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Textbook by: Carlos E. Davila. E-mail the author

# Continuous-Time Signals: Introduction

Module by: Carlos E. Davila. E-mail the author

Summary: Defines and gives some examples of continuous-time (analog) signals.

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 information can 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 massive scale. So while our primary emphasis in this book will be on the theoretical foundations of 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 focus our attention on continuous-time signals. Fortunately, continuous-time signals have a very convenient mathematical representation. We represent a continuous-time signal as a function x(t)x(t) of the real variable tt. Here, tt represents continuous time and we can assign to tt any unit of time we deem appropriate (seconds, hours, years, etc.). We do not have to make any particular assumptions about x(t)x(t) such as boundedness (a signal is bounded if it has a finite value). Some of the signals we will work with are in fact, not bounded (i.e. they take on an infinite value). However most of the continuous-time signals we will deal 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 Engineering Building on the SMU campus as a function of time. The graph might look something like in Figure 1. This is an example of a signal which represents the physical quantity temperature as it changes with time during the course of a week. Figure 2 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 the point in space where the microphone was located when the speech was recorded. The large deviations which the speech signal undergoes corresponds 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 Figure 3, we see yet another signal called an electrocardiogram (EKG). The EKG is a voltage which is generated by the heart and measured by subtracting the voltage recorded from two points on the human body as seen in Figure 4. Since the heart generates very low-level voltages, the difference signal must be amplified by a high-gain amplifier.

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