### Introduction

Signal processing using digital computers and special purpose digital hardware has taken on major significance in the past decade. The inherent flexibility of digital elements permits the utilization of a variety of sophisticated signal processing techniques which had previously been impractical to implement.

Advances in integrated circuit technology have had a major impact on the technical areas to which digital signal processing techniques and hardware are being applied. Applications of these techniques are now prevalent in such diverse areas as biomedical engineering, acoustics, sonar, radar, seismology, speech communication, telephony, nuclear science, image processing and many others. Thus, a thorough understanding of digital signal processing fundamentals and techniques is essential for anyone concerned with signal processing applications.

### Goals

This set of lectures corresponds to a one-semester introduction to digital signal processing fundamentals. It is intended to provide an understanding and working familiarity with the fundamentals of digital signal processing and is suitable for a wide range of people involved with and/or interested in signal processing applications. Its goals are to enable you to apply digital signal processing concepts to your own field of interest, to make it possible for you to read the technical literature on digital signal processing, and to provide the background for the study of more advanced topics and applications.

### Prerequisites

Advanced calculus and familiarity with introductory complex variable theory. Previous exposure to linear system theory for continuous-time signals, including Laplace and Fourier transforms, is required. No experience with discrete-time signals, z-transforms, or discrete Fourier transforms is assumed.

### Course Topics

The course begins with a discussion of the analysis and representation of discrete-time signals and systems including a discussion of discrete-time convolution, difference equations, the z-transform and the discrete Fourier transform. Considerable emphasis is placed on the similarities with and distinctions between discrete-time and continuous-time signals and systems. The course then proceeds to a consideration of digital network structures for implementation of both recursive (infinite impulse response) and nonrecursive (finite impulse response) digital filters.

A major consideration in digital signal processing is the design of digital filters to meet prescribed specifications. Thus a set of four lectures is devoted to a detailed discussion of digital filter design for both recursive and nonrecursive filters. The course concludes with a thorough presentation of the fast Fourier transform algorithm for computation of the discrete Fourier transform.

### Format

Each lesson consists of a taped lecture, a reading assignment in the text, and problems. It is expected that each lesson will require approximately five hours—more or less depending on your ability and interests. The suggested sequence is to first view the lecture, then read the text and finally work the problems. In viewing the lecture you should feel free to run the lecture back and listen to some sections over again or in fact, to watch an entire lecture more than once if that would be helpful. In addition to the assigned reading in the text you may wish to read some of the sections not assigned. This is optional and probably most profitably done after the problems have been worked.

Perhaps the most important component of the course is the exercises. There is absolutely nothing like successfully completing an exercise to give you confidence that you have understood the lectures and the text and that you are ready to go on to new material. And, there is no surer indicator that you are not ready to go on than your not being able to solve an exercise. If you can’t solve an exercise after diligent effort (and don’t give up easily), look over the solution in the exercise solution book. If you have difficulty following the solution, get help. Don’t try to forge ahead thinking the next chapter or lecture will clear up the difficulty; it probably won’t, and you’ll be in still deeper trouble. In each lesson you should work all of the problems without an asterisk. The problems with asterisks are optional. If you have the time and feel that you would like more experience with the material you should try these also. If you wish to go still further, you may want to select some additional problems from the text.

### Texts

#### Required

Oppenheim, Alan V., and Ronald W. Schafer. *Digital Signal Processing*. Prentice Hall, 1975. ISBN: 9780132146357.

#### Recommended

Cooper, George, and Clare D. McGillem. *Methods of Signal and System Analysis*. Holt, Rinehart and Winston, 1967. ISBN: 9780030637452.

Lathi, B. P. *Signals, Systems and Communication*. John Wiley and Sons, 1965.

Oppenheim, Alan V., and A. S. Willsky. *Signals and Systems*. Prentice Hall, 1982. ISBN: 9780138097318.

Papoulis, A. *The Fourier Integral and Its Applications*. McGraw-Hill Book Company, 1962. ISBN: 9780070484474.