This is a textbook for senior/graduate level students for courses in electrical engineering departments commonly called digital signal processing. It may also be useful to engineers and scientists who use digital computers to process measured data. Two major topics of the text are: Computer computation of frequency contents of signal and design filters to process signals. These two topics follow logically a basic text or course on Signals and Systems. Although most topics in the text are standard, the presentation and emphasis are significantly different from other existing DSP texts. MATLAB is an integral part of the text, but is not the main emphasis, the text being mostly centered on the basic ideas and procedures in digital signal processing. Thus, the text lists only essential MATLAB functions in the most commonly used programs and skips functions that adjust shapes and sizes of plots, and draw horizontal and vertical coordinates. Some elementary knowledge of signals and systems is helpful, but not necessary. This text is as self contained as possible.