82.1 Discrete-Time Signals Time-Domain Representation E Camp oe Timet Timet Boxedcar signal Digital signal
§2.1 Discrete-Time Signals: Time-Domain Representation Example - Amplitude Digital signal Amplitude Boxedcar signal Time,t Time,t
82.1 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 or a finite time interval:N1≤n≤N2 where -oo<N and n2< oo with n<n2 Length or duration of the above finite length sequence is N=n2-N+1
§2.1 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:N1 n N2 where - < N1 and N2 < with N1 N2 • Length or duration of the above finitelength sequence is N= N2 - N1+ 1
82.1 Discrete-Time Signals Time-Domain Representation · Example-x[m=n2,-3≤n≤4isa finite-length sequence of length 4-(-3)+1=8 yIn]=cos0 4n is an infinite-length sequence
§2.1 Discrete-Time Signals: Time-Domain Representation • Example - x[n]=n2 , -3 n 4 is a finite-length sequence of length 4 – (-3) + 1 = 8 y[n]=cos0.4n is an infinite-length sequence
82.1 Discrete-Time Signals Time-Domain Representation .. A right-sided sequence xin has zero valued samples forn <N A right-sided sequence oIfN20, 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 A right-sided sequence •If N1 0, a right-sided sequence is called a causal sequence
82.2 Operations on Sequences A single-input, single-output discrete Ime system operates on a sequence, cale d the input sequence, according some prescribed rules and develops another sequence, called the output sequence, with more desirable properties Discrete-time yIn system Input sequence Output sequence
§2.2 Operations on Sequences • A single-input, single-output discretetime system operates on a sequence, called the input sequence, according some prescribed rules and develops another sequence, called the output sequence, with more desirable properties x[n] y[n] Input sequence Output sequence Discrete-time system