Palestine University Faculty of Information Technology IGGC Understanding Telecommunications Instructor: Dr. Eng. Mohammed Alhanjouri 2 nd Lecture: Introduction to Signals

Signals A signal, as the term implies, is a set of information or data. Examples include a telephone or a television signal, monthly sales of a corporation, or the daily closing prices of a stock market (e.g., the Dow Jones averages). In all these examples, the signals are functions of the independent variable time.

Systems Signals may be processed further by systems, which may modify them or extract additional information from them. For example, an antiaircraft gun operator may want to know the future location of a hostile moving target, which is being tracked by a radar. Knowing the radar signal, the antiaircraft gun operator knows the past location and velocity of the target. By properly processing the radar signal (the input), we can approximately estimate the future location of the target. Thus, a system is an entity that processes a set of signals (inputs) to yield another set of signals (outputs). A system may be made up of physical components, as in electrical, mechanical, or hydraulic systems (hardware realization), or it may be an algorithm that computes an output from an input signal (software realization).

SIZE OF A SIGNAL The size of any entity is a number that indicates the largeness or strength of that entity. For instance, if we are to devise a single number V as a measure of the size of a human being, we must consider not only his or her width (girth), but also the height. The product of girth and height is a reasonable measure of the size of a person. Π r 2 h

Signal Energy we may consider the area under a signal g(t) as a possible measure of its size, because it takes account of not only the amplitude, but also the duration. We call this measure the signal energy E g defined (for a real signals) as

The signal energy must be finite for it to be a meaningful measure of the signal size. A necessary condition for the energy to be finite is that the signal amplitude  0 as│t│  ∞ (Fig.). Otherwise the integral Equation will not converge.

Signal Power If the amplitude of g (t) does not  0 as│t│  ∞ the signal energy is infinite. A more meaningful measure of the signal size in such a case would be the time average of the energy (if it exists), which is the average power Pg defined (for a real signal) by We can generalize this definition for a complex signal g (t) as

CLASSIFICATION OF SIGNALS There are several classes of signals. Here we shall consider only the following classes, which are suitable for the scope of this course: 1. Continuous-time and discrete-time signals 2. Analog and digital signals 3. Periodic and aperiodic signals 4. Energy and power signals 5. Deterministic and probabilistic signals

1- Continuous-Time and Discrete-Time Signals A signal that is specified for every value of time t (Fig.a) is a continuous-time signal, and a signal that is specified only at discrete values of t (Fig.b) is a discrete-time signal. Telephone and video camera outputs are continuous-time signals, whereas the quarterly gross national product (GNP), monthly sales of a corporation, and stock market daily averages are discrete-time signals.

2- Analog and Digital Signals The concept of continuous time is often confused with that of analog. The two are not the same. The same is true of the concepts of discrete time and digital. A signal whose amplitude can take on any value in a continuous range is an analog signal. This means that an analog signal amplitude can take on an infinite number of values. A digital signal, on the other hand, is one whose amplitude can take on only a finite number of values. Signals associated with a digital computer are digital because they take on only two values (binary signals).

3- Periodic and Aperiodic Signals A signal g(t) is said to be periodic if for some positive constant To, The smallest value of To that satisfies the periodicity condition is the period of g(t). The signal in (Fig.b) is a periodic signal with period 2. A signal is aperiodic if it is not periodic. The signal in (Fig.a) is aperiodic.

Therefore, a periodic signal, by definition, must start at -∞ and continue forever, as shown in Fig. Observe that a periodic signal shifted by an integral multiple of To remains unchanged. The second important property of a periodic signal g(t) is that g(t) can be generated by periodic extension of any segment of g(t) of duration To (the period). This means that we can generate g(t) from any segment of g(t) with a duration of one period by placing this segment and the reproduction

3- Energy and Power Signals A signal with finite energy is an energy signal, and a signal with finite power is a power signal. In other words, a signal g(t) is an energy signal if Similarly, a signal with a finite and nonzero power (mean square value) is a power signal. In other words, a signal is a power signal if a signal cannot both be an energy and a power signal. If it is one, it cannot be the other. On the other hand, there are signals that are neither energy nor power signals. The ramp signal is such an example.

5- Deterministic and Random Signals A signal whose physical description is known completely, in either a mathematical form or a graphical form, is a deterministic signal. If a signal is known only in terms of probabilistic description, such as mean value, mean squared value, and so on, rather than its complete mathematical or graphical description, is a random signal.

SOME USEFUL SIGNAL OPERATIONS Time Shifting Consider a signal g(t) (Fig.a) and the same signal delayed by T seconds (Fig.b), which we shall denote by φ(t), then

Time Scaling The compression or expansion of a signal in time is known as time scaling.