THIS SPEC IS OBSOLETE Spec No: 001-32902 Spec Title: BINARY WEIGHTED SINGLE-POLE IIR LOW-PASS FILTERS IN PSOC(R) 1 - AN2276 Sunset Owner: Meenakshi Sundaram Ravindran [msur] Replaced by: 001-38007 Binary Weighted Single-Pole IIR Low-Pass Filters in PSoC® 1 AN2276 Author: Dave Van Ess Associated Project: Yes ® Associated Part Family: Any PSoC 1 Parts Software Version: PSoC Designer™ 5.1 Associated Application Notes: AN2099 Abstract ® AN2276 describes how to implement binary weighted single pole infinite impulse response (IIR) low-pass filters in PSoC 1. Many applications require filtering data after it is in a sampled digital form. This was previously discussed in Application Note ® AN2099 – PSoC 1/3/5 - Single-Pole IIR Filters: To Infinity And Beyond. A brief review of low-pass IIR filters is given. Equations are developed and software is presented to implement this topology giving the user access to filter routines in either assembly or ‘C’. PSoC 3 and 5 are capable of implementing digital filters in their dedicated digital filter block (DFB), and are not covered in this application note. Introduction A single-pole IIR low-pass filter is easy to implement. It requires: Equation 1 defines the system while Equation 2 defines the transfer function: Vin Vlp z 1 a Subtraction Vlp Division Addition This was covered in Application Note AN2099 – ® PSoC 1/3/5 - Single-Pole IIR Filters: To Infinity And Beyond and should be reviewed by the reader prior to reading this application note. n For special cases, where the divisor is a binary value (2 ), the division can be reduced to a number ( n ) of shifts. Infinite Impulse Response Filters Figure 1 shows the topology for an IIR low-pass filter. In this type of filter, the current output is made up of the previous output attenuated by some amount, plus the current input attenuated by some amount. Figure 1. IIR Topology for Low-Pass Filter V(n)in Vin 1 a Accum V(n)lp Vlp z 1 Vlp 1 1 a( z 1) Equation 1 Equation 2 The conversion from a z transform to a Laplace transform requires Equation 3: s z e fs 1 s fs { f s : SampleRate} Equation 3 Substituting Equation 3 into Equation 2 results in the Laplace transfer Equation 4: Vlp Vin 1 Equation 4 a 1 s fs The roll-off frequency f 0 is shown in Equation 5: f0 fs 2a Equation 5 The roll-off frequency is dependent on the sample frequency fs, but more importantly, the attenuation value a . Merely changing the attenuation value easily changes the filter’s roll-off frequency. n If the attenuation value is limited to a binary value (2 ), the division operation is simplified and can be implemented with a series ( n ) of right shifts. May 6, 2014 Document No. 001-32902 Rev. *C 1 AN2276 An IIR Low-Pass Filter in Three Easy Steps The three steps to implement the filter just described are listed as follows: 1. Subtract the old output signal from the input signal. vin vout z 1 2. Shift right n times. vin vout z 1 2n 3. Equation 6 Equation 7 swap A,X ; rrc A ; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; adc [cAccum + 1],A ;cAccum += iTemp swap A,X adc [cAccum],A mov A,[cAccum + 1] ;return(cAccum) add A,80h mov A,[cAccum] adc A,0 RAM_EPILOGUE RAM_USE_CLASS_4 ret Add to old output. vout z 1 vin vout z 1 2n Equation 8 Two examples of this type of filter are shown. Both have an attenuation value of 4 (achieved with 2 bitwise shifts to the right). cLowPass4th implements a filter for 8-bit signed values and is located in cLowPass.asm. iLowPass4th implements a filter for 16-bit signed values and is located in iLowPass.asm. The functions SetAccum_for_cLowPass and SetAccum_for_iLowPass are included to initialize the filters’ accumulators. cLowPass.h and iLowPass.h are also included to allow ‘C’ programs access to these functions. All four of these files are located in the project file associated with this Application Note. This project was implemented using the CY8C27xxx base part, but it easily can be cloned to any member of the PSoC 1 family. The function cLowPass4th requires 101 CPU cycles. This is shown in Code 1. Code 1. The Function cLowPass4th ;;--------------------------------------;; char cLowPass4th(int) ;; iAcumm = iAccum + (Input-iAccum)/4 ;; Input = A ;; Output = A ;;--------------------------------------cLowPass4th: _cLowPass4th: RAM_PROLOGUE RAM_USE_CLASS_4 RAM_SETPAGE_CUR (>iAccum) mov X,0 ;cTemp = Input swap A,X sub A,[cAccum + 1] ;cTemp -= iAccum swap A,X sbb A,[cAccum] asr swap rrc ;one swap asr A ;cTemp >> A,X A section per addition shift; A,X ;cTemp ; A ; May 6, 2014 The function iLowPass4th requires 182 CPU cycles as shown in Code 2. Code 2. The function iLowPass4th ;--------------------------------------; int iLowPass4th(int) ; iAcumm = iAccum + (Input-iAccum)/4 ; Input = X,A ; Output = X,A ;--------------------------------------iLowPass4th: _iLowPass4th: RAM_PROLOGUE RAM_USE_CLASS_2 RAM_PROLOGUE RAM_USE_CLASS_4 RAM_SETPAGE_CUR (>lAccum_) push X ;&iTemp = Input mov X,SP push A mov A,0 sub A,[iAccum + Residue] ;iTemp-=iAccum push A mov A,[iAccum + LowByte] sbb [X +LowByte],A mov A,[iAccum + HighByte] sbb [X + HighByte],A pop A ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; asr [X + HighByte] ;iTemp >> rrc [X + LowByte] rrc A ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;one for each shift;;;;;;;;;;;;;;;;;;; asr [X + HighByte] ;iTemp >> ; rrc [X + LowByte] ; rrc A ; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; adc [iAccum +Residue],A ;iAcumm+= iTemp pop A adc [iAccum + LowByte],A Document No. 001-32902 Rev. *C 2 AN2276 pop adc A [iAccum + HighByte],A Build Your Own Both filters shown have attenuation of 4 and, by definition, a roll-off frequency approximately 4% of the sample frequency, as shown in Equation 5. If a steeper roll off is required, the attenuation needs to be increased. For this example, the iLowPass4th function is used to construct an iLowPass8th function. It is done in four steps. ;return(iAccum) mov A,[iAccum + Residue] add A,80h mov A,[iAccum + LowByte] adc A,0 swap A,X mov A,[iAccum + HighByte] adc A,0 swap A,X RAM_EPILOGUE RAM_USE_CLASS_4 RAM_EPILOGUE RAM_USE_CLASS_2 Ret 1. #pragma fastcall16 iLowPass4th extern int iLowPass4th(int iSample); Duplicate these two lines and change the names from iLowPass4th to iLowPass8th as follows: #pragma fastcall16 iLowPass4th extern int iLowPass4th(int iSample); #pragma fastcall16 iLowPass8th extern int iLowPass8th(int iSample); This allows the ‘C’ programs access to the new function. The code to test these functions is shown in Code 3. Code 3. IIR Test Program //------------------// IRR Test Program //------------------#include <m8c.h> #include "PSoCAPI.h" #include "cLowPass.h" #include "iLowPass.h" 2. Open iLowPass.asm and find the two lines shown as follows: export iLowPass4th export _iLowPass4th Again, duplicate these lines and change the name to match the new function. The result is shown as follows: int iTemp; char cTemp; long lTemp; void main() { lTemp = lAccum_for_iLowPass; SetAccum_for_cLowPass(0); SetAccum_for_iLowPass(0); while(1){ iTemp = iLowPass4th(512); cTemp = cLowPass4th(100); } } Open iLowPass.h. The first two lines are shown as follows: export iLowPass4th export _iLowPass4th export iLowPass8th export _iLowPass8th This allows all programs access to this new function. 3. Duplicate the function and change the names from iLowPass4th to iLowPass8th. The top 8 lines of the duplicated function are shown as follows: ;-------------------------------------; int iLowPass4th(int) ; iAcumm = iAccum + (Input-iAccum)/4 ; Input = X,A ; Output = X,A ;-------------------------------------iLowPass4th: _iLowPass4th: The change is shown as follows: ;-------------------------------------; int iLowPass8th(int) ; iAcumm = iAccum + (Input-iAccum)/8 ; Input = X,A ; Output = X,A ;-------------------------------------iLowPass8th: _iLowPass8th: May 6, 2014 Document No. 001-32902 Rev. *C 3 AN2276 The new function now exists, however its operation has not been altered. 4. Find the following lines in the new function: ;;one for each shift;;;;;;;;;;;;;;;;;;; asr [X + HighByte] ;iTemp >> ; rrc [X + LowByte] ; rrc A ; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Duplicate as follows: ;;one for each shift;;;;;;;;;;;;;;;;;;; asr [X + HighByte] ;iTemp >> ; rrc [X + LowByte] ; rrc A ; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;one for each shift;;;;;;;;;;;;;;;;;;; asr [X + HighByte] ;iTemp >> ; rrc [X + LowByte] ; rrc A ; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; The new function has been successfully implemented. It now shifts the difference three times for an attenuation value of 8. Its roll-off frequency is now approximately 2% of the sample frequency, or half the frequency for the attenuation 4 IIR filter. The implementation of filters with even greater attenuation is an exercise left to the reader. The Whole is Greater Than the Sum of the Parts Back in college, you most likely learned that averaging a number of signals together caused the noise to be reduced by the square root of the number of samples. When signal are averaged, it is done in a linear fashion. The results are shown in Equation 9: a 1 Signal Signal a m0 Signal avg Equation 9 However, noise being random, averages are in an RMS fashion. This is shown in Equation 10: Noiseavg a 1 2 Noise Noise a a m 0 Equation 10 So averaging four samples should reduce the noise by a factor of 2. For an IIR filter, again the signals add linearly. The results are shown in Equation 11: Signal avg Signal a 1 Signal avg Signal a a Equation 11 However, the noise, still random, adds in an RMS fashion. The results are shown in Equation 12: May 6, 2014 Noise Noise a 1 Noise Noiseavg a a 2a 1 2 2 Equation 12 So processing the samples with an IIR filter, with an attenuation of 4, reduces the noise by a factor of 2.65. Clearly, this is an improvement over averaging four signals. Seven samples would have to be averaged to get the equivalent reduction. What this boils down to is that the data, when filtered, may pick up resolution. It is possible that it may pick up more resolution than the function type normally returns. To remedy this, the Accumulator, which