The purpose of this lab is to enhance the ECE311 student's understanding of filter behavior and filter design and to provide the student the opportunity to demonstrate skills in linear system analysis and design that may not be apparent from their exams.

In Lab 4 you learned about Butterworth and Chebychev I and II filters, used as low pass filters. In this lab you will learn more about these filters as well as Elliptic filters, used as bandpass filters rather than low pass filters. You will not be given explicit, step-by-step instructions. Rather, these instructions are broadly stated, and it is your responsibility to create the specific steps to achieve the objectives of the lab.

1. Understanding Elliptic filters: Elliptic filters are a class of filters that are well understood and well documented, even though their treatment in our textbook is extremely brief. Using whatever resources you choose, describe:

a) The filter characteristic which these filters optimize (do a better job than any other filter) and

b) The equations describing n-th order elliptic filters.

Use the MATLAB 'help' command to investigate the built-in elliptic function. Then build some filters and display the results using 'plotLTP.m'. Include a sample of these results in your lab report.

2. While low pass filters are easy to create using MATLAB and are well described in references, bandpass filters are frequently used, especially in modern communication systems. Transformation of low pass filters to bandpass filters is straightforward, and is described in your textbook as well as many other references. Understand this transformation by reading whatever references you may need to help you understand how a lowpass filter design can become a band pass filter.

State the transformation equation for lowpass to band pass filter. Can this transformation also move the cutoff frequencies to those used in real problems?

That is, can you move a 1 rad/sec cutoff frequency to 100 MHz?

3. Next you are to design four bandpass filters (Butterworth, Chebychev I, Chebychev II, and Elliptic) with the following characteristics:

a) Lower cutoff frequency, fL, = 99.995 MHz

b) Upper cutoff frequency, fH, = 100.005 MHz

c) For each type, design filters of order 3, 9, and 15.

d) Extra credit: At higher orders, numerical errors limit the uselfuleness of filter design. Determine the highest order (approximately) for which you can get the best Elliptic filter. Include this in your Elliptic plot below.

For each of the 4 filter type, plot the magnitude response, overlaid if possible, with a useable frequency scale, full page, for each order. That is 3 or 4 pages, one plot (and one order) per page, with 4 overlaid filter responses on each plot.

Now for each filter type create a one page plot overlaying the magnitude response of that filter for each of the 3 or 4 orders you have created, to show the difference filter order makes. This will be a total of 4 pages: one per filter type.

In your report discuss the advantages of each of the filter types and the various filter orders you have created.

4. Finally, experimenting with filter types and orders above, create a very narrow band filter with the following frequency characteristics:

a) Lower cutoff frequency, fL, = 99.9995 MHz

b) Upper cutoff frequency, fH, = 100.0005 MHz

What is the bandwidth of this filter (in Hz)? In your report discuss any difficulties in creating a filter with this specifications and what filter types/orders would be appropriate for this filter.

5. Lab report: You are expected to create a high quality printed lab report showing the designs you analyzed, results you obtained, and any interesting observations about filter types and orders. Since you need to do some research about Elliptic filters and bandpass frequency transformations, please include a bibliography showing where you actually obtained this information. In a section at the very end of this report, please create a separate paragraph critiquing this lab. That is, what you liked about it, what extraordinary problems you had with it, and how you would change it to make it a more useful learning experience that could be added to the other ECE311 labs.