); 
+      /* acc +=  a2 * y[n-2] */ 
+      acc += mult32x64(Yn1, a2); 
+ 
+      /* The result is converted to 1.63, Yn1 variable is reused */ 
+      Yn1 = acc << shift; 
+ 
+      /* The result is converted to 1.31 */ 
+      /* Store the output in the destination buffer. */ 
+      *pOut++ = (q31_t) (acc >> (32 - shift)); 
+ 
+      /* Read the third input into Xn1, to reuse the value */ 
+      Xn1 = *pIn++; 
+ 
+      /* The value is shifted to the MSB to perform 32x64 multiplication */ 
+      Xn1 = Xn1 << 32; 
+ 
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ 
+      /* acc =  b0 * x[n] */ 
+      acc = mult32x64(Xn1, b0); 
+      /* acc +=  b1 * x[n-1] */ 
+      acc += mult32x64(Xn2, b1); 
+      /* acc +=  b[2] * x[n-2] */ 
+      acc += mult32x64(Xn, b2); 
+      /* acc +=  a1 * y[n-1] */ 
+      acc += mult32x64(Yn1, a1); 
+      /* acc +=  a2 * y[n-2] */ 
+      acc += mult32x64(Yn2, a2); 
+ 
+      /* The result is converted to 1.63, Yn2 variable is reused  */ 
+      Yn2 = acc << shift; 
+ 
+      /* Store the output in the destination buffer in 1.31 format. */ 
+      *pOut++ = (q31_t) (acc >> (32 - shift)); 
+ 
+      /* Read the fourth input into Xn, to reuse the value */ 
+      Xn = *pIn++; 
+ 
+      /* The value is shifted to the MSB to perform 32x64 multiplication */ 
+      Xn = Xn << 32; 
+ 
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ 
+      /* acc =  b0 * x[n] */ 
+      acc = mult32x64(Xn, b0); 
+      /* acc +=  b1 * x[n-1] */ 
+      acc += mult32x64(Xn1, b1); 
+      /* acc +=  b[2] * x[n-2] */ 
+      acc += mult32x64(Xn2, b2); 
+      /* acc +=  a1 * y[n-1] */ 
+      acc += mult32x64(Yn2, a1); 
+      /* acc +=  a2 * y[n-2] */ 
+      acc += mult32x64(Yn1, a2); 
+ 
+      /* The result is converted to 1.63, Yn1 variable is reused  */ 
+      Yn1 = acc << shift; 
+ 
+      /* Every time after the output is computed state should be updated. */ 
+      /* The states should be updated as:  */ 
+      /* Xn2 = Xn1    */ 
+      /* Xn1 = Xn     */ 
+      /* Yn2 = Yn1    */ 
+      /* Yn1 = acc    */ 
+      Xn2 = Xn1; 
+      Xn1 = Xn; 
+ 
+      /* Store the output in the destination buffer in 1.31 format. */ 
+      *pOut++ = (q31_t) (acc >> (32 - shift)); 
+ 
+      /* 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++; 
+ 
+      /* The value is shifted to the MSB to perform 32x64 multiplication */ 
+      Xn = Xn << 32; 
+ 
+      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ 
+      /* acc =  b0 * x[n] */ 
+      acc = mult32x64(Xn, b0); 
+      /* acc +=  b1 * x[n-1] */ 
+      acc += mult32x64(Xn1, b1); 
+      /* acc +=  b[2] * x[n-2] */ 
+      acc += mult32x64(Xn2, b2); 
+      /* acc +=  a1 * y[n-1] */ 
+      acc += mult32x64(Yn1, a1); 
+      /* acc +=  a2 * y[n-2] */ 
+      acc += mult32x64(Yn2, a2); 
+ 
+      /* Every time after the output is computed state should be updated. */ 
+      /* The states should be updated as:  */ 
+      /* Xn2 = Xn1    */ 
+      /* Xn1 = Xn     */ 
+      /* Yn2 = Yn1    */ 
+      /* Yn1 = acc    */ 
+      Xn2 = Xn1; 
+      Xn1 = Xn; 
+      Yn2 = Yn1; 
+      Yn1 = acc << shift; 
+ 
+      /* Store the output in the destination buffer in 1.31 format. */ 
+      *pOut++ = (q31_t) (acc >> (32 - shift)); 
+ 
+      /* decrement the loop counter */ 
+      sample--; 
+    } 
+ 
+    /*  The first stage output is given as input to the second stage. */ 
+    pIn = pDst; 
+ 
+    /* Reset to destination buffer working pointer */ 
+    pOut = pDst; 
+ 
+    /*  Store the updated state variables back into the pState array */ 
+    *pState++ = Xn1; 
+    *pState++ = Xn2; 
+    *pState++ = Yn1; 
+    *pState++ = Yn2; 
+ 
+  } while(--stage); 
+} 
+ 
+  /**  
+   * @} end of BiquadCascadeDF1_32x64 group  
+   */