ECET 350 Topic 1 Analog Active Filter Design Sallen-Key and Multifeedback Circuits
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ECET 350 Full Course DeVry
ECET 350 Topic 1 Analog Active Filter Design Sallen-Key and Multifeedback
Circuits
ECET 350 Topic 1 Discussion
WEEK 1: ACTIVE FILTER DESIGN PARAMETERS
What are the features you would consider
essential if you were designing your perfect amplifier? Define the values for
parameters, such as input resistance, output resistance, and voltage gain.
WEEK 1: ACTIVE FILTER COMPONENT CHOICES
Give a thorough discussion about why you
chose a certain value for your perfect amplifier parameter (one of input
resistance, output resistance, and voltage gain only).
ECET 350 Topic 1 Lab 1 Sallen-Key Active Filter Design
Objectives
- Design and simulate a Butterworth, low-pass
Sallen-Key active filter
Tools Needed
- Multisim Software
Introduction
Active filters are key elements in both analog and
digital signal processing. In this lab, you will first design, and using
Multisim, simulate a Butterworth type, Sallen-Key low-pass filter comparing the
design specifications against the simulation. Next, you are to actually
construct the designed Butterworth and test its response measured against the
design specifications, noting any differences between the simulated filter and
the actual filter.
Deliverables
Answer all questions, complete all tables, and paste all
figures and graphs in the Week 1 Lab Cover Sheet here (Links
to an external site.) .
Submit your Week 1 Lab Cover Sheet.
You can also download the Week 1 Cover Sheet for the Week
1 Lab in the Files section of the Course Menu.
Required Software
Multisim and Excel
Lab Steps
STEP 1: Butterworth, Low-Pass Sallen-Key Active Filter
Design
In this part, you will design an active
low-pass filter with the following specifications.
Second-order low-pass filter, 3-dB ripple at
the cut-off frequency of 3 kHz, type: Butterworth, circuit topology (VCVS):
low-pass Sallen-Key circuit
The second-order, low-pass prototype for
Butterworth type is given as
HP(s)=Hos2+1.4142s+1HP(s)=Hos2+1.4142s+1where
HoHois DC gain to be determined, and the cut-off frequency
ωC=2π.3000ωC=2π.3000rad/s.
1. Determine the transfer function using
low-pass to low-pass transformation:
s=sωCs=sωC. Include your answer in the Lab cover report and from the
transform function, identify the b0 and b1 coefficients.
H (s) = H (s) = bo = bo =
b1=b1=Choose the second-order, Sallen-Key low-pass filter shown
in Figure 1.
Figure 1: Second-Order, Sallen-Key Low-Pass
Filter
Based on circuit analysis, the circuit
transfer function of the Sallen-Key low-pass filter shown in Figure 1 is given
below.
G(s)=VoutVin=Gbos2+b1s+boG(s)=VoutVin=Gbos2+b1s+boWhere
G=1+R4R3,bo=1R1R2C1C2G=1+R4R3,bo=1R1R2C1C2b1=1R1C2+1R2C2−R4R2R3C1b1=1R1C2+1R2C2−R4R2R3C1To solve for
circuit parameters, one of the solutions could be determined using the
following conditions.
C1=C2=0.01μFC1=C2=0.01μFand
R1=R2R1=R2.
2. By matching coefficients of the
Butterworth filter transfer function,
H(s),H(s),with the Sallen-Key circuit transfer function
,G(s),G(s), the design formulas are found below. Calculate values
for the circuit parameters, and include your answers in the Lab cover report.
R1=R2=√1boC1C2=R1=R2=1boC1C2=For a Butterworth response, the ratio of
R4R3R4R3may be set at 0.586. If R3 is selected to be 10 kΩ,
calculate the value for R4 and copy all calculation and values for R1, R2, R3,
and R4 in the Week 1 Lab cover report.
R1=R2=R3=R4=R1=R2=R3=R4=3. Calculate the theoretical filter gains, and complete
the calculated entries in Table 1 in the Lab cover report for verification.
Note: The pass band ripple, Ap, for this type of Butterworth filter you may
assume is approximately 3 dB.
Ho=G=1+R4R3=G(dB)=20logG=Ho=G=1+R4R3=G(dB)=20logG=ϵ2=10Ap(dB)10−1=ϵ2=10Ap(dB)10−1=MC=Ho√1+ϵ2=MC(dB)=20logMC=MC=Ho1+ϵ2=MC(dB)=20logMC=Roll-off
rate:
RR≅−20N=RR≅−20N=(dB/decade) where N is the order of the filter.
