WEEK 7: COMPARISON OF BUTTERWORTH AND CHEBYSHEV TYPE I FILTERS
Just Click on Below Link To Download This Course:
http://bit.ly/2JUgYxV
ECET 350 Topic 7 Complete DeVry
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.
Comments
Post a Comment