Signal detection and estimation by mourad barkat pdf

You are not allowed to possess, look at, use, or in anyway derive advantage from existing solutions that you may come across. This applies to all aspects of the course. If the grader or I detect a violation of the Honor Code, we are obligated to bring the matter before the Honor Council. Students with Disabilities Any student with a documented disability needing academic adjustments or accommodations is requested to speak with me during the first two weeks of class.

W 2 2 nd ball drawn is white. R 3 3 rd ball drawn is red. Hence, Let B denote drawing a black ball and W a white ball. For example 1 Therefore, the probability of obtaining 3 ones in 4 tosses is We need to determine the total probability of drawing a red ball, which is Hence, x f X is a density function. Solving the 2 equations in 2 unknowns, we obtain. Then, the variance of X is Signal Detection and Estimation 12 1.

Then, the mean of X is. Then, the mean of Y is. Graphically, we have Hence, we have fY y 0 0. Chapter 2 Distributions 2. Hence, 0 6 5 6 1! The other number of different ways of obtaining 3 other balls not white is. Hence, the probability of obtaining the fourth white ball in the seventh trial is Hence, 22 Distributions Signal Detection and Estimation 24 a The probability of more than 15 calls per a given hour is. That is,! Therefore, Distributions 25 2. Hence, we have success with.

The density function is. We determine the constant k to be. Note that the joint density function of X and Y is just the product of the individual density functions since we assume X and Y independent. Taking the derivative of F T t using Leibnizs rule, we obtain the required density function given by 2.

Using the tables of integrals, we obtain. We need to determine the mean square value, which is. Therefore, the process t X is not ergodic in the mean b. Therefore, Y t is wide-sense stationary. Therefore, t X is wide-sense stationary. From 3. Therefore, the joint density function is just the product of the marginal density functions to yield 4 1 2 1 2 1 5. N df e N df e N df f S f f xx Therefore, the mean square value.

It follows that the samples are uncorrelated provided. Hence, 2 4 4 2! Also, ] 0. Vn t j Z Signal Detection and Estimation 52 3. Therefore, the root mean square value is. Hence, we have, for the circuit below, 2 2 2 2. The system function is given by. The modal matrix is then. The generalized eigenvector is.

Therefore, the eigenvectors i v and j v are ortogonal. From 4. Note that x 1 and x 2 are orthogonal. From a , the semi-major axis is The ellipse is shown below 4. Applying this to our system, we have.

S 3 : aperiodic and transient. S 4 : absorbing. Thus, ] Therefore, this chain is a regular Markov chain. Therefore, ] The minimum probability of error is Statistical Decision Theory 83 5. Signal detection and estimation 84 5.

This is equivalent to choosing H j for which j m y is smallest. Therefore, a UMP test exists. Change Location. Signal Detection and Estimation, Second Edition. By author : Mourad Barkat. Description Contents Author Reviews This newly revised edition of a classic Artech House book provides you with a comprehensive and current understanding of signal detection and estimation.

The book provides complete explanations of the mathematics you need to fully master the material, including probability theory, distributions, and random processes.

Containing numerous solved examples, the book helps you apply the material to projects in the field involving signal processing, radar, and communications. Packed with over 2, equations, figures and problems, this authoritative resource covers a wide range of critical topics, from parameter estimation and filtering, to representation of signals and Gaussian processes.

The problems presented at the end of each chapter make this book particularly well suited for self-study and for use as a text for graduate-level electrical engineering courses. Probability Concepts - Sets and Probability. Random Variables. Two and Higher Dimensional Random Variables. Transformation of Random Variables. Properties of Correlation Functions. Some Random Processes.

Power Spectral Density. Linear Time Invariant Systems. Sampling Theorem.