DSP Final Paper: Digital Filtering Implementation

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DIGITAL

FILTERINGIMPLEMENTATION

12/10/2012 Digital Signal Processing Final ProjectKerry Chayka

Abstract: The purpose of this project is to implement digital filtering in the

audio frequency range on a physical system designed by the author. The

system will include several digital filters, three with variable parameters

based on user input, and one adaptive to the signal itself. The output of

the filters can be observed using a set of speakers and/or an oscilloscope

as seen in the picture above.


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Digital Filtering Implementation

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Digital Filtering ImplementationD I G I T AL S I G N A L P R O C E S S I N G F I N A L P R O J E C T K E R R Y C H A Y K A

Table of Contents

1|INTRODUCTION AND BACKGROUND ...................................................................................................... 2

2|TECHNICAL APPROACH AND DETAILED ANALYSIS.................................................................................... 3

Microprocessor Selection ................................................................................................................................................... 3

Analog Design ..................................................................................................................................................................... 4Digital Filter Design ............................................................................................................................................................ 6

Programming Requirements .............................................................................................................................................. 7

PCB Design ........................................................................................................................................................................... 8

3|SYSTEM OPERATION .............................................................................................................................. 12

Diagram of Boards Used ................................................................................................................................................. 12

PCB and Breadboard Diagram .................................................................................................................................... 13

Low-Pass Filter ................................................................................................................................................................... 14

High-Pass Filter .................................................................................................................................................................. 15

Band-Pass Filter ................................................................................................................................................................ 16

4|RESULTS ................................................................................................................................................ 17

Normal Operation ........................................................................................................................................................... 17

Low-Pass Filter .................................................................................................................................................................. 18

High-Pass Filter ................................................................................................................................................................. 20

Band-Pass Filter ................................................................................................................................................................ 21

Coefficient Analysis ......................................................................................................................................................... 23

Notable Phenomena ........................................................................................................................................................ 26

5|CONCLUSIONS, RECOMMENDATIONS, AND IMPACT OF WORK .......................................................... 28

Conclusions ........................................................................................................................................................................ 28

Impact on the Education of the Author ......................................................................................................................... 28

Mobile Studio Discussion ................................................................................................................................................. 29

6|REFERENCES ........................................................................................................................................... 30

7|APPENDICES........................................................................................................................................... 31

Appendix A| Microprocessor Code ............................................................................................................................. 31


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1|INTRODUCTION AND BACKGROUND

Digital Filters are used in an enormous number of applications. Digital

communications (as seen in cell phones), audio processing, radar / sonar and data-

acquisition systems are just a few examples. While designing the proper filter for any

given application is difficult in and of itself, implementing that filter on a physical

system becomes a new challenge. Hardware has to be chosen very carefully based on

the frequency range being processed, the range of the data, required bits of

quantization, accuracy of reconstruction required, as well as the architecture of the

processor itself if special functionality is needed. An analog input stage is necessary toprepare the signal for digital processing, as is an output stage for proper

reconstruction. Specially designed PCBs are necessary in most cases to minimize noise

and for high-frequency operation. The challenges of this process are significant;

however the flexibility and power of digital filtering make it worth the extra

complexity.

This project will act as a teaching tool both for the author and for future users of

the system in all of the areas mentioned above. For users, the operation of the onboard

variable digital filters and the observation of the output, both visually and aurally, will

help demonstrate filter design and operation. For the author, the process of designing

and manufacturing such a system provided valuable insight into the design of complex,

multi-discipline systems, a subject which is not taught in any depth in school, and

experience in designing digital filters and creating digital signal processing systems in

general.

To this end, the entire design process will be carried out by the author, using

manufacturers tools and libraries as necessary. This includes microprocessor selection,

analog input & output stage design, digital filter design, code generation, and design

of a printed circuit board to house the system. The system will be manufactured anddemonstrated so the results can be observed. This entire process will be carried out in

the period of seven weeks.


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2|TECHNICAL APPROACH AND DETAILED ANALYSIS

M I C R O P RO C E S S O R S E L E C T I O N

The microprocessor is the most important part of the system because it is where

the digital filtering actually takes place. In this case it is also what samples and

quantizes the input signal (with the integrated analog to digital converter (ADC)), and

reconstructs the output signal (with the integrated digital to analog converter (DAC)).

