Lecture-2 Signals, Systems and Spectral Analysis.pdf

Yangon Technological University Department of Computer Engineering and Information Technology CEIT 31022 Digital Communication Computer Engineering and Information Technology Dept....

Yangon Technological University Department of Computer Engineering and Information Technology CEIT 31022 Digital Communication Computer Engineering and Information Technology Dept. Yangon Technological University 1/26  Course Contents Topic 1 Fundamental Aspects of Digital Communications Topic 2 Analog to Digital Conversion Topic 3 Digital Modulation Techniques Topic 4 Baseband & Passband Digital Transmission Topic 5 Communication on Networks 2/26  Course Contents Topic 1 Fundamental Aspects of Digital Communications Topic 2 Analog to Digital Conversion Topic 3 Digital Modulation Techniques Topic 4 Baseband & Passband Digital Transmission Topic 5 Communication on Networks 3/26  Topic 3 Signals, Systems and Spectral Analysis 4/26  Lecture Objectives To introduce What is a Signal? Classification of Signals Basic Operations on Signals Classification of Systems 5/26 5  What is a Signal? A signal is a pattern of variation of some form. Signals are variables that carry information. Examples of signal include: Electrical signals o Voltages and currents in a circuit Acoustic signals o Acoustic pressure (sound) over time Mechanical signals o Velocity of a car over time Video signals o Intensity level of a pixel (camera, video) over time 6/26  How is a Signal Represented? Mathematically, signals are represented as a function of one or more independent variables. For instance a black & white video signal intensity is dependent on x, y coordinates and time t f(x,y,t) On this course, we shall be exclusively concerned with signals that are a function of a single variable: time f(t) t 7/26  What a Signal is? A signal is a mathematical representation that describes a physical phenomenon. Only one-dimensional signals are considered and the independent variable is referred to as the time. Examples: Speech Signal Picture Signal 8/26  Classification of Signals A signal is a continuous-time (CT) signal if it is defined for a continuum of values of the independent variable, t. A signal is discrete-time (DT) if it is defined only at discrete times and the independent variable takes on only a discrete set of values. 9/26  Analog vs. Digital If a continuous-time signal x(l) can take on any value in the continuous interval (a, b), where may be -  and b may be +, then the continuous-time signal x(t) is called an analog signal. Digital is a discrete or non-continuous waveform with examples such as computer 1s and 0s. 10/26  Real and complex signals A signal x(t) is a real signal if its value is a real number, and a signal x(t) is a complex signal if its value is a complex number. A general complex signal x(t) is a function of the form x( t ) = x1( t ) + j x2( t ) where x1( t ) and x2( t ) are real signals and j= 1 11/26  Even and Odd Signals A signal x(t) or x[n] is referred to as an even signal if x(-t) = x(t) x[-n] = x[n] 12/26  Even and Odd Signals cont., A signal x(t) or x[n] is referred to as an odd signal if x(-t) = -x(t) x[-n] = -x[n] 13/26  Periodic and Non-periodic Signals A continuous-time signal x(t) is said to be periodic with period T if there is a positive nonzero value of T for which x(t + T) = x(t) for all t An example of such a signal is shown below 14/26  Periodic and Non-periodic Signals cont., From this equation x(t + T) = x(t) it follows that x(t + mT) = x(t) for all t and any integer m. Note that this definition does not work for a constant signal x(t). Any continuous-time signal which is not periodic is called a non-periodic (or aperiodic) signal. 15/26  Periodic and Non-periodic Signals cont., Periodic discrete-time signals are defined analogously. A sequence (discrete-time signal) x[n] is periodic with period N if there is a positive integer N for which x[n + N] = x[n] for all n 16/26  Periodic and Non-periodic Signals cont., From the following equation x[n + N] = x[n] It follows that x[n + mN] = x[n] for all n and any integer m. Any sequence which is not periodic is called a non-periodic (or aperiodic) sequence. 17/26  Causal vs. Anticausal vs. Noncausal Signals Causal signals are signals that are zero for all negative time. Anti-causal signals are signals that are zero for all positive time. 18/26  Causal vs. Anticausal vs. Noncausal Signals Non-causal signals are signals that have nonzero values in both positive and negative time. 19/26  Signal Energy and Power The total energy over an interval t1