This core ECE course covers the basics of signal processing and data analysis. The first half of the course covers the fundamentals of signals and systems, including the discrete Fourier transform, transfer functions, adaptive filtering and applications in noise cancellation and communication systems. The second half covers the basics of probabilistic models, stochastic simulation Markov processes and Bayesian inference. Finally, topics in high dimensional signal processing including model selection, sparse signal processing and principal component analysis are covered. Throughout the course, applications in communication systems, sensing systems and machine learning will be emphasized.