The goal of this course is to expose students to multiresolution signal processing methods and their use in practical applications as well as to guide them through the steps of the research process. The course is roughly divided in two parts: 1. The first part introduces the necessary mathematical tools with a great emphasis on intuitive understanding of how they operate on real-life signals. 2. The second part is project-based, where, through a project, students will learn how to choose a research area, formulate a problem, research previous work, propose solutions, carry out experiments and interpret results. The focus is on training students to become researchers. To that end, students will write papers in a standard conference format, rehearse presentations with feedback from both the instructor and other students in the class, as well as present projects in a seminar-like setting. Upon successful completion of this course, students will be able to:

• Explain the importance and use of signal representations in building sophisticated signal processing tools such as wavelets;
• Describe how Fourier theory fits in a bigger picture of signal representations;
• Use basic multirate building blocks, such as a two-channel filter bank and characterize the discrete wavelet transform and its variations;
• Construct a time-frequency decomposition to fit the signal provided, and;
• Apply these concepts to solve a practical problem through an independent project.

There will be 2-3 hours of pre-recorded video per week thatcan be viewed online at any time. There will also be two 1-hour sessions in person that are not mandatory and can be viewed later online. The instructor will also be available for meetings in person or online as needed. Thetotal amount of work per week is expected to be around 12 hours on average This course is crosslisted with 42-732