1.Time-Domain Representation 2.Operations on Sequences 2.Operations on Sequences The length of a finite-length sequence can be .A single-input,single-output discrete-time Basic Operations increased by zero-padding,i.e.,by appending system operates on a sequence,called the input ·Product it with zeros sequence,according to some prescribed rules and develops another sequence,called the ●Addition Infinite-length sequences can be classified as output sequence,with more desirable ·Multiplication following properties ·Time-Shifting x(n)=0 for n<N right-sided sequence x(n) Discrete-Time v(n) left-sided sequence Time-Reverse (folding) x(n)=0 for n>N2 Input Sequence System Output Sequence x(m)≠0 for oo≤n≤o double-sided sequence ◆Branching 13 h(n) 15 2.Operations on Sequences 2.Operations on Sequences 2.Operations on Sequences Product (modulation)operation: 。Addition operation: + Time-shifting operation:y(n)=x(n-N) 8 If N>0,it is delaying operation --Modulator w(m) --Unit delay --Adder ynx(n+w(n) →n-) An application is in forming a finite-length 回 sequence from an infinite-length sequence by Multiplication operation: If N<0,it is an advance operation multiplying the latter with a finite-length sequence called an window sequence.The --Unit advance process is called windowing(加窗) --Multiplier y(n)=Ax(n) 月 回 1813 The length of a finite-length sequence can be increased by zero-padding, i.e., by appending it with zeros Infinite-length sequences can be classified as following x(n) =0 for n <N1 right-sided sequence sided sequence x(n) =0 for n >N2 left-sided sequence sided sequence x(n)Į0 for ĞİnİĞ double-sided sequence sided sequence 1. Time-Domain Representation 14 2. Operations on Sequences A single-input, single-output discrete-time system operates on a sequence, called the input sequence sequence, according to some prescribed rules and develops another sequence, called the output sequence output sequence, with more desirable properties Discrete-Time Input Sequence System Output Sequence x(n) y(n) h(n) 15 2. Operations on Sequences Basic Operations Product Product Addition Multiplication Time-Shifting Time-Reverse (folding) Reverse (folding) Branching 16 2. Operations on Sequences Product Product (modulation) operation: (modulation) --Modulator Modulator An application is in forming a finite-length sequence from an infinite-length sequence by multiplying the latter with a finite-length sequence called an window sequence window sequence. The process is called windowing˄࣐デ˅ w(n) x(n) h y(n) 17 2. Operations on Sequences Addition operation: --Adder y(n)=x(n)+w(n) Multiplication operation: --Multiplier Multiplier y(n)=Ax(n) x(n) + w(n) y(n) x(n) A y(n) 18 2. Operations on Sequences Time-shifting operation: y(n)=x(nˉN) If N > 0, it is delaying operation --Unit delay If N < 0, it is an advance operation --Unit advance x(n) z ˉ y(n)=x(nˉ1) 1 x(n) z y(n)=x(n+1)