/* ---------------------------------------------------------------------- * Copyright (C) 2010-2013 ARM Limited. All rights reserved. * * $Date: 17. January 2013 * $Revision: V1.4.1 * * Project: CMSIS DSP Library * Title: arm_fir_interpolate_f32.c * * Description: FIR interpolation for floating-point sequences. * * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * - Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * - Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in * the documentation and/or other materials provided with the * distribution. * - Neither the name of ARM LIMITED nor the names of its contributors * may be used to endorse or promote products derived from this * software without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE * POSSIBILITY OF SUCH DAMAGE. * -------------------------------------------------------------------- */ #include "arm_math.h" /** * @defgroup FIR_Interpolate Finite Impulse Response (FIR) Interpolator * * These functions combine an upsampler (zero stuffer) and an FIR filter. * They are used in multirate systems for increasing the sample rate of a signal without introducing high frequency images. * Conceptually, the functions are equivalent to the block diagram below: * \image html FIRInterpolator.gif "Components included in the FIR Interpolator functions" * After upsampling by a factor of L, the signal should be filtered by a lowpass filter with a normalized * cutoff frequency of 1/L in order to eliminate high frequency copies of the spectrum. * The user of the function is responsible for providing the filter coefficients. * * The FIR interpolator functions provided in the CMSIS DSP Library combine the upsampler and FIR filter in an efficient manner. * The upsampler inserts L-1 zeros between each sample. * Instead of multiplying by these zero values, the FIR filter is designed to skip them. * This leads to an efficient implementation without any wasted effort. * The functions operate on blocks of input and output data. * pSrc points to an array of blockSize input values and * pDst points to an array of blockSize*L output values. * * The library provides separate functions for Q15, Q31, and floating-point data types. * * \par Algorithm: * The functions use a polyphase filter structure: * 
    
 *    y[n] = b[0] * x[n] + b[L]   * x[n-1] + ... + b[L*(phaseLength-1)] * x[n-phaseLength+1]    
 *    y[n+1] = b[1] * x[n] + b[L+1] * x[n-1] + ... + b[L*(phaseLength-1)+1] * x[n-phaseLength+1]    
 *    ...    
 *    y[n+(L-1)] = b[L-1] * x[n] + b[2*L-1] * x[n-1] + ....+ b[L*(phaseLength-1)+(L-1)] * x[n-phaseLength+1]    
 *
* This approach is more efficient than straightforward upsample-then-filter algorithms. * With this method the computation is reduced by a factor of 1/L when compared to using a standard FIR filter. * \par * pCoeffs points to a coefficient array of size numTaps. * numTaps must be a multiple of the interpolation factor L and this is checked by the * initialization functions. * Internally, the function divides the FIR filter's impulse response into shorter filters of length * phaseLength=numTaps/L. * Coefficients are stored in time reversed order. * \par * 
    
 *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
 *
* \par * pState points to a state array of size blockSize + phaseLength - 1. * Samples in the state buffer are stored in the order: * \par * 
    
 *    {x[n-phaseLength+1], x[n-phaseLength], x[n-phaseLength-1], x[n-phaseLength-2]....x[0], x[1], ..., x[blockSize-1]}    
 *
