82.1 Discrete-Time Signals: Time-Domain Representation Example Time t 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 for a finite time interval Snsn, where -oo<N,and n2 <oo with nsn, Length or duration of the above finite length sequence is n=n-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-xm=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 xn] has zero valued samples forn<N a right-sided sequence ●dfN1≥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
82.2 Operations on Sequences a single-input, single-output discrete time system operates on a sequence called the input sequence, accordin some prescribed rules and develops another sequence, called the output sequence, with more desirable properties Discrete-time 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