Where
G(dB)G(dB): the filter DC gain
MC(dB)MC(dB): the gain at
ωCωC(radians/sec)
ωCωC: the cut-off frequency
APAP: the passband ripple (dB)
HoHo: the filter passband gain
RRRR: the roll-off rate (dB/decade)
4. Use MultiSim to simulate the designed
Sallen-Key circuit and verify DC gain, gain at the cutoff frequency, and
roll-off rate from the Bode plotter. Copy the Multisim schematic of your
filter, and paste it into the Week 1 Lab cover report. Next, copy the steady
state frequency response from the Bode-plotter, and paste it into the Week 1
Lab cover report, as well.
Complete the measured entries in Table 1 in
the Week 1 Lab cover report.
Note that for the low-pass filters, the
estimated roll-off rate is
RR(dbdecde)=G1(dB)−G2(dB)logf1−logf2=G1(dB)−G2(dB)log(f1f2)RR(dbdecde)=G1(dB)−G2(dB)logf1−logf2=G1(dB)−G2(dB)log(f1f2)where
G1G1at frequency
f1f1and
G2G2at frequency
f2f2are two measured gains beyond the cutoff frequency. You
may also want to modify the Bode output window to record measurements over a
wider range of frequencies and magnitudes.
Figure 2: Multisim Example of Filter Simulation—Values
Are Not Correct for This Lab
ECET 350 Topic 1 Course Project
TEAM FORMATION
The class will be organized into teams with 3-4 students
per team. In Week 1, you will work on team formation and selection of the focus
of the course project. Week by week, you will work as a team to build out the
final course project deliverable due in week 7. Note! All teams must be approved by the instructor.
See the Course Project Overview in Introduction and
Resources.
ECET 350 Topic 2 Sampling and Reconstruction of Signals
ECET 350 Topic 2 Discussion
WEEK 2: NYQUIST SAMPLING REQUIREMENTS
You are given an input signal with a maximum
input frequency of 1 kHz. Also, given that the Nyquist criteria of a minimum
sampling frequency is two times the highest input frequency, are there any
potential problems of sampling the input signal at a sampling rate of exactly 2
kHz?
WEEK 2: SAMPLING FREQUENCY AND BIT RESOLUTION
Given a real-time digital signal processing
system, how do the sampling frequency and the number of bits used in performing
the analog-to-digital conversion of an analog input signal impact the design
and performance of the system? What features of the system are affected by
these two factors?
ECET 350 Topic 2 Lab 2 Signal
Sampling and Reconstruction
Objectives
- Use principles of signal sampling and reconstruction to construct
an electronic circuit to sample, hold, and reconstruct the signal.
- Apply the antialiasing and anti-imaging filters to
perform proper simulation of signal sampling and reconstruction.
Software
- Multisim
Introduction
Signal sampling is usually performed by
sampling an analog signal at appropriate rates according to the Nyquist theorem
and then holding the sampled voltage during the time required for the ADC to
convert the voltage level to a binary code (digital value). The analog signal
should be band-limited so that the sampling frequency can be chosen according
to the Nyquist theorem, namely , in which is the maximum frequency or the upper
band of the analog signal.
To ensure that the signal is band-limited, an
antialiasing filter (restricting low-pass filter) is deployed as the first
block in the path of the input signal.
The digital value, the output of ADC, could
be processed using a DSP algorithm mainly composed of a digital filter. After
digitally processing the signal, it has to be reconstructed and delivered back
to the analog world, which is the binary code, and the result of DSP operation
is converted back to a sample and hold voltage level. The converted voltage
levels are further fed to the anti-image filter (smoothing low-pass filter) to
reconstruct the analog signal.
Figure 1A shows the complete signal sampling
and reconstruction system. To investigate signal sampling and reconstruction in
this lab experiment, a simplified system that omits the DSP section is shown in
Figure 1B.
Figures 1A and 1B: Signal Sampling and Reconstruction
If the sampling condition is violated, the
aliasing would occur. This effect will cause undesired frequencies known as
alias frequencies within the information frequency band.
To avoid aliasing, Figure 2A shows the
sampling and reconstruction using an antialiasing filter. Figure 2B shows the
simplified system that omits the DSP section and will be used in this lab
experiment for simulation.
Figures 2A
and 2B: Signal Sampling and Reconstruction With an Antialiasing Filter
Deliverables
Answer all questions, complete all tables, and paste all
figures and graphs in the Week 2 Lab Cover Sheet here (Links
to an external site.) .
Submit your Week 2 Lab assignment.
You can also download the cover sheet for Week 2 Lab in
the Files section of the Course Menu.