* 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 array should be allocated separately. * There are separate instance structure declarations for each of the 3 supported data types. * * \par Initialization Functions * There is also an associated initialization function for each data type. * The initialization function performs the following operations: * - Sets the values of the internal structure fields. * - Zeros out the values in the state buffer. * - Checks to make sure that the length of the filter is a multiple of the interpolation factor. * To do this manually without calling the init function, assign the follow subfields of the instance structure: * L (interpolation factor), pCoeffs, phaseLength (numTaps / L), pState. Also set all of the values in pState to zero. * * \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. * The code below statically initializes each of the 3 different data type filter instance structures * 
    
 * arm_fir_interpolate_instance_f32 S = {L, phaseLength, pCoeffs, pState};    
 * arm_fir_interpolate_instance_q31 S = {L, phaseLength, pCoeffs, pState};    
 * arm_fir_interpolate_instance_q15 S = {L, phaseLength, pCoeffs, pState};    
 *
* where L is the interpolation factor; phaseLength=numTaps/L is the * length of each of the shorter FIR filters used internally, * pCoeffs is the address of the coefficient buffer; * pState is the address of the state buffer. * Be sure to set the values in the state buffer to zeros when doing static initialization. * * \par Fixed-Point Behavior * Care must be taken when using the fixed-point versions of the FIR interpolate filter functions. * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered. * Refer to the function specific documentation below for usage guidelines. */ /** * @addtogroup FIR_Interpolate * @{ */ /** * @brief Processing function for the floating-point FIR interpolator. * @param[in] *S points to an instance of the floating-point FIR interpolator 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 input samples to process per call. * @return none. */ #ifndef ARM_MATH_CM0_FAMILY /* Run the below code for Cortex-M4 and Cortex-M3 */ void arm_fir_interpolate_f32( const arm_fir_interpolate_instance_f32 * S, float32_t * pSrc, float32_t * pDst, uint32_t blockSize) { float32_t *pState = S->pState; /* State pointer */ float32_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */ float32_t *pStateCurnt; /* Points to the current sample of the state */ float32_t *ptr1, *ptr2; /* Temporary pointers for state and coefficient buffers */ float32_t sum0; /* Accumulators */ float32_t x0, c0; /* Temporary variables to hold state and coefficient values */ uint32_t i, blkCnt, j; /* Loop counters */ uint16_t phaseLen = S->phaseLength, tapCnt; /* Length of each polyphase filter component */ float32_t acc0, acc1, acc2, acc3; float32_t x1, x2, x3; uint32_t blkCntN4; float32_t c1, c2, c3; /* S->pState buffer contains previous frame (phaseLen - 1) samples */ /* pStateCurnt points to the location where the new input data should be written */ pStateCurnt = S->pState + (phaseLen - 1u); /* Initialise blkCnt */ blkCnt = blockSize / 4; blkCntN4 = blockSize - (4 * blkCnt); /* Samples loop unrolled by 4 */ while(blkCnt > 0u) { /* Copy new input sample into the state buffer */ *pStateCurnt++ = *pSrc++; *pStateCurnt++ = *pSrc++; *pStateCurnt++ = *pSrc++; *pStateCurnt++ = *pSrc++; /* Address modifier index of coefficient buffer */ j = 1u; /* Loop over the Interpolation factor. */ i = (S->L); while(i > 0u) { /* Set accumulator to zero */ acc0 = 0.0f; acc1 = 0.0f; acc2 = 0.0f; acc3 = 0.0f; /* Initialize state pointer */ ptr1 = pState; /* Initialize coefficient pointer */ ptr2 = pCoeffs + (S->L - j); /* Loop over the polyPhase length. Unroll by a factor of 4. ** Repeat until we've computed numTaps-(4*S->L) coefficients. */ tapCnt = phaseLen >> 