1.Time-Domain Representation 1.Time-Domain Representation 1.Time-Domain Representation Graphical representation of a discrete-time .In some applications,a discrete-time sequence Here,n-th sample is given by signal with real-valued samples is as shown (x(n))may be generated by periodically x(n斤x(0l-mFx(nD2n=.,-2,-1,0,-1 below: sampling a continuous-time signal at uniform -5 intervals of timex(r) The spacing T between two consecutive x(n) x-sn samples is called the sampling interval or sampling period Reciprocal of sampling interval T.denoted as, is called the sampling frequency: FFVT 1.Time-Domain Representation 1.Time-Domain Representation 1.Time-Domain Representation Unit of sampling frequency is cycles per A discrete-time signal may be a finite-length second,or hertz(Hz),if Tis in seconds Two types of discrete-time signals: or an infinite-length sequence --Sampled-data signals Whether or not the sequence (x(n))has been -Digital signals Finite-length (also called finite-duration or obtained by sampling.the quantity x(n)is finite-extent)sequence is defined only for a called the n-th sample of the sequence Signals in a practical digital signal processing finite time interval NnN2, system are digital signals obtained by .(x(n))is a real sequence,if the n-th sample x(n) quantizing the sample values either by where-<N and N <o with N<N2 is real for all values ofn ounding(取整)or truncation(舍位) Length or duration of the above sequence is Otherwise,(x(n))is a complex sequence N=N-N+17 Graphical representation of a discrete-time signal with real-valued samples is as shown below: 1. Time-Domain Representation x( 5) x( ) n x(3) 8 In some applications, a discrete-time sequence {x(n)} may be generated by periodically sampling a continuous-time signal at uniform intervals of time xa(t) 1. Time-Domain Representation (5) a x T ( ) a x t (3 ) a x T 9 Here, n-th sample is given by x(n)=xa(t)|t=nT=xa(nT), n =…, ˉ2, ˉ1,0, ˉ1,… The spacing T between two consecutive samples is called the sampling interval sampling interval or sampling period Reciprocal of sampling interval T, denoted as , is called the sampling frequency: FT=1/T 1. Time-Domain Representation 10 Unit of sampling frequency is cycles per second, or hertz (Hz), if T is in seconds Whether or not the sequence {x(n)} has been obtained by sampling, the quantity x(n) is called the n-th sample of the sequence {x(n)} is a real sequence real sequence, if the n-th sample x(n) is real for all values of n Otherwise, {x(n)} is a complex sequence complex sequence 1. Time-Domain Representation 11 Two types of discrete-time signals: -- Sampled-data signals data signals -- Digital signals Digital signals Signals in a practical digital signal processing system are digital signals obtained by quantizing the sample values either by rounding ˄ਆᮤ˅ or truncation ˄㠽ս˅ 1. Time-Domain Representation 12 A discrete-time signal may be a finite-length or an infinite infinite-length sequence Finite-length (also called finite-duration or finite-extent) sequence is defined only for a finite time interval N1 İ n İ N2 , where ˉĞ< N1 and N2 <Ğ with N1 < N2 Length or duration of the above sequence is N = N2ˉN1 + 1 1. Time-Domain Representation