This document is a lecture on discrete-time convolutions. It discusses various methods for processing discrete-time samples, including block processing and sample processing. Block processing deals with finite blocks of data and applications like FIR filtering and DFT computations. Sample processing is used in real-time applications like filtering and control systems. The document presents different equivalent forms of the convolution operation, including direct form, LTI form, matrix form, and overlap-add. It provides examples of computing convolution using these different forms. The document concludes with exercises involving computing convolutions using different methods.