Chapter 2 Discrete-Time Signals and systems
Chapter 2 Discrete-Time Signals and Systems
82.1 Discrete-Time Signals: Time-Domain Representation Signals represented as sequences of numbers, called samples Sample value of a typi ical signal or sequence denoted as xn with n being an nteger in the range -oos n <oo xn defined only for integer values of n and undefined for noninteger values of n Discrete-time signal represented by xng
§2.1 Discrete-Time Signals: Time-Domain Representation • Signals represented as sequences of numbers, called samples • Sample value of a typical signal or sequence denoted as x[n] with n being an integer in the range -∞≤ n ≤∞ • x[n] defined only for integer values of n and undefined for noninteger values of n • Discrete-time signal represented by {x[n]}
82.1 Discrete-Time Signals: Time-Domain Representation Discrete-time signal may also be written as a sequence of numbers inside braces {xn}={,0.2,2.2,1.1,0.2,3.7,2.9, °· The arrow is placed under the sample at time index n=o In the above, x-1=-0.2, x 0=2.2 X1F1.1, etc
§2.1 Discrete-Time Signals: Time-Domain Representation • Discrete-time signal may also be written as a sequence of numbers inside braces: {x[n]}={…,-0.2,2.2,1.1,0.2,-3.7,2.9,…} ↑ • The arrow is placed under the sample at time index n = 0 • In the above, x[-1]= -0.2, x[0]=2.2, x[1]=1.1, etc
82.1 Discrete-Time Signals: Time-Domain Representation Graphical representation of a discrete-time signal with real valued samples is as shown below. x[-5 x 3456789101112 10-9-8-7-6-5-4-3-2-10120 1314151617
§2.1 Discrete-Time Signals: Time-Domain Representation • Graphical representation of a discrete-time signal with realvalued samples is as shown below:
82.1 Discrete-Time Signals: Time-Domain Representation In some applications, a discrete-time sequence xn may be generated by periodically sampling a continuous-time signalxa (t) at uniform intervals of time x4-57 a 3T -5T-37-70T x2(37)
§2.1 Discrete-Time Signals: Time-Domain Representation In some applications, a discrete-time sequence {x[n]} may be generated by periodically sampling a continuous-time signal xa (t) at uniform intervals of time