1Introduction

This first lecture is intended to broadly introduce the scope and direction ofthe course. We are concerned, of course, with signals and with systems thatprocess signals. Signals can be categorized as either continuous-time signals,for which the independent variable is a continuous variable, or discrete-timesignals, for which the independent variable is an integer. Examples of con-tinuous-time signals include the sound pressure at a microphone as a functionof time or image brightness as a function of two spatial variables. In the firstcase the signal is a one-dimensional signal, in the second a two-dimensionalsignal. Common examples of discrete-time signals are economic time series,such as the daily or weekly stock market index, antenna arrays, etc. Whilethese examples include both one-dimensional and two-dimensional signals,our detailed discussions in this course focus only on one-dimensional signals.Many of the general concepts and results, however, will be illustrated withtwo-dimensional signals, specifically images.

There are some very strong similarities and also some very important dif-ferences between discrete-time signals and systems and continuous-time sig-nals and systems. Discussing both classes together provides an opportunity toshare intuition and to use both the similarities and the differences as a furtheremphasis of important concepts. Furthermore, as we will see as the courseproceeds, current technology provides an important mechanism-throughthe concept of sampling-for converting between continuous-time and dis-crete-time signals. It is often very advantageous to process continuous-timesignals by first converting them to discrete time.

For the most part, our discussion of systems throughout is restricted to aspecific class, namely linear, time-invariant systems. Extremely powerfultools and techniques exist for both analysis and design of this class of sys-tems. In particular, in discussing this class of systems we develop signal andsystem representations in both the time domain and thefrequency domain.These two domains of representation are tied together through the Fouriertransform, which we discuss and exploit in considerable detail.

As I emphasize in this lecture, it is extremely important to use both thecourse text and the video course manual in conjunction with watching thetapes. The material presented in the lectures is very closely tied to the text. In

Signals and Systems1-2

addition, the recommended and optional problems in the video course man-ual have been carefully chosen to emphasize and amplify important issuesraised in the associated lecture. Consequently, it is extremely important that,in addition to watching a taped lecture, you do the accompanying suggestedreading and recommended problems before proceeding to the next lecture.

Suggested ReadingChapter 1, page 1

Section 2.0, Introduction, page 7

Section 2.1, Signals, pages 7-12

Introduction

MARKERBOARD1.1 (a)

DEMONSTRATION1.1An example of animage. [Jean BaptisteJoseph Fourier fromOeuvre de Fourier,Vol. II (Paris: Gauthier-Villars et Fils, 1890).]

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Signals and Systems

DEMONSTRATION1.2Aerial photograph ofroads with cloudcover.

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Introduction

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Signals and Systems1-6

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Introduction

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Signals and Systems

DEMONSTRATION1.4Aerial photograph ofroads with cloudcover.

DEMONSTRATION1.5Enhancement of theaerial photographshown in Demon-stration 1.4.

Introduction

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Introduction1-11

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Resource: Signals and Systems Professor Alan V. Oppenheim

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