Since both the ADC and DAC are integrated, additional constraints were put on the

microprocessor, including maximum ADC frequency and DAC sample and hold time. It

was decided, by using the Nyquist Theorem that the sample rate and DAC frequency

should be 50kHz in order to properly sample and reconstruct the signal, and thenumber of bits of quantization should be between 8 and 16 (# of bits of quantization

in radio and CDs respectively.) These numbers also require that the microprocessors CPU

clock speed be high enough to manage all of the data being generated, processed,

and moved around. By calculating the number of instructions required to implement the

most processor-intensive filter (band pass, worst case 100 instructions), multiplying by 3

to find the number of CPU cycles, and dividing the ADC sample period by this number,

the minimum possible CPU clock was found to be 15MHz. Using this information, and

other concerns like manufacturability and cost, the Atmel AT32UC3C264 was selected.

The AT32UC3C264 has maximum ADC clock 1.5MHz, maximum DAC clock 1MHz,

maximum CPU clock 60MHz, and enough memory to implement the program (64kB.)

Although other requirements were considered (GPIO, Peripheral Event Controller, etc)

they are beyond the scope of this report.


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A N A L O G D E S I G N

In order to properly sample and quantize an analog signal, it must be band-

limited and be within a specific voltage range. In this case, the input was band-limited

to 20kHz, and the input voltage limited to 0 1V. For reconstruction, a similar

frequency limit is required due to the high frequency quantization noise of the DAC.

Band-limiting in both the input and output case was accomplished through the

use of a filter network. The original design utilized third order Bessel filters with cutoff

frequency 20kHz due to their linear phase characteristics, however these were later

replaced by second order RC filters due to manufacturing cost. An output high-pass

filter with cutoff frequency 1Hz was included to remove any DC bias added by the

system. A diagram of the input and output networks is shown below. Note that the

system is designed to function with stereo audio signals.

Since audio signals are centered on 0 volts and range from -0.4V to +0.4Vdepending on the source volume, an input stage was needed to add a 0.5V DC bias to

the signal in order to center it in the required range of 0 1V. This was accomplished

with a simple resistor network. It is not shown in the board schematic because it was

added post-manufacturing.

Other concerns included having an appropriate input (and output) impedance so

that the majority of the signal voltage drop would occur over the input stage, and in

the case of the output stage, an appropriate impedance so that most of the signal

voltage drop would occur in the output device (speakers, headphones.) This wasaccomplished through the use of an audio-grade op-amp (TLV2772) and appropriate

resistor values in the input stage. Trimmers are included in the feedback loops of allinput and output op-amps to tune for maximum resolution and for volume control,

respectively.


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Input Filtering Network

Output Filtering Network


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D I G I T AL F I L T E R D E S I G N

The main purpose of this project was to implement variable digital filters to

demonstrate, among other things, the effect of pole and zero locations on the impulse

response of the filter. This presents a major design challenge because filters are almost

always designed to have very specific, known transfer functions, and therefore indirect

design through the analog domain is possible. However, for this project it was necessary

to find the exact effect that each coefficient had on the transfer function and therefore

direct design was necessary. The design process was carried out by hand on paper, but

the final transfer functions of each filter are shown below in the following order: low-

pass, high-pass, band-pass, notch. Hand calculations will be shown on request. The

design parameters , 0, andwill be discussed in the system operation section.

=1

1

=1 +

1

=120 +

+ 120 +

120 +

.05 < < .95

.05 < < .95

= 120

+

120 +

+ 1 20 +


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P R O G R A M M I N G R E Q U I R E M E N T S

Although a microprocessor was selected that exceeds the minimum requirements of

the project, it does not function at these rates initially. In fact, it does not function at all

until code is written to it that initializes the necessary processing blocks. Code wasgenerated by the author to initialize the main clock, CPU clock, peripheral bus clocks,

ADC, DAC, PDCA (peripheral DMA controller), INTC (interrupt controller) and GPIO

(general purpose I/O controller.) Manufacturer libraries were used wherever possible due

to the prototype nature of this project. Additional code was generated to use the ADC,

DAC, PDCA, INTC and GPIO processing blocks as required to implement the filters shown

above. The initialization code will not be described in detail here, as it is beyond the

scope of this report, however the entire program can be found in Appendix A.

