By Harry L. Van Trees
Chapter 1 advent (pages 1–18):
Chapter 2 Classical Detection and Estimation concept (pages 19–165):
Chapter three Representations of Random tactics (pages 166–238):
Chapter four Detection of Signals—Estimation of sign Parameters (pages 239–422):
Chapter five Estimation of constant Waveforms (pages 423–466):
Chapter 6 Linear Estimation (pages 467–622):
Chapter 7 dialogue (pages 623–633):
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Additional resources for Detection, Estimation, and Modulation Theory: Detection, Estimation, and Linear Modulation Theory
The signal s(t) is a known function with energy E, T ES = s”(t) dt, (26) s0 and w(t) is a sample function from a zero-mean random process with a covariance function : &St, u> = No 2 8(t-u). (27) We are concerned with the output of the system at time T. The output due to the signal is a deterministic quantity: so(T) = T h(r) s(T - r) dr. s0 (28) Structured Approach 13 The output due to the noise is a random variable: c,(T) = T h(r) n(T - 7) dr. s0 We can define the output signal-to-noise s, (29 ratio at time T as so2(T) (30) N - E[no2(T)f where E(e) denotes expectation.
A case in which this is not true is illustrated in Example 2. Example 2. Several different physical situations lead to the mathematical model of interest in this example. The observations consist of a set of N values: rl, y2, r3, . , rN* Under both hypotheses, the ri are independent, identically distributed, zero-mean Gaussian random variables. Under HI each rr has a variance a12. Under Ho each ri has a variance o02. Because the variables are independent, the joint density is simply the product of the individual densities.
Values of R where the two terms are equal have no effect on the cost and may be assigned arbitrarily. We shall assume that these points are assigned to H1 and ignore them in our subsequent discussion. Thus the decision regions are defined by the statement: If assign R to Z1 and consequently say that H1 is true. Otherwise assign R to Z. and say Ho is true. Alternately, we may write p,,,,(RIH,) ">'~OWlO - p,l~,(RlH,) H