Required Software
Multisim
Lab Steps
STEP 1: Antialiasing and Anti-imaging Filter
Specifications
Using MultiSim, construct the circuit shown
as Figure 3.
Set the sampling
rectangular pulses (sampling clock) as the following.
Vp (pulse value) = -5
volts
Period: 0.125 ms
Pulse width 0.02 ms
Set the sinusoidal
voltage source as the following.
Frequency = 1000 Hz
Vp (amplitude)=1
volts=0.707 rms,
DC offset = 1 volt
Explanation of the circuit: Two opamps on the
top are the buffer amplifiers before and after the sampler. Sampler is a JFET
used as analog switch; its gate is driven by the narrow pulse train as
specified above. There are two identical active low-pass filters used for
antialiasing and anti-imaging with second order, Sallen-Key topology.
Before simulation, address the following
questions and include your answers in the Lab cover report.
- Determine the cutoff frequency of the antialiasing and anti-imaging
active filters used in the circuit.
- Frequency of the signal to be sampled
- Sampling period
- Sampling frequency
- Is the sampling theorem satisfied? Justify your answer.
- Predict the frequencies and estimated voltage
amplitude of each frequency in the range from 0 Hz to 10 kHz of the
sampled signals according to the sampling theorem.
Figure 3: Sampling and Reconstruction Circuit As Built in
MultiSim
STEP 2: Antialiasing and Anti-imaging Filter Simulation
Open the first spectrum analyzer by left
double clicking on the icon.
In the frequency section, set start to 0 Hz
and end to 10 kHz. Then click on Enter.
Set the amplitude range to 0.25 V/Div and
Lin(Linear) display.
Set the frequency resolution to 100 Hz.
Start the simulation by clicking on the power
switch in the top right hand corner of the window.
Copy the screen display on the spectrum
analyzer to include in your report, use Alt+Print Scrn buttons to capture the
spectrum analyzer view only when it is selected, and paste it in your Lab cover
report in the section marked antialiasing and anti-imaging spectrum analyzer
screen capture.
Using the mouse, move the cursor so that it overlays the
center of the spectral signal on the simulator. Use the cursor to measure the
frequency and RMS voltage for each peak from 0 to 10 kHz, and record your
measurements in Table 1 in your Lab cover report.
STEP 3: Signal Reconstruction Simulation
The original signal can be fully recovered by
low-pass filtering (anti-image filtering) the sampled signal if the sampling
condition is satisfied.
Left double click on the second spectrum
analyzer attached to the low-pass filter.
Run the simulation using the same setting of
the spectrum analyzer.
Copy the screen display on the spectrum analyzer to
include in your Lab cover report in the space provided, and label the graph.
Use the spectrum analyzer to answer the questions at the end of the lab.
Include your answers in the Week 2 Lab cover report in the space provided.
STEP 4: Antialiasing Simulation
Now disconnect the input sinusoidal source
from the antialiasing filter, and connect it directly to the buffer preceding
the sampler (see Figure 4).
Set the sinusoidal function as the following.
Frequency = 7000 Hz
Vp (amplitude) =1
volts=0.707 rms,
DC offset = 1 volt
Figure 4: Sampling and Reconstruction Circuit
While Skipping Antialiasing Filter
Left double click on the first spectrum
analyzer attached to the second buffer amplifier before the anti-imaging
filter.
Run the simulation using the same setting of
the spectrum analyzer.
Copy the screen display on the spectrum
analyzer to include in your Lab cover report. Label the graph.
The original signal cannot be fully recovered
by anti-image filtering the sampled signal if the sampling condition is not
satisfied.
Left double click on the second spectrum
analyzer attached to the anti-imaging filter.
Run the simulation using the same setting of
the spectrum analyzer.
Copy the screen display on the spectrum analyzer to
include in your Lab cover report. Label the graph.
STEP 5: Signal Reconstruction Simulation
Now, use the same setting for the sinusoidal
function as the following.
Frequency = 7000 Hz
Vp (amplitude) =1
volts=0.707 rms,
DC offset = 1 volt
Connect the sinusoidal function output to the
input of the antialiasing filter as in Figure 3.
Run the simulation using the same setting for
both of the spectrum analyzers.
Copy the screen display on the spectrum
analyzer 2 on the output of the anti-imaging filter to include in your Week 2
Lab cover report and paste it in the space provided.
Graded Questions
From the first spectrum analyzer captured in Step 3:
- What is the expected frequency after signal reconstruction?
- What is the frequency measured from the spectrum?
- Did you fully recover the original signal?
