Consider the following binary hypothesis testing problem on 0 tT: Ho:g(t) = w(t) H: y(t) =...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider the following binary hypothesis testing problem on 0 tT: Ho:g(t) = w(t) H: y(t) = s(t) + w(t) where s(t) is a given deterministic waveform with fos (t) dt = 1, w(t) is a zero-mean, white Gaussian noise process with Rw (T) = 8(7). Suppose that the two hypothesis are a priori equally likely. We desire the minimum probability of error decision rule for deciding between Ho and H at t = T. (a) What is the optimal threshold to compare with the Likelihood Ratio for this detection problem? (b) What are a good choice of basis vectors for a Karhunen-Love expansion of y(t) for this problem? What are the corresponding expansion coefficients for y(t) with respect to this basis and their distributions under each hypothesis? Hint: They are Gaussian. (c) Determine the minimum probability of error decision rule for this problem, i.e., specify the required processing of y(t) and the subsequent threshold test. (d) Determine the probability of error for the decision rule of part (c) in terms of Q(). Recall: 1-Q(-x) = Q(x) Consider the following binary hypothesis testing problem on 0 tT: Ho:g(t) = w(t) H: y(t) = s(t) + w(t) where s(t) is a given deterministic waveform with fos (t) dt = 1, w(t) is a zero-mean, white Gaussian noise process with Rw (T) = 8(7). Suppose that the two hypothesis are a priori equally likely. We desire the minimum probability of error decision rule for deciding between Ho and H at t = T. (a) What is the optimal threshold to compare with the Likelihood Ratio for this detection problem? (b) What are a good choice of basis vectors for a Karhunen-Love expansion of y(t) for this problem? What are the corresponding expansion coefficients for y(t) with respect to this basis and their distributions under each hypothesis? Hint: They are Gaussian. (c) Determine the minimum probability of error decision rule for this problem, i.e., specify the required processing of y(t) and the subsequent threshold test. (d) Determine the probability of error for the decision rule of part (c) in terms of Q(). Recall: 1-Q(-x) = Q(x)
Expert Answer:
Related Book For
Posted Date:
Students also viewed these business communication questions
-
"internet radios" for streaming audio, and personal video recorders and players. Describe design and evaluation processes that could be used by a start-up company to improve the usability of such...
-
QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...
-
Danbury Inc is a resident Canadian corporation with worldwide operations. Canadian operations resulted in taxable income of $ 1 . 1 0 million and non - Canadian operations resulted in taxable income...
-
On January 1, 2012, Swen paid $184,000 for $200,000 of the 8%, 20-year bonds of Penn Corporation, issued on January 1, 2008, at par. The bonds are held as an investment. Determine the gain and the...
-
Consider the following data for Wooster Company. Total variable manufacturing costs, including direct material costs, were $3 per unit; the standard production rate was 10 units per machine hour. For...
-
On April 23, 2014, Calvin Loyer admitted his wife, Edeltrud Loyer, to a nursing home administered by Signature Healthcare. During the admissions process, Calvin signed an arbitration agreement...
-
Bronkowski is a retailer for high-tech recording disks. The projected operating profit for the current year is $200,000 based on a sales volume of 200,000 units. The company has been selling the...
-
The trial balance for Lindor Corporation, a manufacturing company, for the year ended December 31, 2024, included the following accounts: Account Title Sales revenue Cost of goods sold Selling and...
-
Discuss the key factors that a lender should consider when thinking about whether to grant a long-term loan to a business. GreenF is a private company established in Germany in the 2000s by Miriam...
-
1. A pharmaceutical company is considering a new three-year expansion project that requires an initial investment of 3.9 million. The asset is depreciated to zero over the three years of the project...
-
Describe why the author's opinion of the article of "Fill Volume as an indicator of Surface Heterogeneity in glass vials for Parenteral Packaging" claims that any glass vial can be made to fail if...
-
Explore why criminal justice organizations may be more willing to invest monies into publicly accessible programs, such as DARE than to allocate resources for leadership development training.
-
Green Furniture (GF) manufactures a variety of furniture for household use and just two items for office use: desks and cabinets. The production process for desks and cabinets is similar, although...
-
The below options show a step in the budget process, EXCEPT: Question 29Answer a. Make financial decisions b. Track income and expenses c. Set goals d. Review and adjust the budget
-
1. Zn-Sn alloys have been studied at particular temperature. The mole fractions and corresponding relative integral gibbs free energies are given below: 0.1 0.3 0.6 0.7 0.9 0.2 0.5 0.8 zn 0.4 AGM...
-
a) Show that (a, b) := {{a}, {b}} does not satisfy the ordered pair axiom. b) Determine whether each of the following statements is true or false. (Give a reason in each case): (i) {a, b} C (a, b)....
-
The transfer function of an FIR filter is H(z) = z 2 (z 2)(z 0.5). (a) Find the impulse response h[n] of this filter and plot it. Comment on any symmetries it might have. (b) Find the phase H(e j )...
-
You wish to recover the original analog signal x(t) from its sampled form x(nT s ). (a) If the sampling period is chosen to be T s = 1 so that the Nyquist sampling rate condition is satisfied,...
-
Suppose you want to design a dc-source using a half-wave rectified signal x(t) and an ideal filter. Let x(t) be periodic, T 0 = 2, and with a period (a) Find the Fourier transform X(Ω) of...
-
Goods are products a business sells like a. haircuts. b. conveyer belts. c. car insurance. d. health care.
-
Which of the following are the factors of production? a. Labor, natural resources, capital, entrepreneurs, technology, and intellectual property b. Labor, capital, entrepreneurs, motivation, and good...
-
Which of the following is a current sociocultural trend? a. A decrease in the overall U.S. population b. An increase in the population of Americans ages 30 to 45 years old c. A decrease in the U.S....
Study smarter with the SolutionInn App