By Van Trees, Harry L.

Initially released in 1968, this ebook is likely one of the nice time-tested classics within the box of sign processing. hugely readable and virtually geared up, it really is as critical this day for execs, researchers, and scholars in optimal sign processing because it used to be over thirty years in the past.

- half III makes a speciality of radar-sonar sign processing and Gaussian signs in noise. the subsequent issues are coated intimately:
- Detection of Gaussian signs in white Gaussian noise
- General binary detection: Gaussian tactics
- Estimation of the parameters of a random method
- The radar-sonar challenge
- Parameter estimation: slowly fluctuating aspect ambitions
- Doppler-spread pursuits and channels
- Range-spread objectives and channels
- Doubly-spread ambitions and channels

the implications are nonetheless mostly appropriate to present structures

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**Extra resources for Detection, Estimation, and Modulation Theory - Part lll - Radar-Sonar Processing and Gaussian Signals in Noise**

**Example text**

2. Consider four special cases of part 1 : (i) M a 0, (ii) mb = 0 , (iii) ua2 = 0, (iv) ubp= 0. Verify that the receiver for each of these special cascs reduces to the correct structure. 9. 6. Assume that s ( r ) is a piecewise constant waveform, 0 < I 5 To, To < I S 2'40. 2To < I S 3To~ s(r) = Ib,:,, (n - 1)To < 5 nTo. The bi are statistically independent, zero-mean Gaussian random variables with variances equal to ubz. Find the optimum receiver. 10. 6. Assume hS(f) =coif', 05 I, i=l where the ui are statistically independent random variables with variances uiz.

In order to exploit the effective computation procedures that we have developed, we now modify our results to obtain an expression for ,/ in which the optimum realizable linear filter specified by (44) is the only filter that we must find. 4 Canonical Realization No. 7 The derivation is of interest because the basic technique is applicable to many problems. For notational simplicity, we let Ti = 0 and T, = T in this section. Initially we shall assume that m(t) = 0 and consider only I,. Clearly, IR is a function of the length of the observation interval T.

Notice that this is not a bound on the percentage error in PF;it is just a bound on the magnitude of the successive terms. In most of our calculations we shall use just the first-order term PP. ; The bound on P$] is computed for several typical systems in the problems. To derive an approximate expression for P M , we go through a similar argument. 465) by a change of variables. - pni = ep(#)+(l-+(a) e ( ~ - s ) 4 i i ~ ~ ) ~dy. pv(y) (172) The first-term approximation is ~ (173) Using the approximation in (165) gives r 1 The higher-order terms are derived exactly as in the PF case.