Discrete-Time Signals Time-Domain Representation Signals are represented as sequences of numbers, called samples Sample value of a typical signal or sequence denoted as xn with n being an integer in the range-∞≤n≤o In] defined only for integer values of n and undefined for non-integer values of n Discrete-time signal represented by x[n Copyright C 2001, S K Mitra
1 Copyright © 2001, S. K. Mitra Discrete-Time Signals: Time-Domain Representation • Signals are 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 • x[n] defined only for integer values of n and undefined for non-integer values of n • Discrete-time signal represented by {x[n]} − n
Discrete-Time Signals Time-Domain Representation Discrete-time signal may also be written as a sequence of numbers inside braces {xrn]}={…,-0.2,2.2,1.0.2,-3.7,2.9,… In the above, x1=-0.2,x0]=2.2,x1=1.1 etc The arrow is placed under the sample at time index n=0 Copyright C 2001, S.K. Mitra
2 Copyright © 2001, S. K. Mitra Discrete-Time Signals: Time-Domain Representation • Discrete-time signal may also be written as a sequence of numbers inside braces: • In the above, etc. • The arrow is placed under the sample at time index n = 0 { [ ]} ={,− 0.2,2.2,1.1,0.2,−3.7,2.9,} x n x[−1] = −0.2, x[0] = 2.2, x[1] =1.1
Discrete-Time Signals. Time-Domain Representation Graphical representation of a discrete-time signal with real-valued samples x 3456789101112 10-98-7-6-5-4-3-2-10120 1314151617 Copyright C 2001, S.K. Mitra
3 Copyright © 2001, S. K. Mitra Discrete-Time Signals: Time-Domain Representation • Graphical representation of a discrete-time signal with real-valued samples
Discrete-Time Signals Time-Domain Representation In some applications, a discrete-time sequence xn may be generated by periodically sampling a continuous-time signal xa(t )at uniform intervals of time K al 3T -5T -T0 T (37 Copyright C 2001, S.K. Mitra
4 Copyright © 2001, S. K. Mitra 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 at uniform intervals of time x (t) a
Discrete-Time Signals. Time-Domain Representation Block-diagram representation of the sampling process xa( t) x[n]=xa(t x(n t=nt C 2.-1.0 Copyright C 2001, S.K. Mitra
5 Copyright © 2001, S. K. Mitra • Block-diagram representation of the sampling process ( ) a x t . . Discrete-Time Signals: Time-Domain Representation [ ] ( ) ( ) a a t nT x n x t x nT = = = n = ,− 2,−1,0,1,