### AN2276.pdf

```THIS SPEC IS OBSOLETE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
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
2a
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
mov A,[cAccum + 1] ;return(cAccum)
mov A,[cAccum]
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
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AN2276
pop
A
[iAccum + HighByte],A
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]
mov A,[iAccum + LowByte]
swap A,X
mov A,[iAccum + HighByte]
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
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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
m0
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.
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
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.
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.
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May 6, 2014
Document No. 001-32902 Rev. *C
6
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