Lecture 1 Signal and Systems PDF

‫الر ِحيم‬ ‫الر ْح َم ِن ه‬ ‫ِب ْس ِم ه‬ ‫اَّللِ ه‬ In the name of God, the Most Gracious, the Most Merciful ‫ب ز ْدني ِ ِع ْلما ً َو ْر ُز ْقني ِ فَ ْهما‬ ِ ‫َر‬ ًً My Lord!...

‫الر ِحيم‬ ‫الر ْح َم ِن ه‬ ‫ِب ْس ِم ه‬ ‫اَّللِ ه‬ In the name of God, the Most Gracious, the Most Merciful ‫ب ز ْدني ِ ِع ْلما ً َو ْر ُز ْقني ِ فَ ْهما‬ ِ ‫َر‬ ًً My Lord! Advance me in Knowledge and true understanding © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 1 EEE 513 – Digital Communications LECTURE I Signal and Systems Engr. Tahir Aja Zarma, Ph.D.c, IEEE [email protected] Room: 312B Tel: +234 (0) 703 822 5063 Dept. of Electrical and Electronics Engineering Nile University of Nigeria, Abuja © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 2 Topics to Cover o Introductions to Signals o Introduction to Systems o Size of Signals o Signal & Spectra o Signal & Functions o Operation on Signal © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 3 Signal and Systems © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 4  Signal – Basic Informations Signals are used to convey information Signals and waveforms (voltage, current and intensity) are central to communication and signal processing Signals can be viewed either in time or frequency domain A signal is any physical quantity that varies with time, space, or any other independent variables (IVs) Often, the IVs for most signals is “time” Theoretical signals can be described mathematically, graphically or in tabular form Real signals are however difficult to describe, and more often can be described approximately © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 5  Signal – II Mathematically, a signal is defined as a function of one or more IVs, e.g., x(t) = 10t , x(t) = 5t2, s(x,y) = 3x + 2xy + 10y2 Sometimes the functional dependence on the IV is not precisely known, e.g., speech signal Sometimes a signal is a combination of other signals e.g., sum of sinusoid of different amplitudes, frequency & phase s(t) =  Ai (t) sin2 Fi (t) +  i (t) i=1 Signals are the inputs outputs, and internal functions that the systems process or produce, such as voltage, current, pressure, displacements, intensity, etc. © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 6  Signal – Types The variable time may be continuous or discrete and the value of the signal may be represented as Continuous-valued x(t) Discrete-valued x(nts) Quantized xQ(t), and Digital x[n] These types of signals occur at different stages Other variables (distance, angle, etc.) can also be the IV, especially for 2-D signals like images and video © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 7  Signal – Types Physical realizable signals must Have time duration Occupy finite frequency spectrum Are continuous (as in analog signal) Have finite peak value, and Are real-valued All real-world signals will have these properties Sometimes we use mathematical signal models which violate these conditions e.g., Dirac delta function (or impulse function) © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 8  Signal The most commonly used analog signals are the sinusoidal signals (sine, cosine, etc.) In communication systems, we are concerned with info bearing signals that evolve as a function of the independent variable, t When signals are corrupted by noise, they no longer convey the required information directly, hence they often require processing Radio receivers are especially sensitive to noise Signals are processed by systems, which may modify them or extract additional information from them © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 9  Systems © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 10  Systems  A system is an entity that processes a set of signals (inputs) to yield another set of signals (outputs) A system can also be associated to the signal as in the source or sink of the signal A system may be made up of physical components (hardware realization), as in electrical, mechanical, or hydraulic systems, or it may be an algorithm (software realization) that computes an output from an input signal © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 11  Systems Many systems have signals that are not wanted (commonly known as noise or interference) A system is a device, process, or algorithm that, given an input x(t), produces an output y(t) A system is characterized by its input (excitation or forcing function), its output (response), and the rules of operation (internal functions) From a communication engineers’ viewpoint, a system is a law that assigns output signals to various input signals Systems may be realized as an integration of sub-systems or as a single entity In practice, systems with feedback is of great importance © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 12  Systems Systems may be classified functionally as in Analyzers, Synthesizers, Transducers, Channels, Filters, and Equalizers, etc. or descriptively as in linear, nonlinear, causal, discrete, continues, time invariant, etc. Examples of Systems Electronic systems: resistors, inductors, Radio/TV, phone networks, sonar and radar, guidance & navigation, satellite, lab instrumentation, biomedical instrumentation, etc. Mechanical systems: loudspeakers, microphones, vibration analyzers, springs, dampers © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 13  Systems To understand the behavior of systems (electronic/mechanical), the response to inputs (usually signals) must be understood Terminology of Systems  State: ◆Variables that allow us to determine the energy level of the system ◆All physical systems are referenced to zero-energy state, e.g., ground state, rest state, relaxed state  Initial Conditions ◆The initial conditions or initial state is the state of the system before an input is applied © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 14  Systems © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 15  Systems © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 16 Why Study Signal & Systems © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 17 Size of a Signal © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 18 Size of a Signal © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 19 Size of a Signal © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 20 Signal & Spectra © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 21 Signal & Spectra © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 22 Signal & Spectra © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 23 Signal & Spectra © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 24 Signal & Spectra © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 25 Signal & Spectra © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 26 Signal & Spectra © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 27 Signal & Spectra – Example © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 28 Common Signals and Functions © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 29 Common Signals and Functions © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 30 Common Signals and Functions © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 31 Common Signals and Functions © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 32 Common Signals and Functions © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 33 Common Signals and Functions © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 34 Common Signals and Functions © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 35 Common Signals and Functions © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 36 Common Signals and Functions © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 37 Common Signals and Functions © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 38 Common Signals and Functions © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 39 Operations on Signals © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 40 Operations on Signals © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 41 Operations on Signals © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 42  Questions © Engr. Tahir Aja Zarma, Ph.D.c, IEEE 43