EECS 225d (3 units)
Audio Signal Processing in Humans and Machines
203 McLaughlin, MWF 1-2
Spring Semester, 1999
Professors Morgan and Gold
HOMEWORKS
Chapter 6----- Exercises 1,2,7,9,10,12
Chapter 7 ---- Exercises 6,9,10
Chapter 8 ---- Exercise 5 (but look at solved problems 1-4 on Web site for spr97)
Chapter 9 ----
1. Suppose that a scalar feature is observed for data that belongs to one of two classes (omega_1 and omega_2). Each is generated according to a Gaussian distribution with a variance of 1, the mean of the data in the first class is 0, and the mean of the second is 2.
(a) Write expressions for log P(x | omega_1) and log P(x | omega_2).
(b) From these expressions, derive a function of x such that a strategy that gives the minimum probability of error tells you to assign the pattern to omega_1 for the function being positive, and to omega_2 for negative values of the function. Assume that the prior probabilities for the two classes are equal (.5 each). Show your work since the answer could be derived by inspection.
(c) Now suppose that P(omega_1) = .99 and P(omega_2) = .01 . What does this change the optimum function of the previous part to? In other words, what ranges of values for x should now be associated with each of the two classes in order to achieve the minimum probability of error?
(d) Given the priors from (c), suppose the value of x is obscured, what should your classification strategy be? What is your probability of error in this case?
(e) Suppose that the variance of the second class is 4 rather than 1. Assuming that the priors are once again equal, recompute P(x | omega_2) and the function required in section (b).
2. Exercise 4, Chapter 9 in the text.
Read Chapter 9 through 9.7 by class, Feb 8.
Read Section 9.8 by class, Feb 10.
Read Chapter 10 by class, Feb 12.
Due date for chapters 6-8 homework, Feb 12.
Due date for chapter 9 homework, Feb 17.
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Chapter 10 exercises: 2,8,11
Chapter 13 exercise: 3
Chapter 11 exercises: 3, 4, 5, 7
Chapter 12 exercise: 4
Read Chapter 13 by class, Feb 17.
Read Chapter 11 by class, Feb 19.
Read Chapter 12 by class, Feb 22.
Due date for chapters 10-13 homework, March 1
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Chapter 14 exercises: 1,2,5
Chapter 15 exercise: 3,4,6
Chapter 16 exercises: 1,4,5
Chapter 17 exercise: 2,7,8
Chapter 18 exercise: 1,2
Read Chapter 14 by class, Feb 24.
Read Chapter 15 by class, Feb 26.
Read Chapter 16 by class, March 1.
Read Chapter 17 by class, March 3.
Read Chapter 18 by class, March 5.
Due date for chapters 14-18 homework, March 12
The readings for the remainder of the chapters will follow through
the book in the order 19-21, 29-33, 22-28, 36, 34, 35. Generally a
chapter corresponds to one lecture, although chapter 26 will be taught
over 2 days.
There are no homeworks per se after the chapters 14-18 homework;
the emphasis should be on the project.