The following is a summary of the program operation. The main function includes

calls to the initialization function of each processing block, and a main loop that starts an

ADC sample, waits until the conversion is done, checks if any buttons are pushed

(indicating a call to one of the filter functions,) and then waits again until the necessary

20uS period is completed. DAC output is triggered by interrupt every 20uS, with data

sent to the output register by the PDCA on each interrupt.

Each filter function re-initializes the ADC as necessary, to accommodate the

additional measurement of the potentiometer(s). It then enters a loop in which it starts the

ADC, delays for a few microseconds to ensure conversion, calculates the filter coefficients

and then computes the output value y[n]. This value is then written to a location in memorythat is linked to the PDCA, to be written to the DAC on each output interrupt. The

adaptive notch filter function attempts to compute the coefficients and output value

automatically based on a comparison of the current and previous output values.


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P C B D E S I G N

Due to the nature of the microprocessor being used, a printed circuit board (PCB) was

required to implement this system. The PCB was manufactured through a third party

(OSHPark PCB Fab,) however it was designed and populated by the author. The design

includes the input and output stages, microprocessor and the components it requires for

operation, push-buttons, JTAG programming interface, USB interface, and headers for

expanded use. The design was created using EAGLE, and occurred in several stages.

The first stage was the design of the schematic seen above. This schematic gives the

program the details of component connections. The datasheet of the microprocessor was

used extensively to create this document, and by extension a functioning board.


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The second stage was board layout, the final result of which is shown above. The

program generated a group of components based on the connections in the schematic.

The parts were then laid out on a board and all necessary connections between them,

called traces, were created by hand. Many design requirements were considered

including trace width, part location, trace length in differential communication and

analog lines, proximity of decoupling capacitors, etc.


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The third stage was fabrication. The design was sent to OSHPark PCB fabrication to be

manufactured. Photo credit: OSHPark PCB Fabrication

The fourth stage was population of the board


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The fifth stage was test & modification. As with any project, the first design does not

always function as expected, so all stages of the design must be tested and modified to

match the desired operation. In this case, the only necessary modification was theaddition of the input DC bias resistor network and the potentiometers to control the

variable filters. In order to accommodate these changes, wires were added to the PCB

for power (red), ground (black), audio signal (yellow, green), and potentiometer value

(orange.) These changes will be included on the PCB in any future revisions.


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3|SYSTEM OPERATION

D I A G R A M O F B OA R D S U S E D

1. Rensselaer Mobile Studio The Rensselaer Mobile Studio board was used

extensively as an oscilloscope, arbitrary waveform generator and spectrum

analyzer. Its use will be described and shown in detail in the results section. This

project would not have been possible without this tool.

2. AVR Dragon Programming & Debugging BoardThis board was created by Atmel,

the manufacturer of the microprocessor. It was used to program and debug themicroprocessor.

3. Audio Processing BoardThis board was designed by the author to house the entire

digital processing system. Its operation is described below.

4. Input BreadboardThis breadboard was created to house extra components andmodifications made to the system post-manufacture. Its components are described

below.


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P C B A N D B R E A D B OA R D D I A G R A M

1. Input StageThe signal enters the system through a generic 3.5mm audio jack. The

resistor network adds a 0.5V DC bias.

2. Gain / filtering The signal goes directly into an audio op-amp (TLV2772, IC in

section 2) where the gain for each channel can be selected by the two

potentiometers. The signal then passes through a series of low-pass filters so it can be

band-limited.

3. Filter PotentiometersThese potentiometers are used to vary the parameters of each

variable filter. They will be discussed in greater depth later in this section.

4. MicroprocessorThis is where the sampling, filtering and reconstruction take place. It

is the main IC on the circuit board and the peripheral components needed to ensure

its operation can be seen to the bottom and left of it (resistors, capacitors, JTAG

programming header.) The IC to its right is included to make serial communication with

a computer possible through a USB cable.

5. Output stage / filters The signal will be reconstructed by the DAC inside the

microprocessor, and then sent to the other op-amp in the top right of the board.

Potentiometers are again included for volume control. The signal then passes to a

high-pass filter to remove the DC bias (this is necessary in order to hear the signal

through speakers) and a second-order low-pass filter to remove DAC quantization

noise.

