EEET2369 – Signals and Systems: Assignment 2 - Assignments should be submitted to Blackboard using the eReport Submission link no later than 11:59 pm on Friday 17thMay 2013 (end of week XXXXXXXXXXThe...

EEET2369 – Signals and Systems: Assignment 2 - Assignments should be submitted to Blackboard using the eReport Submission link no later than 11:59 pm on Friday 17thMay 2013 (end of week XXXXXXXXXXThe assignment is an individual task and is worth 10% of the overall course mark. - The assignment should be presented as follows: 1. Page 1: Cover Page (example): RMIT University School of Electrical and Computer Engineering EEET2369 – Signals and Systems Assignment #2 Lecturer: Dr. Katrina Neville Student Name: …….. Student Number: ……… Submission Due Date: ……. 2. Page 2 onwards: 3. Answers to questions with appropriate predictions, calculations, MATLAB graphs and discussions. 4. References: Any sources used to find out more information. I.e. textbooks, journal/conference papers, websites, etc. must be in IEEE style format. 5. Appendix: MATLAB code and other results and calculations. The assignment will be assessed on the depth of conceptual understanding shown for each task. It is important not only to present correct results/ graphs/code but also to be able to analyse and discuss what your results are showing and how they link in with the concepts behind FIR and IIR filters. Assignment 2: Design of Nulling Filters This assignment is going to examine how we can design filters that null out specific frequencies in a signal. To start with a simple nulling filter will be designed that removes a single frequency. Secondly a nulling filter will be designed to filter out multiple frequencies. a) In MATLAB design a nulling filter that filters out a single frequency. That frequency will be selected based on the 5th number in your student number (see table 1) Student Number Normalised Radian Frequency (? XXXXXXXXXX1p 2 0.2p 3 0.3p 4 0.4p 5 0.5p 6 0.6p 7 0.7p 8 0.8p 9 0.9p 0 0 Table 1: Frequencies to be nulled - For example if your student number was XXXXXXXXXXyou will design a filter to remove the normalised radian frequency: 0.9p Where normalised radian frequency is defined as: ? ? ? ? ? ? ? ? = s f f ?ˆ 2p - Write out (by hand) the difference equation, impulse response and z-transform for your nulling filter. - Again (by hand) draw what the pole-zero (z-plane) diagram should look like for this nulling filter. - Use the freqz() and zplane() functions in MATLAB to confirm your prediction of the filter’s behaviour by plotting the actual pole-zero diagram and frequency response plots of this filter. Label all MATLAB figures including x and y axes. Discuss: 1. Explain how the pole-zero (z-plane) diagram can be used to describe the behaviour of your filter? 2. Is your filter stable, unstable or marginally stable? b) In this task you will design a nulling filter that filters out two frequencies. This time the frequencies will be selected based on the 5 th and 2nd numbers in your student number (if these are both the same numbers select one frequency to be p ). Again if your student number was XXXXXXXXXXyou will design a filter to remove the normalised radian frequencies: 0.9p and 0.2p . - Again write out (by hand) the difference equation, impulse response and z-transform for this nulling filter. - Draw what the pole-zero (z-plane) diagram should look like for this new nulling filter. - Use the freqz() and zplane() functions in MATLAB to confirm your prediction of the filter’s behaviour by plotting the actual pole-zero diagram and frequency response plots of this filter. Discuss: 1. This new filter could be described as two cascaded LTI systems. Use block diagrams, the theory of convolution/polynomial factorising (and any other method) to explain how two second-order systems could be cascaded to create this new filter (see section 7-5.1 of the McClellan textbook for an explanation on cascading LTI systems). 2. Draw a Direct Form I diagram of these cascaded systems. Assessment Guide For Signals and Systems Assignment 0-49 Fail NN 50-59 Pass PA 60-69 Credit CR 70-79 Distinction DI XXXXXXXXXXHigh Distinc’n HD Results (e.g. MATLAB figures/output) (30%) No results presented or results are all incorrect. Fundamental flaws in MATLAB code resulting in meaningless results. Some results are correct. Has presented results containing errors resulting from poor MATLAB coding. Results are mostly correct, may be one or two graphs that have minor errors. May have some superfluous results included. All results are correct. Minimum required results presented to successfully answer assignment questions. All results are correct. Extra results have been generated to help explain advanced concepts relating to the project. Discussion and analysis (50%) No analysis performed on results obtained. Unable to make links to theoretical concepts and/or irrelevant facts were used to try to explain results. Superficial analysis of results presented. Can make basic links to theoretical concepts but lacks in-depth understanding. A reasonable analysis has been made of results, but may be lacking some depth. Can make reasonable links to concepts to explain results. A good analysis of results presented. Can make links to advanced theoretical concepts to explain results. In-depth analysis of results presented. Makes links to advanced concepts/ theories from several topics to explain results. Referencing and citations (10%) Poor referencing style or no references used. Material may be copied without citing sources. References may be inappropriate and/or lack relevancy (e.g. use of Wikipedia or opinion pieces). Citations may be missing in places. References are mostly appropriate and show some variation in type. Reference/citation style mostly correct (good attempt at using IEEE format). References used are appropriate. May be very minor errors in referencing style (IEEE style). Has used a wide range of appropriate references. IEEE format used. Layout (10%) Report contains a large number of spelling and grammatical errors. Figures are unreadable and lack numbers/titles. Some spelling and grammatical errors present. Some graphs/figures may not be 100% clear. Spelling and grammar of an acceptable level. Graphs and figures are clear but may have unclear titles/captions. Spelling and grammar mostly correct. Graphs and figures are mostly clear and labelled. Exceptional use of language. No spelling/ grammatical errors. All figures are clear and well labelled.