82.2 Operations on Sequences For example, the input may be a signal corrupted with additive noise Discrete-time system is designed to generate an output by removing the noise component from the input In most cases, the operation defining a particular discrete-time system is composed of some basic operations
§2.2 Operations on Sequences • For example, the input may be a signal corrupted with additive noise • Discrete-time system is designed to generate an output by removing the noise component from the input • In most cases, the operation defining a particular discrete-time system is composed of some basic operations
§221 Basic operations Product(modulation) operation: Modulator xn yIn]=xnwn wIn 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 The process is called windowing
§2.2.1 Basic Operations • Product (modulation) operation: Modulator x[n] y[n] w[n] y[n]=x[n].w[n] • 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 • The process is called windowing
§221 Basic operations Addition operation: Adder x[n]+→y yIn yn=xn+w Multiplication operation Multiplier xn] yIn] yIn=A.xnI
§2.2.1 Basic Operations • Addition operation: x[n] y[n] w[n] –Adder + y[n]=x[n]+w[n] A x[n] y[n] y[n]=A.x[n] –Multiplier • Multiplication operation
§221 Basic operations Time-shifting operation, where n is an integer Ifn>0, it is delaying operation Unit delay yIn yIn=xn-1 Ifn<0, it is an advance operation Unit advance yIn=xn+
§2.2.1 Basic Operations • Time-shifting operation, where N is an integer • If N > 0, it is delaying operation −1 x[n] z y[n] –Unit delay y[n]=x[n-1] x[n] z y[n] -Unit advance y[n]=x[n+1] If N < 0, it is an advance operation
§221 Basic operations Time-reversal (folding)operation: y Xl-n Branching operation: Used to provide multiple copies of a sequence xn
§2.2.1 Basic Operations • Time-reversal (folding) operation: y[n]=x[-n] • Branching operation: Used to provide multiple copies of a sequence x[n] x[n] x[n]