From the first spectrum analyzer captured in Step 4:
- Frequency of the signal to be sampled
- Sampling frequency
- Is the sampling theorem satisfied?
- List frequencies of the sampled signals in the range
from 0 to 10 kHz.
From the second spectrum analyzer captured in Step 4:
- Did you fully recover the original signal?
- List the aliasing frequencies, if any.
From the spectrum analyzer captured in Step 5:
- Frequency of the signal to be sampled
- Sampling frequency
- Is the sampling theorem satisfied?
- Can you find frequencies of the sampled signals for the
range from 0 to 10 kHz?
ECET 350 Topic 2 HOMEWORK
Chapter 2, pages 49 – 56, problems 2a, 2b, 5,
6, 8, 14, 16, 28
Don’t forget to submit your assignment.
ECET 350 Topic 2 COURSE PROJECT
PRELIMINARY PROJECT DESIGN & PARTS ORDERING
The teams must start to research the design
and find a low power op amp. Don’t forget to order parts that are needed for
the design.
See the Course Project Overview in Introduction and
Resources. Nothing is to be submitted this week.
ECET 350 Topic 3 Difference Equations, Convolution, and Moving Filters
ECET 350 Topic 3 Discussion
WEEK 3: MOVING AVERAGE FILTERS
This stock market uses moving average filters
sometimes to determine the trend analysis of a stock’s performance. Discuss how
you think this filtering of a stock’s value compares to filtering an input
signal. Why do you think this is used for stocks? Can you think of any other
applications of a moving average filter and why it would be useful?
WEEK 3: RECURSIVE AND NONRECURSIVE FILTERS
This week, both infinite (recursive) and
finite (nonrecursive) filters and their responses, along with impulse and step
responses, were discussed. List and discuss examples that might be seen in your
daily life that might be modeled by either of these filters, and tell why you
think they are either recursive or nonrecursive. Would an input to this example
be a step or impulse function? For example, if you are in a large, empty room,
such as a gymnasium, and someone yells out hey, what kind of input is the
shout, and what is the effect or response of the gymnasium?
ECET 350 Topic 3 Lab 3: Digital Filtering and Spectral Effect
Objectives
- To learn how to determine the difference equation given FIR
(Finite-impulse response) or IIR (Infinite Impulse Response) system
coefficients.
- To learn how to determine the FIR transfer function based on the
given difference equation, and learn how to calculate and display
frequency responses of the FIR system and perform digital filtering.
- To learn how to determine the IIR transfer function based on the given
difference equation, and learn how to calculate and display frequency
responses of the IIR systems and perform digital filtering.
- To use Simulink FIR design tool to design various
types of filters and demonstrate the filtering process by composite input
signals.
Software
MATLAB software
Deliverables
Submit your Week 3 Lab for grading.
ECET 350 Topic 3 Homework
Chapter 3 Homework Problems: page 80,
1.a, 1.b, 1.c, 1.d, 2.a, 2.b, 7.a, 7b, 8.a, 8.b,
10. 13, 14, 16.a, 16.b,
Chapter 6 Homework Problems: Page 208
2.a, 9, 10.a, 10.b, 21, 25.a, 25.b
Don’t forget to submit your assignment.
ECET 350 Topic 4 Introduction to Finite Impulse Response Filter Design and
Implementation
ECET 350 Topic 4 Discussion
WEEK 4: COURSE PROJECT (VIDEO POST/PEER REVIEW)
ASSEMBLY OF DESIGN & VIDEO POST 1
The team should have a preliminary design and
parts should be assembled. You should have your first video post this week and
you should also comment on other team discussion post about their design.
See the Course Project Overview in
Introduction and Resources. Remember to submit your video.
ECET 350 Topic 4 Lab 4 IIR and FIR Notch and DC_Blocker Digital
Filter Design
Objectives
- To learn how to determine the difference equation given FIR
(Finite-impulse response) or IIR (Infinite Impulse Response) system
coefficients.
- To learn how to determine the FIR transfer function based on the
given difference equation, and learn how to calculate and display
frequency responses of the FIR system and perform digital filtering using
Matlab.\
- To learn how to determine the IIR transfer function based on the
given difference equation, and learn how to calculate and display
frequency responses of the IIR systems and perform digital filtering using
Matl
Software Needed
- MATLAB
Instructions
ECET 350 Topic 4 Homework
Chapter 7 Homework Problems: Page 290 1.a,
1.b, 7, 28,
ECET 350 Topic 5 Introduction to Band Pass, High-Pass, and Band Stop Finite Impulse
Response Filter Design and Implementation
ECET 350 Topic 5 Discussion
WEEK 5: COURSE PROJECT
INITIAL DESIGN TESTING & VIDEO POST 2
The team should have a design assembled and
ready for testing. You should have your second video post this week and you
should also comment on other team discussion post about their design. You
should have started your research report and oral presentation.
