Syllabus

Discrete Random Process: Expectation, Variance and Co‐variance, Uniform, Gaussian and Exponentially distributed noise, Hillbert space and inner product for discrete signals, Energy of discrete signals, Parseval’s theorem, Wiener Khintchine relation, power spectral density, Sum decomposition theorem, Spectral factorization theorem.

Spectrum Estimation: periodogram, Non – parametric methods of spectral estimation Correlation method, WELCH method – AR, MA, ARMA models. Tule – Walker method. Linear Estimation and Prediction: ML estimate –Efficiency of estimator, Cramer Rao bound ‐ LMS criterion. Wiener filter – Recursive estimator – Kalman estimator – Linear prediction, Analysis and synthesis filters, Levinson resursion, Lattice realization. Adaptive filters: FIR adaptive filter – Newton’s Steepest descent algorithm – Widrow Hoff LMS adaptation algorithms – Adaptive noise cancellation, Adaptive equalizer, Adaptive echo cancellors.