Signal estimation and detection

           A problem frequently come across in signal processing is the estimation of the true value of the signal from the received noisy data. Consider the received noisy signal given by
                                       
           where is the desired transmitted signal buried in the noise .

           Simple frequency selective filters cannot be applied here, because random noise cannot be localized to any spectral band and does not have a specific spectral pattern. We have to do this by dissociating the noise from the signal in the probabilistic sense. Optimal filters like the Wiener filter, adaptive filters and Kalman filter deals with this problem.         

            In estimation, we try to find a value that is close enough to the transmitted signal. The process is explained in Figure 6. Detection is a related process that decides the best choice out of a finite number of possible values of the transmitted signal with minimum error probability. In binary communication, for example, the receiver has to decide about 'zero' and 'one' on the basis of the received waveform. Signal detection theory, also known as decision theory, is based on hypothesis testing and other related techniques and widely applied in pattern classification, target detection etc.