See the Course Project Overview in
Introduction and Resources. Remember to submit your assignment.
ECET 350 Topic 5 Lab 5 Matlab Designed Band Pass Finite Impulse
Response Filters
Objectives
- Design a high order, FIR band pass using Matlab, and
analyze the performance of that filter
Software Needed
- Lab 5 Band Pass FIR, available in the Files section of the Course
Menu
- Excel
- Matlab with Signal Processing Toolbox
Deliverables
Answer all questions, complete all tables, and paste all
figures and graphs in the Week 5 Lab Cover Sheet (Links
to an external site.).
Submit your Week 5 Lab Cover Sheet for
grading.
You can also download the Week 5 Lab Cover Sheet for the
Week 5 Lab in the Files section of the Course Menu.
Lab Steps
STEP 1: Introduction
This lab uses the Parks-McClellan FIR design
algorithm within Matlab to create a relatively high-order bandpass FIR filter
that is to be designed according to specifications given in this handout.
You are to design a band pass FIR filter
using the Sptools Matlab toolbox according to the following specification.
Unlike the windowed, impulse response method discussed in the textbook and
implemented in the previous lab, Matlab uses a completely different algorithm
called the Parks-McClellan filter design algorithm.
This algorithm is an iterative algorithm, meaning it
performs the filter coefficient calculations repeatedly, comparing the design
results with a predetermined error factor until the design results are below
the error factor. The Parks-McClellan algorithm is very efficient, usually
obtaining the desired design criteria with 10 to 12 iterations of the design loop
and error process.
STEP 2: Band Pass Filter Design
The specification for the filter is shown
below. Please note that the specifications correspond directly to parameters
that are to be entered in the Matlab Sptool graphical filter design program.
|
Filter
Type:
|
Equiripple
Band pass
|
|
Filter
Order:
|
Minimum
Order
|
|
Frequency
Specification
|
|
|
Units:
|
Hertz
|
|
Fs
(Sampling Frequency):
|
2000
|
|
Fstop1:
|
380
|
|
Fpass1:
|
400
|
|
Fpass2:
|
600
|
|
Fstop2:
|
620
|
|
Magnitude
Specifications
|
|
|
Units:
|
dB
|
|
Astop1(stop
band attenuation below Fstop1):
|
40
|
|
Apass(pass
band ripple):
|
1
|
|
Astop2(stop
band attenuation above Fstop2):
|
40
|
Once you have opened Matlab, you will need to
open the signal processing toolbox. To do so, from the Matlab command window,
type Sptool, and then press enter. The Sptool session window, shown in Figure
1, should now open. In the filters column, click on New. This should now open
the filter designer window as shown in Figure 2.
Figure 1: Sptool Session Start-Up Window
Figure 2: Filter Designer Window
Reopen the Sptool session window and click on file | save session as
and save your filter design to a location of your choice for later reference.
Please name your filter design session, but please note that Matlab does not
accept long file names or file names with spaces in them.
Next, while still in the Sptool window, move
the cursor to the filters field and click on filt1[design]. Next, click on
edit|name and select filt1. Enter a descriptive name for your filter. Again,
please note that Matlab is fussy about file names so no spaces or special
characters may be used, and it is recommended you use the same name as your
saved session name.
Reopen the filter designer window and using
the parameters provided in the previous section of this lab, enter the band
pass filter design parameters in the appropriate boxes as shown in Figure 2.
Please check your entries, and once you have verified all parameters are
correct, click the Design Filter button at the bottom of the window.
Figure 3: Filter Designer Band Pass Filter
Results
The filter designer window should now change
to a graph of your designed filter’s response as shown in Figure 3.
Leave the filter designer window open, but
click on the Sptool session window and select the name of your filter in the
Filters column.
Click on View, and a new window as shown in
Figure 4 should appear with a new magnitude plot of your filter. Click on Edit
in the menu bar, and then edit the title of the graph to ECET350 Lab 5 Band
Pass Magnitude Response (dB). Copy and paste this graph into your Week 5 Lab
Cover Sheet—Graph 1: FIR Band Pass Filter Frequency Magnitude Response
Graph.
Figure 4: FIR Band Pass Magnitude Response
View
Next, click on analysis and select phase
response on the drop-down menu. A new window with a plot of the phase response
of your filter should appear as shown in Figure 5. Edit the title of this graph
as well to state ECET350 Lab 5 Band Pass Phase Response. Copy and paste this
graph into your Week 5 Lab Cover Sheet—Graph 2: FIR Band Pass Filter Phase
Response Graph.