6. Pushbutton Filter Selectors These buttons are used to select which filter is applied.

The order is band-pass, low-pass, high-pass, and vocals (the optional extensionfilter.)


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L O W - P A S S F I L T E R

=1

1 -.95 < < .95

The figureshown to the right is a

diagram of this particular low-

pass filter. Poles and zeros wereconstrained to the real axis for

simplicity. The potentiometer

shown below is mapped directly

to the parameter . In the low-

pass function, the value of that

potentiometer is read

immediately after the audio

channel, and the coefficients are

calculated accordingly. The

segment of code that calculates

the coefficients and computes the

output is shown in the bottom

right.


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H I G H - PA S S F I L T E R

=1

1 -.95 < < .95

The figure shown to the right is a

diagram of this particular high-

pass filter. Poles and zeros wereconstrained to the real axis for

simplicity. The potentiometer

shown below is mapped directly

to the parameter . In the high-

pass function, the value of that

potentiometer is read

immediately after the audio

channel, and the coefficients are

calculated accordingly. The

segment of code that calculates

the coefficients and computes the

output is shown in the bottom

right. =

1 +

1


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B A N D - P A S S F I L T E R

The figure shown to the right is a

diagram of this particular band-pass

filter. A group of poles and zeros wasdesigned such that the entire group will

move together with the parameters r, 0,

and Q (since T is the sample rate

constant).The potentiometers responsible

for r and 0 are shown below. Q is set in

the program header. In the band-pass

function, the value of these

potentiometers is read immediately after

the audio channel, and the coefficientsare calculated accordingly. The segment

of code that calculates the coefficients

and computes the output is shown in the

bottom right.

= 120 +

+ 120 +

120 +


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4|RESULTS

The following sections include screenshots and discussion of the performance of the system

during normal operation (no filter selected), within each filter function, and at any othernotable instance (output quantization, unexpected results). In each figure, the blue

waveform is the input to the board and the green waveform is the output from the board.

Also note that the oscilloscope channel amplitude on the output is half that of the input due

to an internal gain of 2 in the system which is required for appropriate output volume.

N O R M A L O P E R AT I O N

The figure above shows the normal operation of the board with no filters selected. It

can be seen that the output signal does not perfectly match the input signal mainly dueto the high-frequency response of the system. This can be attributed to the use of simple

2nd order RC filters where higher order filters with steeper roll-off would be preferred.

This decision was made for cost and manufacturing purposes and is therefore an

acceptable design trade-off. It is worth noting that the loss of such high frequencies has

very little effect on the music and (for aural concerns) can be ignored.


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L O W - P A S S F I L T E R

From the figure above, the operation of the low-pass filter can be observed. For this test, the

low-pass filter was set with the lowest possible cutoff frequency. Note that the high frequency

oscillations were blocked while the underlying base frequency was passed. In another test, the

system was given a sine wave input that swept from 16Hz to 20kHz and its response was

measured by a spectrum analyzer in order to characterize the impulse response of the low-

pass filter. Several screenshots from the test are shown below.


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H I G H - PA S S F I L T E R

The operation of the high-pass filter can be seen in the figure above. For this test the high-pass filter was set with the highest possible cutoff frequency. Some low frequencyattenuation can be seen, however it is not as much as expected. Although the high

frequencies passed by this filter are partially stopped by the output low-pass filternetwork, it can still be seen that higher frequencies are more present in this signal than innormal operation or the low-pass filter. A frequency sweep was not conducted for thisfilter due to the confounding effects noted above.


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B A N D - P A S S F I L T E R

The operation of the band-pass filter can be seen in the figure above. The potentiometersthat correspond to r and 0 were set to roughly half of the maximum value. Theparameter Q was chosen to be 100 in order to have a very narrow pass-band. This

narrow band can be seen very easily above. The narrow pass band was alsodemonstrated through a sine-sweep test shown in the figures on the next page.


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C O E F F I C I E N T A N A L Y S I S

The main goal of this project was to create a teaching tool for the design of digital filters.

This is possible through examining the output of the system with an oscilloscope, as well as

listening to the output through speakers. However, the best demonstration of the design ofdigital filtering occurs within the code itself. Through the debugger, it is possible to make a

change to just one of the potentiometers and examine the effect that this change has onthe coefficients of the filter. This is best seen in the band-pass filter.

