ENGIN_112_Homework_7

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University of Massachusetts, Amherst *

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112

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Electrical Engineering

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Apr 3, 2024

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© 2015–23 Tilman Wolf ENGIN 112 Homework 7 Please submit your answers on Gradescope via the course page on Canvas. You can write your answers electronically or by hand and submit a scan or photo. Question 1 Assume you are measuring a distance (in feet) with different implementations of ultrasound sensors. After conducting six measurements with each sensor, you obtain the results in the following table: measurement 1 measurement 2 measurement 3 measurement 4 measurement 5 measurement 6 sensor A 9.3 9.2 9.3 9.1 9.3 9.0 sensor B 9.8 10.4 10.9 9.8 10.1 11.4 sensor C 8.7 8.5 8.7 8.7 8.7 8.6 sensor D 9.4 7.5 6.1 10.5 10.7 11.1 sensor E 9.4 9.6 9.5 9.5 9.9 9.6 You can assume that each sensor may introduce systematic errors into the measurement (e.g., due to the alignment of the sensor). However, errors in each measurement taken by a given sensor are independent. a) How would you determine the best estimate for the true value of the distance? What is this value here? b) How do you determine which sensor is most accurate? Which sensor is that here? c) How do you determine which sensor is most precise? Which sensor is that here? Question 2 Please answer the following questions using MATLAB. a) The following MATLAB command generates a vector with 10 random ``measurements": x = normrnd(50,0.01,[10 1]) Each vector element has an expected value of 50. (The parameter 0.01 indicates the level of variation between different measurements and can be left unchanged for this problem.) Use the mean function to calculate the mean of x . What result do you get? Explain how this result does or does not match your expectation. Note: Every time you run x = normrnd(50,0.01,[10 1]) in MATLAB, a new set of random values are assigned to the components of x .
© 2015–23 Tilman Wolf Example Matlab code and output: b) Repeat the above experiment with larger vectors of sizes 100 and 1000. When calculating the mean of those larger vectors, what do you observe? Explain how this result does or does not match your expectation. Question 3 Go to the following astronomy software website: https://stellarium-web.org/ The page will show you the night sky at a particular location and time: Click on the location in the lower left to ensure that a location on the northern hemisphere is selected (anywhere in the U.S. is fine). Pan and zoom so that you can see most of the sky in your window. Click on the time window in the lower right to pull up the time controls. a) Advance time by pulling the time slider to the right. What do you observe? b) Identify the north star (Polaris) from your activity in a). You can click on the star you think is Polaris to verify (or you can search in the search bar on top of the screen). Submit a screenshot of your screen with Polaris marked.
© 2015–23 Tilman Wolf Question 4 Please answer the following question about propagation delay in signals. a) Assume you have two microphones that are placed 0.2 meters apart. What is the maximum difference in reception time of a sound wave on the two microphones (i.e., the maximum phase shift between the microphones expressed in time)? b) Repeat the above calculation, but assume that you are using electromagnetic waves instead of sound waves (i.e., a radio receiver instead of a microphone and a radio signal instead of a sound wave). c) Assume you can choose to do beamforming with sound or with electromagnetic signals. Based on the results from (a) and (b), discuss which beamforming approach is easier to implement and why. Question 5 Consider the location of three beacons, A, B, and C, and the location of an object, X, in the following 2-D plane (1 unit = 1 km): a) What are the distances between each beacon and X? b) Assuming that all beacons send a synchronized radio signal at time t = 0. At what time do the signals from the beacons arrive at X? (Please order your answer in order of arrival time.) c) Assume that X moves to the right. How do you expect the arrival order to change (if it does change)? If you expect multiple changes, list each change. Question 6 If technology was available to implement GPS-style positioning that works indoors with accuracy and precision of a few inches, what useful application could you envision implementing? Your answer should be at least 4–5 substantive sentences.
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