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 Copyright C 2001, S K Mitra
11 Copyright © 2001, S. K. Mitra Discrete-Time Signals: Time-Domain Representation • Two types of discrete-time signals: - Sampled-data signals in which samples are continuous-valued - Digital signalsin 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
Discrete-Time Signals. Time-Domain Representation Example 三 time t time t Sampled-data signal Digital signal 12 Copyright C 2001, S K Mitra
12 Copyright © 2001, S. K. Mitra Discrete-Time Signals: Time-Domain Representation • Example - Sampled-data signal Digital signal Amplitude time, t Amplitude time, t
Discrete-Time Signals. Time-Domain Representation a discrete-time signal may be a finite length or an infinite-length sequence Finite-length(also called finite-duration or finite-extent sequence is defined only for a finite time interval:N1≤n≤N where-∞<M1andN2< oo with m1≤N2 Length or duration of the above finite length sequence is N=N2-N1+ 13 Copyright C 2001, S K Mitra
13 Copyright © 2001, S. K. Mitra Discrete-Time Signals: Time-Domain Representation • A discrete-time signal may be a finitelength or an infinite-length sequence • Finite-length (also called finite-duration or finite-extent) sequence is defined only for a finite time interval: where and with • Length or duration of the above finitelength sequence is N1 n N2 − N1 N2 N1 N2 N = N2 − N1 +1
Discrete-Time Signals. Time-Domain Representation Example-x团l]=n2,-3≤n≤4 is a finite length sequence of length 4(3)+1=8 Example-yn=cos0 4n is an infinite length sequence 14 Copyright C 2001, S K Mitra
14 Copyright © 2001, S. K. Mitra Discrete-Time Signals: Time-Domain Representation • Example - is a finitelength sequence of length • Example - is an infinitelength sequence 3 4 2 x[n] = n , − n 4−(−3) +1= 8 y[n] = cos0.4n
Discrete-Time Signals. Time-Domain Representation A length-N sequence is often referred to as N an N-p point sequence The length of a finite-length sequence can be increased by zero-padding 1 e, by appending it with zeros 15 Copyright C 2001, S K Mitra
15 Copyright © 2001, S. K. Mitra Discrete-Time Signals: Time-Domain Representation • A length-N sequence is often referred to as an N-pointsequence • The length of a finite-length sequence can be increased by zero-padding, i.e., by appending it with zeros