To obtain the actual filter coefficients
generated by the filter designer, reopen the Sptool session window. Make sure
that your filter is selected and highlighted in the filters column and then
click on the file menu bar item. Once the menu opens, select the export
function as shown in Figure 6.
Once the export window opens, make sure that ONLY your
filter is highlighted in the export list, as shown in Figure 7. Also, make sure
that the export filters as TF objects is unchecked . Once you have
verified this, click on the export to workspace button to export the filter
coefficients into the Matlab workspace window.
Figure 5: FIR Band Pass Phase Response View
Figure 6: Sptool Session Export Menu
Figure 7: Export Filter to Workspace Window
Once the export is complete, open the Matlab
workspace and type the name of your filter appended with .tf.num. For example,
if your filter design name was MyBPFIR, then enter MyBPFIR.tf.num and then
press enter. A listing of your filter coefficients should scroll by on the
screen as shown in Figure 8.
Figure 8: Exported Filter
Coefficients—Floating Point
You should note that all of the filters are
listed as floating point numbers. However, for this high of an order digital
filter, there is a good possibility that using floating point emulation on the
Tower system may take too long and corrupt the filter output. The next steps
then involve converting the coefficients to a fixed-point representation and
then exporting the coefficients to a text file, which could be copied into your
CodeWarrior source code and filter coefficients array.
To convert the floating point coefficients to
fixed point, enter the following command in the Matlab command window,
substituting your filter name for filt1.
coefs =
round(filt1.tf.num * 2^15) <ENTER>
This command takes the floating point coefficients, which
are all less than 1.0, and multiplies them by 2 raised to the 15 thpower, which performs the proper integer
scaling for the 9S12 fixed-point math operations. The command then rounds them
to the nearest integer value and saves them in the new vector called coefs.
After you have entered this command, the new integer values should appear in
the Matlab workspace window.
Before you can save your coefficients to a
file, you will need to change the output directory of Matlab. At the top of the
Matlab workspace, change the current directory by clicking the browse (three
dots …) button to change the directory to a location of your choice, such as
your flash drive. After you have done this, save the filter coefficients in a
comma-separated, variable (csv) text file by entering the following command.
csvwrite
(‘filtcoef.txt’, coefs) <ENTER>
Examine your file save location, and you should now see
the file filtcoef.txt. Open the file with a text editor, such as Notepad, and
then copy and paste the filter coefficients into your Week 5 Lab Cover
Sheet—Listing 1: FIR Band Pass Filter Coefficients.
ECET 350 Topic 5 Homework
Chapter 7 Homework Problems: Page
290 2.a, 2.b, 4.a, 4.b, 8, 9, 10, 29, 30,
ECET 350 Topic 6 Introduction to Infinite Impulse Response Filters and Design
Methodologies
ECET 350 Topic 6 Discussion
WEEK 6: COURSE PROJECT (VIDEO/PEER REVIEW)
FINAL DESIGN TESTING & VIDEO POST 3
The team should have a final design assembled
and tested. You should have your third video post this week and you should also
comment on other team discussion post about their design. You should also be
fine tuning your research report and oral presentation. Next week is show
time!!
See the Course Project Overview in
Introduction and Resources. Remember to submit your assignment.
ECET 350 Topic 6 Lab 6 IIR Digital Filter Design using Bilinear
Transformation
Objectives
- To learn about how to design IIR filters using
Matlab’s bilinear transform command.
Software Needed
- MATLAB
Deliverables
Submit your Week 6 Lab for grading.
Lab Steps
STEP 1:IIR Digital Filter Design using Bilinear
Transformation
ECET 350 Topic 6 Homework
Chapter 8 Homework Problems: Page 392
1, 3, 6, 9
ECET 350 Topic 7 Advanced Infinite Impulse Response Filters and Design Methodologies
ECET 350 Topic 7 Discussion
WEEK 7: COMPARISON OF BUTTERWORTH AND CHEBYSHEV TYPE I
FILTERS
Various comparisons are stated in the text and the
lecture material between Butterworth and Chebyshev Type I IIR filters. What
sort of criteria do you think should be used in deciding which type of filter
to use?
WEEK 7: COEFFICIENT QUANTIZATION IN IIR FILTERS
Coefficient quantization has been demonstrated to have a
significant effect on the processing of digital IIR filters. How do you think
the introduction of feedback terms in IIR filters is affected by quantization,
and is it more or less critical than the effect upon FIR filters? Include in
your answer any differences or comparisons you have noticed between the aky[n-k] filter coefficients and the bkx[n-k] filter coefficients.
