Orhan Gazi - Principles of Signals and Systems

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Complex Fourier Transform Coefficients

Discrete-Time Fourier Series Coefficients

Fourier Transform

Imaginary Part

Laplace Transform

Linear and Time-Invariant

Real Part

Region of Convergence

Z-Transform

A signal can be defined as a physical phenomenon that carries information. Examples of signals are human voice, electromagnetic waves, and sonar waves. Any quantity does not necessarily have to be in a waveform type to be considered as a signal. For example, Indians in ancient times used smoke to report any danger. The smoke used here is the signal carrier, and the shape of the smoke contains information. To give another example, let us say two persons are sitting in a room and one of these persons wants to describe an item to the other. For this, he only makes movements with his hands and tries to describe the item. We can accept the hands of the person as signal carriers and meaningful movements as signal. However, since movements containing meaning have to be with the carrier, in this case, we can accept the persons hands and the movements of the hands containing meaning as signal. Even a blink event and a facial expression can be given as an example of a signal. Signals change over time, and some are defined over a period of time. In order to show the changes of signals over time, it is necessary to describe them with some mathematical functions. The mathematical function used describes the changes in the signal over time and becomes a kind of synonym for the signal. For example, the mathematical expression

(1.1)

can be called both a sine function and a sine signal.

In this book, we will use the signal word and its corresponding mathematical function name interchangeably. Electromagnetic waves are one of the most common types of signals used today. Electromagnetic wave is used to transfer information from one place to another. The electromagnetic wave is the preferred type of signal carrier in the world of communication because it spreads with the speed of light and has the ability to pass through solid objects. Apart from this, laser or infrared signals are also used in short-distance communication systems.

The electromagnetic wave has a sinusoidal graph of change. To send the information with this wave, we change the shape of the wave according to the information. For each different information, the wave takes a new shape. In this way, the information-loaded wave acquires the signal feature and is used for communication. Communication can be of two types which are analog communication and digital (digital) communication. The communication systems used in the past are based on analog communication. Today, digital communication systems are mostly preferred. In analog communication, the amplitude, frequency, and phase of the electromagnetic wave are changed according to the information wave, and the communication is performed. In digital communication, the continuous time data wave is first sampled. In other words, samples are taken from the data wave at certain time instances within a certain period of time. Each sample is expressed by a real number.

Real numbers are quantized to obtain integers, and their binary equivalents are calculated. For this purpose, a fixed number of bits can be used, for example, 8 bits. Later, groups of bits in the binary system are converted into data waves using square waves, analog modulation is performed, and the resulting wave is transmitted through an antenna. The steps of digital communication are shown in baseband in Fig..

A flow diagram of the conversion of the analog signal into binary and is transmitted in 4 steps. The signal is received via an antenna and converted into decimal and digital analog.