1.2 Discrete-time signals O Time-Domain representation Note: It should be noted that xn] is defined only for integer values of n and undefined for noninteger values of n It should be noted that, whether or not a sequence ixn] has been obtained by sampling the quantity x[n] is called the nth sample of the sequence
1.2 Discrete-time signals Note: • It should be noted that x[n] is defined only for integer values of n and undefined for noninteger values of n. • It should be noted that, whether or not a sequence {x[n]} has been obtained by sampling, the quantity x[n] is called the nth sample of the sequence. ⚫ Time-Domain representation
1.2 Discrete-time signals Time-Domain representation 3. For a sequence xnj, the nth sample value can, in general, take any real or complex value. If xn] is real for all values of n, then ix[nls is a real sequence. On the other hand if nth sample value is complex for one or more values of n, then it is a complex sequence
1.2 Discrete-time signals 3 .For a sequence {x[n]}, the nth sample value can, in general, take any real or complex value. If x[n] is real for all values of n, then {x[n]} is a real sequence. On the other hand, if nth sample value is complex for one or more values of n, then it is a complex sequence. ⚫ Time-Domain representation
1.2 Discrete-time signals Time-Domain representation By separating the real and imaginary parts of x[n ,we can write a complex sequence ixn as x[小}={xm[}+{xm[]}
1.2 Discrete-time signals By separating the real and imaginary parts of x[n], we can write a complex sequence {x[n]} as x n x n j x n = + re im ⚫ Time-Domain representation
1.2 Discrete-time signals Time-Domain representation There are basically two types of discrete-time signals sampled-data signals, in which the samples are continuous-valued and digital signals, in which the samples are discrete-valued
1.2 Discrete-time signals There are basically two types of discrete-time signals: sampled-data signals, in which the samples are continuous-valued, and digital signals, in which the samples are discrete-valued. ⚫ Time-Domain representation
1.2 Discrete-time signals MATLAB Implementation n=-5:5; xsin(pi*n/5) 06 stem(n, x,.) ine(-5,6],[0,0]) aXis(-5,6,-1.2,12]) Xlabel(n) -04 ylabel((x(n)) -0.6 -0.8
1.2 Discrete-time signals ◼ MATLAB Implementation n=-5:5; x=sin(pi*n/5); stem(n,x,’.’); line([-5,6],[0,0]); axis([-5,6,-1.2,1.2]); xlabel(‘n’); ylabel((‘x(n)’) -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 n x(n)