ECET 350 Topic 7 Lab 7 Infinite Impulse Response Band Pass Filters
Objectives
- Design an IIR band pass using Matlab and analyze
Software Needed
- Lab 7 Band Pass FIR, available in the Files section of the
Course Menu
- Excel
- Matlab with Signal Processing Toolbox
Deliverables
Answer all questions, complete all tables, and paste all
figures and graphs in the Week 7 Lab Cover Sheet (Links
to an external site.).
Submit your Week 7 Lab Cover Sheet for
grading.
You can also download the Week 7 Lab Cover Sheet for the
Week 7 Lab in the Files section of the Course Menu.
Lab Steps
STEP 1: Introduction
This lab uses the Sptool box and filter
design and analysis tool within Matlab to design a Chebyshev Type I band pass
IIR filter using specifications given in this handout.
You are to design a band pass IIR filter using the Sptool
s Matlab toolbox according to the provided specification. This algorithm is an
iterative algorithm, meaning it performs the filter coefficient calculations
repeatedly, comparing the design results with a predetermined error factor
until the design results are below the error factor. The algorithm is very
efficient, usually obtaining the desired design criteria with 10- to
12-iterations of the design loop and error process.
High-Order Pass Band Pass Filter Design
The specification for the filter is shown
below. Please note that the specifications correspond directly to parameters
that are to be entered in the Matlab Sptool graphical filter design program.
|
Filter
Type:
|
Band
pass
|
|
Design
Method:
|
IIR
Chebyshev Type I
|
|
Filter
Order:
|
Minimum
Order
|
|
Frequency
Specification
|
|
|
Units:
|
Hertz
|
|
Fs
(Sampling Frequency):
|
2,000
|
|
Fstop1:
|
380
|
|
Fpass1:
|
400
|
|
Fpass2:
|
600
|
|
Fstop2:
|
620
|
|
Magnitude
Specifications
|
|
|
Units:
|
dB
|
|
Astop1
(stop band attenuation below Fstop1):
|
40
|
|
Apass
(pass band ripple):
|
1
|
|
Astop2
(stop band attenuation above Fstop2):
|
40
|
Once you have opened Matlab, you will need to
open the signal processing toolbox. To do so, from the Matlab command window,
type Sptool and then press enter. The Sptool session window, shown in Figure 1,
should now open. In the filters column, click on new. This should now open the filter
designer window, as shown in Figure 2.
Figure 1: Sptool Session Startup Window
Figure 2: Filter designer Window
Reopen the Sptool session window and click on file | save session
as, and save your filter design to a location of your choice for later
reference. Please name your filter design session, but please note that Matlab
does not accept long file names or file names with spaces in them.
Next, while still in the Sptool window, move
the cursor to the filters field and click on filt1[design]. Next, click on
edit|name and select filt1. Enter a descriptive name for your filter. Again,
please note that Matlab is fussy about file names so no spaces or special
characters may be used, and it is recommended you use the same name as your
saved session name.
Reopen the filter designer window and, using
the parameters provided in the previous section of this lab, enter the band
pass filter design parameters in the appropriate boxes as shown in Figure 2.
Please check your entries, and once you have verified all parameters are
correct, click the design filter button at the bottom of the window.
Figure 3: Filter Designer Band Pass Filter
Results
The filter designer window should now change
to a graph of your designed filter’s response as shown in Figure 3 and that the
magnitude response matches that of the desired filter specifications.
Notice that in the top left-hand box, it
states that the order of the filter is 20 and that the sections are 10 and that
the structure is direct-form II, second order sections. This means that the
filter coefficients that the filter design software has calculated are in 10,
second-order polynomials. In order to implement this in software, we will need
to modify the filter implementation software to calculate the product of 10,
second-order polynomials.
A new issue that we are facing with IIR
filters that was not so large of a problem with FIR filters is that of the
coefficient precision and dynamic range. To see this, go to the filter designer
menu bar, click on analysis, and then filter coefficients as shown in Figure 4.
Figure 4: IIR Band Pass Filter Coefficient
Analysis Menu
What should appear next is shown in Figure 5.
This is a listing of all of the numerator and denominator coefficients of the
10, second-order polynomials that would be used to implement the filter that
has been designed. You can scroll up and down to view the coefficients. This
may be done as a product of polynomials, which would require a significant
modification to the software that was used in earlier labs that implemented the
FIR filters.
