1.2 Discrete-time signals Time-Domain representation In digital processing, a discrete-time signal can be represented as a sequence of numbers called samples with the independent time variable represented as an nteger in range from -oo to +oo
1.2 Discrete-time signals In digital processing, a discrete-time signal can be represented as a sequence of numbers called samples, with the independent time variable represented as an integer in range from -∞ to +∞. ⚫ Time-Domain representation
1.2 Discrete-time signals O Time-Domain representation If a discrete-time signal is written as a sequence of numbers inside braces, the location of the sample value associated with the time index n=o is indicated by an arrow under it the sample values to its right are for positive values of n, and the sample values to its left are for negative values of n {xm]={,0.95,0.2,2.17,1.1,0,2,-367,29,-0.8,4.1,}
1.2 Discrete-time signals If a discrete-time signal is written as a sequence of numbers inside braces, the location of the sample value associated with the time index n=0 is indicated by an arrow under it. The sample values to its right are for positive values of n, and the sample values to its left are for negative values of n. ⚫ Time-Domain representation
1.2 Discrete-time signals Time-Domain representation The graphical representation of a sequence xn]] with real-valued samples is illustrated in Figure 2. 1 x[-5] 345678910113 1_98-76-54-3-2-102 314J5161n r[3 Figure 21: Graphical representation of a discrete-time sequence kx[n])
1.2 Discrete-time signals The graphical representation of a sequence {x[n]} with real-valued samples is illustrated in Figure 2.1. ⚫ Time-Domain representation
1.2 Discrete-time signals O Time-Domain representation In some applications, a discrete-valued sequence xn is generated by periodically sampling a continuous-time signal x, (t at uniform time intervals [川]=x()=m=x、(nT),n=…,-2,-10,2, tanr- T is called the sampling interval or sampling period, the reciprocal of T, denoted as Fr, is called the sampling frequency
1.2 Discrete-time signals In some applications, a discrete-valued sequence {x[n]} is generated by periodically sampling a continuous-time signal x t a ( ) at uniform time intervals ( ) ( ), , 2, 1,0,1,2, a t nT a x n x t x nT n = = = − − = T is called the sampling interval or sampling period, the reciprocal of T, denoted as , is called the sampling frequency FT ⚫ Time-Domain representation
2 Discrete-time signals Time-Domain representation 3了T . -T -T 0 T Figure 2.2: Sequence generated by sampling a continuous-time signal xa()
1.2 Discrete-time signals ⚫ Time-Domain representation