2u; x0 = *(ptr1++); x1 = *(ptr1++); x2 = *(ptr1++); while(tapCnt > 0u) { /* Read the input sample */ x3 = *(ptr1++); /* Read the coefficient */ c0 = *(ptr2); /* Perform the multiply-accumulate */ acc0 += x0 * c0; acc1 += x1 * c0; acc2 += x2 * c0; acc3 += x3 * c0; /* Read the coefficient */ c1 = *(ptr2 + S->L); /* Read the input sample */ x0 = *(ptr1++); /* Perform the multiply-accumulate */ acc0 += x1 * c1; acc1 += x2 * c1; acc2 += x3 * c1; acc3 += x0 * c1; /* Read the coefficient */ c2 = *(ptr2 + S->L * 2); /* Read the input sample */ x1 = *(ptr1++); /* Perform the multiply-accumulate */ acc0 += x2 * c2; acc1 += x3 * c2; acc2 += x0 * c2; acc3 += x1 * c2; /* Read the coefficient */ c3 = *(ptr2 + S->L * 3); /* Read the input sample */ x2 = *(ptr1++); /* Perform the multiply-accumulate */ acc0 += x3 * c3; acc1 += x0 * c3; acc2 += x1 * c3; acc3 += x2 * c3; /* Upsampling is done by stuffing L-1 zeros between each sample. * So instead of multiplying zeros with coefficients, * Increment the coefficient pointer by interpolation factor times. */ ptr2 += 4 * S->L; /* Decrement the loop counter */ tapCnt--; } /* If the polyPhase length is not a multiple of 4, compute the remaining filter taps */ tapCnt = phaseLen % 0x4u; while(tapCnt > 0u) { /* Read the input sample */ x3 = *(ptr1++); /* Read the coefficient */ c0 = *(ptr2); /* Perform the multiply-accumulate */ acc0 += x0 * c0; acc1 += x1 * c0; acc2 += x2 * c0; acc3 += x3 * c0; /* Increment the coefficient pointer by interpolation factor times. */ ptr2 += S->L; /* update states for next sample processing */ x0 = x1; x1 = x2; x2 = x3; /* Decrement the loop counter */ tapCnt--; } /* The result is in the accumulator, store in the destination buffer. */ *pDst = acc0; *(pDst + S->L) = acc1; *(pDst + 2 * S->L) = acc2; *(pDst + 3 * S->L) = acc3; pDst++; /* Increment the address modifier index of coefficient buffer */ j++; /* Decrement the loop counter */ i--; } /* Advance the state pointer by 1 * to process the next group of interpolation factor number samples */ pState = pState + 4; pDst += S->L * 3; /* Decrement the loop counter */ blkCnt--; } /* If the blockSize is not a multiple of 4, compute any remaining output samples here. ** No loop unrolling is used. */ while(blkCntN4 > 0u) { /* Copy new input sample into the state buffer */ *pStateCurnt++ = *pSrc++; /* Address modifier index of coefficient buffer */ j = 1u; /* Loop over the Interpolation factor. */ i = S->L; while(i > 0u) { /* Set accumulator to zero */ sum0 = 0.0f; /* Initialize state pointer */ ptr1 = pState; /* Initialize coefficient pointer */ ptr2 = pCoeffs + (S->L - j); /* Loop over the polyPhase length. Unroll by a factor of 4. ** Repeat until we've computed numTaps-(4*S->L) coefficients. */ tapCnt = phaseLen >> 2u; while(tapCnt > 0u) { /* Read the coefficient */ c0 = *(ptr2); /* Upsampling is done by stuffing L-1 zeros between each sample. * So instead of multiplying zeros with coefficients, * Increment the coefficient pointer by interpolation factor times. */ ptr2 += S->L; /* Read the input sample */ x0 = *(ptr1++); /* Perform the multiply-accumulate */ sum0 += x0 * c0; /* Read the coefficient */ c0 = *(ptr2); /* Increment the coefficient pointer by interpolation factor times. */ ptr2 += S->L; /* Read the input sample */ x0 = *(ptr1++); /* Perform the multiply-accumulate */ sum0 += x0 * c0; /* Read the coefficient */ c0 = *(ptr2); /* Increment the coefficient pointer by interpolation factor times. */ ptr2 += S->L; /* Read the input sample */ x0 = *(ptr1++); /* Perform the multiply-accumulate */ sum0 += x0 * c0; /* Read the coefficient */ c0 = *(ptr2); /* Increment the coefficient pointer by interpolation factor times. */ ptr2 += S->L; /* Read the input sample */ x0 = *(ptr1++); /* Perform the multiply-accumulate */ sum0 += x0 * c0; /* Decrement the loop counter */ tapCnt--; } /* If the polyPhase length is not a multiple of 4, compute the remaining filter taps */ tapCnt = phaseLen % 0x4u; while(tapCnt > 0u) { /* Perform the multiply-accumulate */ sum0 += *(ptr1++) * (*ptr2); /* Increment the coefficient pointer by interpolation factor times. */ ptr2 += S->L; /* Decrement the loop counter */ tapCnt--; } /* The result is in the accumulator, store in the destination buffer. */ *pDst++ = sum0; /* Increment the address modifier index of coefficient buffer */ j++; /* Decrement the loop counter */ i--; } /* Advance the state pointer by 1 * to process the next group of interpolation factor number samples */ pState = pState + 1; /* Decrement the loop counter */ blkCntN4--; } /* Processing is complete. ** Now copy the last phaseLen - 1 samples to the satrt of the state buffer. ** This prepares the state buffer for the next function call. */ /* Points to the start of the state buffer */ pStateCurnt = S->pState; tapCnt = (phaseLen - 1u) >> 2u; /* copy data */ while(tapCnt > 0u) { *pStateCurnt++ = *pState++; *pStateCurnt++ = *pState++; *pStateCurnt++ = *pState++; *pStateCurnt++ = *pState++; /* Decrement the loop counter */ tapCnt--; } tapCnt = (phaseLen - 1u) % 0x04u; /* copy data */ while(tapCnt > 0u) { *pStateCurnt++ = *pState++; /* Decrement the loop counter */ tapCnt--; } } #else /* Run the below code for Cortex-M0 */ void arm_fir_interpolate_f32( const arm_fir_interpolate_instance_f32 * S, float32_t * pSrc, float32_t * pDst, uint32_t blockSize) { float32_t *pState = S->pState; /* State pointer */ float32_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */ float32_t *pStateCurnt; /* Points to the current sample of the state */ float32_t *ptr1, *ptr2; /* Temporary pointers for state and coefficient buffers */ float32_t sum; /* Accumulator */ uint32_t i, blkCnt; /* Loop counters */ uint16_t phaseLen = S->phaseLength, tapCnt; /* Length of each polyphase filter component */ /* S->pState buffer contains previous frame (phaseLen - 1) samples */ /* pStateCurnt points to the location where the new input data should be written */ pStateCurnt = S->pState + (phaseLen - 1u); /* Total number of intput samples */ blkCnt = blockSize; /* Loop over the blockSize. */ while(blkCnt > 0u) { /* Copy new input sample into the state buffer */ *pStateCurnt++ = *pSrc++; /* Loop over the Interpolation factor. */ i = S->L; while(i > 0u) { /* Set accumulator to zero */ sum = 0.0f; /* Initialize state pointer */ ptr1 = pState; /* Initialize coefficient pointer */ ptr2 = pCoeffs + (i - 1u); /* Loop over the polyPhase length */ tapCnt = phaseLen; while(tapCnt > 0u) { /* Perform the multiply-accumulate */ sum += *ptr1++ * *ptr2; /* Increment the coefficient pointer by interpolation factor times. */ ptr2 += S->L; /* Decrement the loop counter */ tapCnt--; } /* The result is in the accumulator, store in the destination buffer. */ *pDst++ = sum; /* Decrement the loop counter */ i--; } /* Advance the state pointer by 1 * to process the next group of interpolation factor number samples */ pState = pState + 1; /* Decrement the loop counter */ blkCnt--; } /* Processing is complete. ** Now copy the last phaseLen - 1 samples to the start of the state buffer. ** This prepares the state buffer for the next function call. */ /* Points to the start of the state buffer */ pStateCurnt = S->pState; tapCnt = phaseLen - 1u; while(tapCnt > 0u) { *pStateCurnt++ = *pState++; /* Decrement the loop counter */ tapCnt--; } } #endif /* #ifndef ARM_MATH_CM0_FAMILY */ /** * @} end of FIR_Interpolate group */