Continuous-time signals: introduction

The Merrian-Webster dictionary defines a signal as:

A detectable physical quantity or impulse (as a voltage, current, or magnetic field strength) by which messages or informationcan be transmitted.

These are the types of signals which will be of interest in this book.Indeed, signals are not only the means by which we perceive the world around us, they also enable individuals to communicate with one another on a massivescale. So while our primary emphasis in this book will be on the theoretical foundationsof signal processing, we will also try to give examples of the tremendous impact that signals and systems have on society.We will focus on two broad classes of signals, discrete-time and continuous-time . We will consider discrete-time signals later on in this book. For now, we will focusour attention on continuous-time signals. Fortunately, continuous-time signals have a very convenient mathematicalrepresentation. We represent a continuous-time signal as a function $x\left(t\right)$ of the real variable $t$ . Here, $t$ represents continuous time and we can assign to $t$ any unit of time we deem appropriate (seconds, hours, years, etc.). We do not have to makeany particular assumptions about $x\left(t\right)$ such as boundedness (a signal is bounded if it has a finite value). Some of the signals wewill work with are in fact, not bounded (i.e. they take on an infinite value). However most of the continuous-time signals we willdeal with in the real world are bounded.

We actually encounter signals every day. Suppose we sketch a graph of the temperature outside the Jerry Junkins Electrical EngineeringBuilding on the SMU campus as a function of time. The graph might look something like in [link] . This is an example of a signal which represents the physical quantity temperature as itchanges with time during the course of a week. [link] shows another common signal, the speech signal. Human speech signals are often measured by converting sound (pressure) waves into an electrical potential using a microphone. The speech signal therefore corresponds to the air pressure measured at thepoint in space where the microphone was located when the speech was recorded. The large deviations which the speech signal undergoescorresponds to vowel sounds such as “ahhh" or “eeeeh" (voiced sounds) while the smaller portions correspond to sounds such as “th"or “sh" (unvoiced sounds). In [link] , we see yet another signal called an electrocardiogram (EKG). The EKG is avoltage which is generated by the heart and measured by subtracting the voltage recorded from two points on the human body as seen in [link] . Since the heart generates very low-level voltages, the difference signal must be amplified by a high-gainamplifier.