Above is the debugging environment for the band-pass filter before any changes are

made. Note the coefficients of the digital filter, B0, B1, B2, etc shown in white next tothe blue bullet points. These values will become red if they are changed by the program.

At this point, the potentiometer controlling 0 was turned to a new value.


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In the figure above, we can see that after this change occurred, more than one coefficient

became red. This is proof to the reader that one parameter does not necessarily

correspond to a single coefficient. In fact, in this case nearly all of the coefficients are

influenced by 0. This is obvious when the equations for each coefficient are laid out as in

the program above, but it is very much the opposite when looking at the factored transfer

function. To prove that this change wasnt a coincidence, the potentiometer corresponding

to r was changed. Looking at the equations in the program above, we would expect all ofthe coefficients to become red since they all depend on r.


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This is indeed what happens, and by extension we see that many coefficients are related

to both 0 and r. Unfortunately for the DSP student, this property causes significant

complexity to occur in even relatively simple filters such as the three shown in this project,

however it is partially due to this complexity that digital filtering is so highly regarded.


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N O T A B L E P H E N O M E N A

During the course of this project, several interesting results were found. Although expected,the transformation from quantized output to smooth analog waveform through the output

filter network was still interesting and instructive. This phenomenon is shown in the two

figures below. These screenshots were taken before the DC bias network was added,

effectively clipping the input sine wave to purely positive values. The filtered output

waveform demonstrates another interesting phenomenon that will be shown in more detail

later.


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The filtered output signal looks surprisingly like the input, even though the input was

clipped at 0V. This shows the second interesting result of partial-reconstruction of the

original signal through filtering. A more extreme case of this can be seen below, where

even though the input is saturated, the output contains that portion of the signal.


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5|CONCLUSIONS, RECOMMENDATIONS, AND IMPACT OF WORK

C O N C L U S I O N S

This project shows some of the flexibility of digital filtering through the design and

operation of variable digital filters, and the attempt at an adaptive filter. The filters

shown in this project, though basic, demonstrate what is possible with modern

microprocessors and cleverly designed filters. Though the complexity of digital filtering is

intimidating, the benefits afforded by this domain far outweigh the drawbacks in almost

all advanced applications such as radar, image processing, and real-time signals analysis.

I M P AC T O N T H E E D U C A T I O N O F T H E A U T H O R

Through the design and manufacture of this system, many new skills were learned,

including PCB design and fabrication, the integration of analog, digital and DSP systems,

troubleshooting complex systems, and the design of a physical product. These lessons are

unique because they are not taught in school and are extremely beneficial in the work

place. These skills will be carried forward into all future projects and experiences.


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M O B I L E S T U D I O D I S C U S S I O N

Throughout this project, the tool that was relied on most heavily was the Rensselaer Mobile

Studio board. It was used in all steps of the physical manufacturing and debugging of the

system, and was invaluable in demonstrating the systems operation. The oscilloscope andspectrum analyzer functions were used mainly, although the digital I/O function was useful

in debugging the filter selection switch connections, and actually led to the discovery of afaulty switch. An advanced project such as this is not possible without the ability to fully

debug any point of the system, and the Mobile Studio was an invaluable tool in this

regard. The Mobile Studio is shown in the picture below, assisting in the debugging of the

system.


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6|REFERENCES

Atmel Corporation, 2012. AT32UC3C Datasheet. [online] Place: Producer/Publisher.

Available at:http://www.atmel.com/images/32117s.pdf[Oct. 2012].

Oppenheim, Alan V., and Ronald W. Schafer. Discrete-time Signal Processing. Upper

Saddle River: Pearson, 2010. Print.

"OSH Park." OSHPark PCB Fabrication. Laen, Jan. 2010. Web. 4 Nov. 2012.

.
http://www.atmel.com/images/32117s.pdfhttp://www.atmel.com/images/32117s.pdfhttp://www.atmel.com/images/32117s.pdfhttp://www.atmel.com/images/32117s.pdf


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7|APPENDICES

A P P E N D I X A | M I C R O P RO C E S S O R C O D E

DSP Final Paper: Digital Filtering Implementation

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