Information on line includes the following semesters:

Signal Processing is the representation, analysis and
manipulation of **indexed quantitative information**. The goal
of this course is to teach you how to optimally understand and
manipulate any indexed series of numbers, regardless of its source
or semantics. Every problem that you will ever solve can be
solved more effectively and efficiently using techniques learned
in ECE 551.

This is an extremely broad field, and ECE 551 is an extremely broad course. Students are encouraged to take ECE 551 to learn the relationships among the following topics, then to proceed into more advanced courses that address each topic in greater depth:

**Transforms:**Banach and Hilbert spaces; finite, countable, and uncountable basis sets; finite and countable basis transformations. Students with particular interest in this area are encouraged to follow up with ECE 513.**Filtering:**The design of linear time-invariant and time-varying systems in order to achieve targeted modifications of the temporal or Fourier basis representations of a signal.**Spectral Estimation:**Algorithms that estimate the autocorrelation and cross-correlation of random signals, and their properties including convergence in the mean and mean-square convergence. Students with particular interest in this area are encouraged to follow up with ECE 534.**Adaptive Filtering:**On-line learning algorithms including LMS and RLS; batch estimators including stochastic gradient descent and coordinate descent. Students with particular interest in this area are encouraged to follow up with ECE 561, STAT 542, or CS 544.**Multirate and Multiband Filtering:**time-frequency signal representations interpreted as transforms and as filterbanks, and the Fourier duality between polyphase and multiband representations. Students with particular interest in this area are encouraged to follow up with ECE 544MD.

M. Hasegawa-Johnson, ECE, University of Illinois, 2012