6.341x is designed to provide both an in-depth and an intuitive understanding of the theory behind modern discrete-time signal processing systems and applications.  The course begins with a review and extension of the basics of signal processing including a discussion of group delay and minimum-phase systems, and the use of discrete-time (DT) systems for processing of continuous-time (CT) signals.  The course develops flow-graph and block diagram structures including lattice filters for implementing DT systems, and techniques for the design of DT filters. Parametric signal modeling and the efficient implementation of DT multirate and sampling rate conversion systems are discussed and developed. An in-depth development of the DFT and its computation as well as its use for spectral analysis and for filtering is presented. This component of the course includes a careful and insightful development of the relationship between the time-dependent Fourier transform and the use of filter banks for both spectral analysis and signal coding. 6.341x is organized around eleven units each typically consisting of a set of two to four topics. The source material for learning each topic includes suggested reading in the course text, clarifying notes, other related reading, and video excerpts and will include an interactive on-line discussion forum. The course text is the widely used text by Oppenheim and Schafer (third edition), available on the course website in viewable format. The video segments are adapted from live video recordings of the MIT residential course.  Each topic includes a set of automatically-graded exercises for self-assessment and to help in digesting and understanding the basics of the topic, and in some cases to preview topics. A typical unit in the course concludes with a set of more extensive problems to help in integrating the topics and developing a deeper understanding. Automatic grading of your answers to these problems as well as solutions will be provided.