Figure 5: IIR Band Pass Filter Coefficients
View
The Matlab filter design software is capable
of modifying the design so that the coefficients are implemented as a
single-stage polynomial. To do this, click on edit and then convert to single
section as shown in Figure 6.
Figure 6: Convert IIR Filter to Single
Section
After this is done, the coefficients may be
viewed by going to the filter designer menu bar, click on analysis, and then
filter coefficients as was shown earlier in Figure 4. Figure 7 now shows the
single stage (or section) filter coefficients, which is now in the form of a
tenth-order polynomial.
Figure 7: IIR Single-Section Filter
Coefficients
Scroll up and down in the filter coefficients
window and inspect the coefficients. One thing that should be instantly
recognized is the very large dynamic range from smallest coefficient in the
numerator to the largest coefficient in the denominator. Ignoring any
coefficients with more than seven leading zeros (which would be set to zero in
the software) yields the following coefficients.
Smallest numerator coefficient:
0.000000029286166789081516
Largest denominator coefficient: 141.81011580196366
STEP 3: Single Section IIR Band Pass Filter Design
While it is possible to implement the 10,
second-order stages, this lab will stay with a single stage implementation
approach by reducing the filter performance specification, and thereby, simplifying
the filter design and order.
Reopen the filter design and analysis tool
window, and modify the filter design to reflect the following new
specifications.
|
Filter
Type:
|
Band
pass
|
|
Design
Method:
|
IIR
Chebyshev Type I
|
|
Filter
Order:
|
Minimum
Order
|
|
Frequency
Specification
|
|
|
Units:
|
Hertz
|
|
Fs
(Sampling Frequency):
|
2,000
|
|
Fstop1:
|
200
|
|
Fpass1:
|
400
|
|
Fpass2:
|
600
|
|
Fstop2:
|
800
|
|
Magnitude
Specifications
|
|
|
Units:
|
dB
|
|
Astop1
(stop band attenuation below Fstop1):
|
40
|
|
Apass
(pass band ripple):
|
1
|
|
Astop2
(stop band attenuation above Fstop2):
|
40
|
Once you have entered these specifications,
click on the design filter button, and you should now see what is shown in
Figure 8.
Figure 8: Single Section IIR Band Pass Filter
Design
Convert the design to a single section design
as you did before, and you should now see the results as shown in Figure 9.
This filter is easily implemented on the Tower system.
Figure 9: Single Section IIR Filter
Coefficients
For your Lab Cover Sheet, you will need to
provide three documents from the filter design and analysis tool.
- IIR Band Pass Filter Frequency Magnitude Response Graph
- IIR Band Pass Filter Phase Response Graph
- IIR Band Pass Filter Single Section Filter
Coefficients
Graph 1: These may all be obtained by opening
the Sptool startup window as shown in Figure 1. Click on view and a new window
should appear with a new magnitude plot of your filter. Click on edit in the
menu bar, and then edit the title of the graph to “ECET 350 Lab 7 IIR Band Pass
Magnitude Response (dB).” Copy and paste this graph into your Week 7 Lab Cover
Sheet.
Graph 2: Next, click on analysis and
select phase response on the drop down menu. A new window with a plot of the
phase response of your filter should appear. Edit the title of this graph as
well to state “ECET 350 Lab 7 IIR Band Pass Phase Response.” Copy and paste
this graph into your Week 7 Lab Cover Sheet.
Graph 3: Lastly, but not least, click on analysis and
select filter coefficients on the drop down menu. A new window with a listing
of your single structure filter coefficients will open. Copy and paste this
graph into your Week 7 Lab Cover Sheet.
ECET 350 Topic 7 Homework
Chapter 8 Homework Problems: Page 394
11, 12, 14, 15
ECET 350 Topic 7 Course Project
Course Project written report and project
presentation due.
See the Course Project Overview in Introduction and
Resources. Remember to submit your assignment.
ECET 350 Topic 8 FINAL EXAM
ECET 350 Topic 8 Discussion
WEEK 8: LOOKING AHEAD
Class, looking back over the Course Objectives for this
course, what are you looking forward to learning more about throughout your
education and career?
WEEK 8: FINAL EXAM
INSTRUCTIONS
Here is some information about the Final Exam.
- This Final Exam covers COs 1, 2, 3, 4, 5, 6, and 7 and Chapters 2,
3, 4, 5, 9, and 10.
- This Final Exam is worth 240 total points and includes
- 14 multiple choice questions worth 5 points each;
- five short answer questions worth 10 points each; and
- six essay questions worth 20 points each.
- You have 3 hours and 30 minutes to finish the Final Exam.
- When the time limit is reached you will be exited
from the exam.
Good luck!
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