Animals have five direct senses: sight, hearing, smell, touch, and taste. However, the effectiveness of direct sensing quickly falls off with distance. Bats in flight primarily use echolocation to navigate and avoid obstacles. Echolocation is a form of remote sensing; that is, sensing at a distance. Remote sensing depends on the use of signals that allow communication between the observer and the remote object. The most important type of signal is the traveling wave, whether mechanical (as in sound) or electromagnetic (as in light). Telescopes and microscopes make use of the electromagnetic waves of light. Radar uses electromagnetic waves in the microwave range. Echocardiograms make use of sound signals to see images of the internal movements of the heart and blood without penetrating the skin. Seismic signals yield accurate 3D images of the underground structure of the earth. Nondestructive testing uses sound signals to find hidden defects without taking the airplane apart. There are two basic types of signals: analog and digital. In an analog signal, some continuously physical variable represents the information. A digital signal is a signal that represents data as a sequence of discrete values. This contrasts with an analog signal, which represents continuous values. Digital signal processing (DSP) is the use of digital processing to perform a wide variety of signal processing operations. DSP can create accurate images. DSP can control security and telephone systems. DSP can compress signals for efficient transmission. DSP can enhance the quality of signals. Although real-world signals can be processed in their analog form, processing signals digitally provides the advantages of high speed and accuracy. This book is in the form of a standard mathematics textbook. It is self-contained and all concepts are defined in mathematical terms. The chapters are divided into articles, and approximately ten problems are given at the end of each article. The answers to all the problems are given at the end of the book.
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