Multirate signal processing. Frequency and z-domain analysis. Fractional sampling. Fractional sampling rate conversion. Polyphase representations and their applications. Filter banks. Perfect reconstruction conditions. Applications of filter banks. Subband analysis and synthesis of signals. Multiresolution analysis. Wavelet transform.

Estimation theory: classical approach.
Minimum variance unbiased estimators.
Cramer-Rao lower bound. Best linear unbiased estimators. Maximum likelihood estimation. Linear models. Least squares estimation.
Bayesian approach: MMSE estimation, scalar and vector MAP estimation. LMMSE. Sequential MMSE. Signal estimation: Wiener filter. Introduction to Kalman filtering.

Signal detection. Statistical decision theory. MAP criterion. Simple hypothesis testing: Neyman-Pearson theorem. Bayes Risk. Multiple hypothesis testing. Deterministic and random signal detection. Matched filter. Generalized likelihood ratio test (GLRT). Composite hypothesis testing. Detection in Gaussian or non-Gaussian noise.