In this chapter the Kalman Smoother, with or without the EM algorithm, has been used for the processing of the EEG signal in two cases, epileptic form spike identification and ERD/ERD analysis. Use of the Kalman Smoother forces to some simplifications of the model. This is performed in order to decrease the number of parameters which must be tuned. Based on the assumptions that the state transition matrix is the identity and the covariance is diagonal with the same element on the diagonal, there is one parameter to be tuned, the variance of the state noise. The value of this parameter defines how smooth or rough will be the evolution of states, in our case the TVAR coefficients. Large values of variance indicate rough estimates for the TVAR coefficients. This has as a result a noisy time varying spectrum. Small values indicated smooth estimates for the TVAR coefficients and hence a smooth time varying spectrum. The value of this parameter depends on the problem. In the case where we expect that the time varying spectrum is smooth, a small value for the variance of the state noise is preferable. However, the parameters can be estimated based on some optimization procedure like the EM algorithm. The EM algorithm provides with estimates of the parameters. So the tuning of the parameters is done automatically based on the dataset, without manual settings. This fact permits the use of full covariance for the state noise and a general transition state matrix. As a consequence the model is more flexible because of the different types of state noise. We observe that the Kalman Smoother with EM provides with smoother estimates than using the Kalman Smoother alone. This happens because the first approach can capture the patterns of the signal more accurately. In the estimation of the IF in the spike problem it is observed that the IF starts to increase before the appearance of the spike. Also, in the ERD/ERS analysis we observe that the IF is modulated when some events take place on the experiment, like the sound at t=2sec which denotes the beginning of the trial. In both problems we observe that the IF is a good measure to track changes in EEG activity.