Review on Fourier Transforms, z-transform functions and Convolution Theorem

SIGNALS AND SYSTEMSECE 120 Signals and Spectra

Engr. Tanya G. Molarto AY 2012-2013 MSU-GenSan Compliments to Dr. Randell U. Espina, PECE,REE of Ateneo De Davao University for the notes on this courseLOGO Engr. Tanya G. Molarto AY 2012-2013 MSU-GenSan Signals and SystemsSignals represent a message or information and are represented mathematically as functions of one or more independent variables, e.g. time, t.

A system is an operation that transforms an input signal u(t) into output signal y(t).

SYSTEMu(t)y (t) Engr. Tanya G. Molarto AY 2012-2013 MSU-GenSan mathematical model of a physical process that relates the input (orexcitation) signal to the output (or response) signal2Types of SignalsSignals can either be continuous or discrete in both time and amplitude

Two basic types of signals areContinuous time and amplitude (analog) signalsDiscrete time and amplitude (digital) signals

Engr. Tanya G. Molarto AY 2012-2013 MSU-GenSan 3Types of SignalsA Continuous time signal is defined for a continuum of values of the independent variable

The domain is an unaccountable set and it will have some value at every instant of time. Examples are sine wave, cosine wave, triangular wave, signals derived in proportion with physical quantities such as temperature, pressure, etc

Engr. Tanya G. Molarto AY 2012-2013 MSU-GenSan 4Types of SignalsA Discrete time signal is an indexed sequence of real or complex numbers, hence, may be any function of an integer-valued variable, n, denoted by x[n].

The domain is a countable set and are often derived by sampling a continuous time signal or by recording the number of events of a given kind over finite time periods

Engr. Tanya G. Molarto AY 2012-2013 MSU-GenSan A discrete-time signal is an indexed sequence of real or complex numbers. Thus, a discrete-time signal is a function of an integer-valued variable, n, that is denoted by x(n).5Real or ComplexA signal x(t) is a real signal if its value is a real number

A signal x(t) is a complex signal if its value is a complex number of the form

Engr. Tanya G. Molarto AY 2012-2013 MSU-GenSan 6Deterministic or RandomDeterministic signals are those signals whose values are completely specified for any given time which means they can be modeled by a known function time, t.

Random signals are those signals that take random values at any given time and must becharacterized statistically.

Engr. Tanya G. Molarto AY 2012-2013 MSU-GenSan 7Even or OddA signal x (t) or x[n] is referred to as an even signal if

Engr. Tanya G. Molarto AY 2012-2013 MSU-GenSan 8Even or OddA signal x (t) or x[n] is referred to as an odd signal if

Engr. Tanya G. Molarto AY 2012-2013 MSU-GenSan 9Periodic or NonperiodicA continuous-time signal x ( t ) is said to be periodic with period T if there is a positive nonzero value of T for which

Where t denotes time and T is a constantThe period T defines the duration of one complete cycleAny signal for which there is no value of T to satisfy the condition stated above is aperiodic or nonperiodic

Engr. Tanya G. Molarto AY 2012-2013 MSU-GenSan 10Edit your company sloganThank You !LOGO Engr. Tanya G. Molarto AY 2012-2013 MSU-GenSan