Design an IIR band pass using Matlab and analyze

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ECET 350 Topic 7 Lab DeVry

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.

1. IIR Band Pass Filter Frequency Magnitude Response Graph
2. IIR Band Pass Filter Phase Response Graph
3. 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.

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