Chapter 2 Discrete-Time Signals and Systems
Chapter 2 Discrete-Time Signals and Systems
2.1 Discrete-Time Signals: Time-Domain Representation Signals represented as sequences of numbers,called samples In some applications,a discrete-time sequence [n} may be generated by periodically sampling a continuous-time signal x(t)at uniform intervals of time xa(-5T 37 -5T -3T-T 0 T xa(3T)
§2.1 Discrete-Time Signals: Time-Domain Representation Signals represented as sequences of numbers, called samples 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
2.1 Discrete-Time Signals: Time-Domain Representation Here,n-th sample is given by x[n=xa()l=nr=xa(nT),n=.,-2,-1,0,1,. The spacing T between two consecutive samples is called the sampling interval or sampling period Reciprocal of sampling interval T,denoted as Fr,is called the sampling frequency: F=1/T
§2.1 Discrete-Time Signals: Time-Domain Representation • Here, n-th sample is given by x[n]=xa(t)| t=nT=xa(nT), n=…,-2,-1,0,1,… • The spacing T between two consecutive samples is called the sampling interval or sampling period • Reciprocal of sampling interval T, denoted as FT , is called the sampling frequency: FT=1/T
2.1 Discrete-Time Signals: Time-Domain Representation Two types of discrete-time signals: Sampled-data signals in which samples are continuous-valued Digital signals in which samples are discrete-valued Signals in a practical digital signal processing system are digital signals obtained by quantizing the sample values either by rounding or truncation
§2.1 Discrete-Time Signals: Time-Domain Representation • Two types of discrete-time signals: - Sampled-data signals in which samples are continuous-valued - Digital signals in which samples are discrete-valued • Signals in a practical digital signal processing system are digital signals obtained by quantizing the sample values either by rounding or truncation
2.1 Discrete-Time Signals: Time-Domain Representation A right-sided sequence xn]has zero- valued samples for nN 00 A right-sided sequence .If N >0,a right-sided sequence is called a causal sequence
§2.1 Discrete-Time Signals: Time-Domain Representation • A right-sided sequence x[n] has zerovalued samples for n < N1 n N1 A right-sided sequence •If N1≥ 0, a right-sided sequence is called a causal sequence