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9)  0 otherwise where bˆ (m) is an estimate of the binary state indicator sequence b(m), and it may be erroneous in particular if the signal–to–noise ratio is low. 1 lists four possible outcomes that together b(m) and its estimate bˆ (m) can assume. 1 Four possible outcomes in a signal detection problem. 13 Sonar: detection of objects using the intensity and time delay of reflected sound waves. detector. The higher the threshold, the less the likelihood that noise would be classified as signal, so the false alarm rate falls, but the probability of misclassification of signal as noise increases.

1991) Statistical Signal Processing: Detection, Estimation, and Time Series Analysis. Addison Wesley, Reading, MA. W. (1992) Discrete Random Signals and Statistical Signal Processing. Prentice-Hall, Englewood Cliffs, NJ. L. (1971) Detection, Estimation and Modulation Theory. Parts I, II and III. Wiley New York. E. (1948) A Mathematical Theory of Communication. Bell Systems Tech. , 27, pp. 379–423, 623–656. S. (1979) Digital Signal Processing, Control and Estimation Theory: Points of Tangency, Areas of Intersection and Parallel Directions.

Linear prediction models have facilitated the development of advanced signal processing methods for a wide range of applications such as low−bit−rate speech coding in cellular mobile telephony, digital video coding, high−resolution spectral analysis, radar signal processing and speech recognition. 3 Bayesian Statistical Signal Processing The fluctuations of a purely random signal, or the distribution of a class of random signals in the signal space, cannot be modelled by a predictive equation, but can be described in terms of the statistical average values, and modelled by a probability distribution function in a multidimensional signal space.

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