The objective of this course is to build upon the Signals and Systems fundamentals provided in 18-290 to prepare the students for Digital Communications and Digital Signal Processing courses. This course will introduce students to the important concept of signals with randomness, in particular to the representation of noise and processing to suppress noise and to extract information. The topics to be covered in this course include:

1. Motivating applications (2 lectures).
2. Review of basic signals and systems concepts (2 lectures)
3. Review of basic probability theory and random variables material (2 lectures)
4. Two and more random variables (4 lectures)
5. Representation of noisy signals (4 lectures).
6. Noise in real-world signals (4 lectures)
7. Optimal filtering (3 lectures)
8. Information extraction from noisy signals (3 lectures)

In addition, there will be four lab projects --- the main goal is to illustrate the role of noise in signals and methods to filter out the noise and/or extract information from noisy signals. The labs will be MATLAB-based and will take advantage of the MATLAB toolboxes and demos. Each project will be a 3-week project and students will be expected to turn in working MATLAB code as well as a report that summarizes their experiments, results and conclusions. Some initial project topics are the following, even though this list is expected to evolve.

• Synthesizing colored noise in MATLAB
• Power spectral estimation, estimating the frequency of noisy tones
• BPSK signal detection, estimating error probabilities
• Time delay estimation, e.g., as in radar
• Speech signal modeling via linear prediction coefficients
• Location of target images in noisy scenes
• Synchronization in noisy received signals
• Noise-cancelling headphones, adaptive noise cancellers
• Identification of linear systems

Prerequisites: 18-202, 18-290, 36-217