This prelim covers deterministic and stochastic signal processing concepts and mathematical tools. The recommended preparatory courses are EECS 123 (deterministic signal processing), EECS 126, and EECS 225A (stochastic signal processing).
The deterministic signal processing component includes Z transforms, poles and zeros, and frequency response. The emphasis is on discrete-time, including multirate systems, but continuous-time systems are also considered in light of their interface to discrete-time systems through sampling and reconstruction. In this context, the relationship between the "four Fourier transforms" (Fourier transform, Fourier series, DTFT, DFT) is important. Digital filter realizations and design are covered, including the simpler quantization effects.
Basic probability: Sample space, events, probability, continuous and discrete random variables. Distributions, expectation, conditional expectation, multiple random variables, transformation of random variables. Hypothesis testing, MAP rule, minimum mean-square estimation, linear least square estimation, maximum likelihood estimation, confidence intervals. Law of large numbers, central-limit theorem. Bernouilli processes, Poisson processes, Markov chains, WSS random processes, power spectra, modulation, LTI filtering of random processes.
Spectral factorization, the innovations process model, and whitening filters for discrete- time random processes are covered. Wiener filtering problems are included (unconstrained, causal, and FIR), together with applications to echo cancellation, noise cancellation, linear equalization, and linear prediction. The normal equations and the orthogonality principle form the basis for much of this. Students should understand as well how to apply these techniques to AR modeling and AR spectral estimation. Adaptive filters for solving Wiener filtering problems are also covered (the LMS algorithm is sufficient). Eigen decomposition and singular value decomposition are also covered at an introductory level, particularly with regard to their connection to the above topics.
NOTE: The following courses may not be used to fulfill the prelim breadth requirement if you take the DSP prelim: EE 120, 123, 126, 225AB, 226, 290S, 290T, and CS 280.