University of Southern Queensland Faculty of Health, Engineering & Sciences School of Mechanical & Electrical Engineering Course Number: ELE3107 Course Name: Signal Processing Internal ? Assessment No: 1 External ? This Assessment carries 200 of the 1000 marks total for this Course. Examiner: John Leis Moderator: Mark Phythian Assignment: Signals and Systems Date Given: Week 1 Date Due: Wednesday Week 9 Penalty for Late Submission: Loss of 20% of total marks for this assignment per day late. Assignments are to be typed, not handwritten and scanned. Assignments are to be submitted electronically, using the link on your Study Desk. Marked assignments are also returned to you electronically. You do not need a coversheet for this assignment, since it is submitted electronically. Please use PDF format to submit your assignment. Please use the naming convention LastName-StudentNumber.pdf, where StudentNumber is your 10-digit student number, and LastName is your last (family) name. By submitting this assignment, you agree to the following Student Declaration: I hereby certify that no part of this assignment has been copied from any other student's work or from any other source except where due acknowledgement is made in the assignment. No part of this assignment has been written for me by any other person except where such collaboration has been authorised by the Examiner. Any non USQ copyright material used herein is reproduced under the provision of Section 200(1)(b) of the copyright Amendment Act 1980.Signal Processing Signals and Systems Page 2 Objectives The aims of this assignment are: 1. To understand different signal models (course objectives 1 and 2) 2. To be able to model a discrete-time system (course objectives 3). 3. To design simple signal processing algorithms (course objective 4) Students are expected to communicate their findings and ideas in a clear and logical manner. Submission • Assignments must: { Be typed, not handwritten. { Be submitted electronically via the Study Desk. { Be submitted in PDF format, and less than 4M in size. { Use the file naming format LastName-StudentNumber.pdf. { State your name and student number at the top of the first page. • You must not use any MATLAB \toolbox" functions { that is, any which are not shown as toolbox\matlab in response to the which command. • For each question, submit a written report, detailing your approach and discussing your findings. Your report should include diagrams, figures, source code, waveforms and/or images as appropriate for this assignment. • Late assignments are not normally accepted. If you wish to apply for consideration for late submission, it must be done at least one week prior to the due date in writing or via email. Include documentary evidence of illness (a medical certificate) or additional work commitments (a written confirmation of changed work circumstances from your supervisor). For extension applications for other reasons, please contact the examiner at least 2 weeks in advance of the due date. • Students are reminded of the penalties applying to plagiarism. Copying all or part of an assessment from another student, or from the web, is unacceptable. Plagiarism may result in loss of marks, or other penalties as determined by the Academic Misconduct Policy. Further helpful hints on how to correctly reference (and how to avoid plagiarism) may be found under the link Academic Honesty on the course Study Desk. . . . / 3Signal Processing Signals and Systems Page 3 Marking Marks are awarded as per the marking guidelines at the end of each question. The breakdown of marks will be noted on the PDF file returned to you via the Study Desk. Where an explanation or description is specifically requested, your response will be assessed according to the following: 85-100: High Distinction Excellent grasp of the problem. Explicitly addresses the question, uses knowledge from course and outside. Well-argued choice of method or approach as appropriate to the question. Correct grammar and spelling. Referenced if appropriate. 75-85: Distinction Very good grasp of the problem. Addresses the question using knowledge from course. Well-argued choice of method or approach as appropriate to the question. Correct grammar and spelling, perhaps with very minor errors. Referenced if appropriate. 65-75: Credit Understands the problem. Addresses the question using knowledge from course. Lacks clarity of expression or uses an imprecise argument. Moderate spelling or grammatical errors. Referenced if appropriate. 50-65: Pass Has some understanding of the problem. Addresses the question but not clearly. Some misconceptions about the question. Moderate spelling or grammatical errors. 