lab4_08

# lab4_08 - ECE220 Spring 2008 Lab 4 FIR Filters Monday...

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Unformatted text preview: ECE220, Spring 2008 Lab 4: FIR Filters Monday, February 18 - Thursday, February 21 Location: 314 Phillips Hall. • This time the Prelab report is due Friday, 5:00pm, February 15th , in the collection boxes next to the south entrance to 219 Phillips Hall. • Matlab is available in most of the computer laboratories on the campus. To identify the lab closest to you visit www.cit.cornell.edu/labs/ . • Very important: Read the entire lab description before you show up in the lab. • Read Chapter 5 and 6 from the textbook. • Make a copy of your prelab report and bring it with you when you come to the lab. You will also need all Matlab programs that you are asked to write for your prelab. • In the lab you will answer questions related to topics covered in this document. Your TA will note on the TAs’ check-out form to what extent your answers were correct. 1 Linear Time Invariant Systems Suppose you are running a retail business. One way of seeing how well you are doing would be to count the money in the cash register at the end of each day. The results would constitute a discrete time sequence. Likely some days you would find a good result and other days a less favorable result. So how do you know if you are doing better over a period of time longer than a day? Clearly you would do some form of averaging (over time). You might average over the last four days, for example, and expect to find that a bad day (perhaps due to weather) would not matter so much in your average. But then you recognize that you generally do three times as much business on Saturday, so the four averages that include Saturday are artificially high. It won’t take you long to recognize that an average over the last seven days would be smart. Whenever a Saturday (or any other day) drops off the end of the average, the most recent Saturday moves in. At this point, you have designed and implemented a digital filter . And you didn’t really need a course in signal processing to do this! Your digital filter is often called, appropriately enough, a moving average filter. Here in this lab we are interested in this filter as an example of a system or operator . We will look at some of the properties of this system as being typical of many other systems. 1.1 Moving average filter We understand a length-7 average to be obtained by adding up seven results and dividing by 7. A moving average is different in that the average is not obtained as the average of 7 results, 2 followed by the average of the next 7 results, and so on. Instead, the output of the averager is the average of the most recent 7 results. There is an output (average) for each new input (result). Thus: y ( n ) = (1 / 7) ( x [ n ] + x [ n- 1] + x [ n- 2] + x [ n- 3] + x [ n- 4] + x [ n- 5] + x [ n- 6]) Prelab question P4.1: Consider the length 24 input sequence x [ n ]: 3 2 5 1 2 1 0 2 2 5 4 9 3 3 1 1 0 6 6 4 2 5 2 2 Compute the length-7 moving average of this sequence....
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lab4_08 - ECE220 Spring 2008 Lab 4 FIR Filters Monday...

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