is really the filter output for iLowPassFilter, is actually a 32-bit wide variable. The next line of code allows ‘C’ access to this variable. extern long lAccum_for_iLowPass And the following code allows assembly language access to this same variable. export lAccum_for_iLowPass export _lAccum_for_iLowPass area bss(RAM) lAccum_for_iLowPass: _lAccum_for_iLowPass: BLK 4 area text(ROM,REL) For the cLowPassFilter, the Accumulator is actually a 16bit wide variable. Its declaration is shown as follows: extern int iAccum_for_cLowPass; Of course, capabilities exist for assembly language access to this variable. The user has two options to retrieve the filter data. 1. Use the output returned by the function call. It is the same resolution as the input data. 2. Call the function and ignore the returned output. Retrieve data in the Accumulator variable. This variable is twice as wide as the input variable, but it now contains the extra resolution. Additional Resources Included with this application note’s project is an excel spreadsheet demonstrating the advantage of an IIR filter over a mere moving average filter. Summary Single-pole IIR filters are very useful in reducing signal noise and are more effective than just averaging the equivalent number of samples. Filters for both 8-bit data (cLowPass4th) and 16-bit data (iLowPass4th) have been presented. Instructions have been given to modify these filters for greater attenuation. Low-pass filters may increase the resolution of the data and methods have been shown to retrieve this extra resolution. Document No. 001-32902 Rev. *C 4 AN2276 About the Author Name: Title: Background: Contact: May 6, 2014 Dave Van Ess Applications Engineer MTS Cypress Semiconductor BSEE from University of California, Berkeley. More than 27 Years experience in circuit, signal processing, digital, software, analog, and system design. Holder of six U.S. Patents (plus three pending) for medical systems, signal processing, and digital block enhancements. Author of numerous Application Notes, web casts, and technical articles. Joined Cypress MicroSystems in 2000. [email protected] Document No. 001-32902 Rev. *C 5 AN2276 Document History ® Document Title: Binary Weighted Single-Pole IIR Low-Pass Filters in PSoC 1 Document Number: 001-32902 Revision ** ECN 1494923 Orig. of Change MAXK Submission Date Description of Change 09/21/2007 OLD APP. NOTE: Obtain spec. # for note to be added to spec. system. Update copyright. Add source disclaimer, revision disclaimer, Samples Request Form link, PSoC App. Note Index link. .pdf has been stamped. **This note had no technical updates. There is an associated project but it was not updated.** *A 3187213 MAXK 03/03/2011 *B 3281359 MAXK 06/13/2011 *C 4371618 MSUR 05/06/2014 Updated title as “AN2276 - Binary Weighted Single-Pole IIR Low-Pass ® Filters in PSoC 1”. Updated Associated Part Family in page 1 as “Any PSoC 1 Parts”. Updated Software Version as “PSoC Designer™ 5.1”. Updated Abstract. Updated Infinite Impulse Response Filters. Updated An IIR Low-Pass Filter in Three Easy Steps. Updated The Whole is Greater Than the Sum of the Parts. Added Additional Resources (information about Excel spreadsheet). No change. Sunset review spec. Removed application note number from the title. Obsolete document In March of 2007, Cypress recataloged all of its Application Notes using a new documentation number and revision code. This new documentation number and revision code (001-xxxxx, beginning with rev. **), located in the footer of the document, will be used in all subsequent revisions. PSoC is a registered trademark of Cypress Semiconductor Corp. "Programmable System-on-Chip," PSoC Designer, and PSoC Express are trademarks of Cypress Semiconductor Corp. All other trademarks or registered trademarks referenced herein are the property of their respective owners. Cypress Semiconductor 198 Champion Court San Jose, CA 95134-1709 Phone: 408-943-2600 Fax: 408-943-4730 http://www.cypress.com/ © Cypress Semiconductor Corporation, 2007-2014. The information contained herein is subject to change without notice. Cypress Semiconductor Corporation assumes no responsibility for the use of any circuitry other than circuitry embodied in a Cypress product. Nor does it convey or imply any license under patent or other rights. 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Cypress does not assume any liability arising out of the application or use of any product or circuit described herein. Cypress does not authorize its products for use as critical components in life-support systems where a malfunction or failure may reasonably be expected to result in significant injury to the user. The inclusion of Cypress’ product in a life-support systems application implies that the manufacturer assumes all risk of such use and in doing so indemnifies Cypress against all charges. Use may be limited by and subject to the applicable Cypress software license agreement. May 6, 2014 Document No. 001-32902 Rev. *C 6

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