0-50: Fail Has little or no understanding of the problem. Does not really address the question. Significant misconceptions or total lack of understanding of the question. Poor spelling and/or obvious grammatical errors. Software You may use MATLAB to complete questions where you are required to plot waveforms or calculate results. You may use any MATLAB notes or tutorials provided in this course as a starting point. You must not use any MATLAB \toolbox" functions { that is, any which are not shown as toolbox\matlab in response to the which command. Where MATLAB coding is required, show all your code for each question as part of your report. . . . / 4Signal Processing Signals and Systems Page 4 Part I Question 1 | 50 Marks Using the audiorecorder() function in MATLAB, make a recording of your voice. Use a sample rate of 8kHz, 16 bits per sample, and aim to record around 2 seconds worth. Part (a) | 25 Marks Quantize the audio samples down from the original 16 bits by removing the least-significant bit (LSB) from the waveform, to make a 15 bit recording. Repeat for 14, 13, 12 bits, down to 1 bit. Explain how you would do this in MATLAB, and implement your approach. Part (b) | 25 Marks Listen to the recordings, and make a table with the number of bits and the corresponding quality assessment. This can simply be a subjective assessment; use terms such as 'no perceptual difference', 'minor noise present', 'quite noisy', 'poor quality' etc. Calculate the signal-to-noise ratio using your data from the previous question, and add that to your table. Explain how you calculated the SNR, and comment on whether it agrees with theoretical predictions. (a) Explanation & MATLAB coding 25 (b) Subjective assessment table with SNR 25 Total 50 Question 2 | 50 Marks This question examines the addition of a (synthetic) echo to the voice recording, such as would be found in a reverberant room. Part (a) | 25 Marks Use a difference equation of the form y(n) = x(n) + αy(n − D) (1) where x(n) is the input audio, y(n) is the output (echoed) audio, D is the echo delay (in samples), and α governs the amount of echo fed back. Select an echo delay of 0.2 seconds, and α = 0:4. Using your reasoning above, implement the reverberation equation, and listen to the result. Experiment with different values of the parameters α and D. In your report, include one sample plot of the waveform, and explain what you found as you tried varying the parameters. . . . / 5Signal Processing Signals and Systems Page 5 Part (b) | 25 Marks Suppose the equation governing the reverberation is y(n) = x(n) + αx(n − D) (2) What is the physical significance of this form, as opposed to that used in equation (1) ? Implement an audio echo system based on equation (2), and listen to the results. Comment on what you have found. (a) Implement echo filter, plot and discuss 25 (b) Explain equation form, comment & discuss 25 Total 50 Part II Question 3 | 50 Marks This question examines discrete-time signal generation, for deterministic and random waveforms. Part (a) | 25 Marks Generate and plot a sampled sine wave with fs=8kHz, of 4 seconds duration, with frequency !o = 10 π rad/samp and amplitude A = 1:2. The waveform equation is x(n) = A sin n! (3) Explain the role of each of the variables in this equation. What is the true (Hertz) frequency generated in this case? Part (b) | 25 Marks Generate a Gaussian random signal vector, v(n), of the same length. Then generate a noisy signal of the form y(n) = x(n) + αv(n) (4) Listen to the resulting signal y(n) for various values of α. You will have to choose the value of α experimentally { try both small and large, and investigate the differences. Plot one of the waveforms, and comment briefly on your results. (a) Plot clean sinusoidal waveform & comment 25 (b) Plot waveform with noise & comment 25 Total 50 . . . / 6Signal Processing Signals and Systems Page 6 Question 4 | 50 Marks This question examines discrete-time filters. A filter of the form G(z) = z2 (z − p)(z − p∗) (5) with poles defined by p = re|!n will be studied. Part (a) | 25 Marks With r = 0:95 and !n = π=10, plot the time response to the input clean sinusoidal waveform generated in the previous question. Show both the transient (initial) and steady-state (after the initial transient) responses. Part (b) | 25 Marks Plot the frequency response of the filter. Explain all your working, particularly how the z transfer function is converted to gain/phase plots. Find the gain and phase from the time-domain response of part (a), and compare to that expected from the frequency response in part (b). Compare the results obtained using these two methods. (a) Time response (transient+steady-state) 25 (b) Frequency response (gain+phase) and compare 25 Total 50 End of Assignment