【正文】 1 外 文 資料 Signals and System Signals are scalarvalued functions of one or more independent variables. Often for convenience, when the signals are onedimensional, the independent variable is referred to as ―time‖ The independent variable may be continues or discrete. Signals that are continuous in both amplitude and time (often referred to as continuous time or analog signals) are the most monly encountered in signal processing contexts. Discretetime signals are typically associated with sampling of continuoustime signals. In a digital implementation of signal processing system, quantization of signal amplitude is also required . Although not precisely Correct in every context, discretetime signal processing is often referred to as digital signal processing. Discretetime signals, also referred to as sequences, are denoted by functions whose arguments are integers. For example , x(n) represents a sequence that is defined for integer values of n and undefined for noninteger value of n . The notation x(n) refers to the discrete time function x or to the value of function x at a specific value of n .The distinction between these two will be obvious from the contest . Some sequences and classes of sequences play a particularly important role in discretetime signal processing .These are summarized below. The unit sample sequence, denoted by δ(n)=1 ,n=0 ， δ(n)=0,otherwise (1) The sequence δ(n) play a role similar to an impulse function in analog analysis . The unit step sequence ,denoted by u(n), is defined as U(n)=1 , n≧ 0 u(n)=0 ,otherwise (2) Exponential sequences of the form X(n)= ?nA (3) Play a role in discrete time signal processing similar to the role played by exponential functions in continuous time signal processing .Specifically, they are eigenfunctions of 2 discrete time linear system and for that reason form the basis for transform analysis techniques. When ︳ α ︳ =1, x(n) takes the form x(n)= Aenj? (4) Because the variable n is an integer ,plex exponential sequences separated by integer multiples of 2π in ω(frequency) are identical sequences ,I .e: ee njkj ??? ?? )2( (5) This fact forms the core of many of the important differences between the representation of discrete time signals and systems . A general sinusoidal sequence can be expressed as x(n)=Acos( 0w n +Φ) (6) where A is the amplitude , 0w the frequency, and Φ the phase . In contrast with continuous time sinusoids, a discrete time sinusoidal signal is not necessarily periodic and if it is the periodic and if it is ,the period is 2π/ω0 is an integer . In both continuous time and discrete time ,the importance of sinusoidal signals lies in the facts that a broad class of signals and that the response of linear time invariant systems to a sinusoidal signal is sinusoidal with the same frequency and with a change in only the amplitude and phase . Systems:In general, a system maps an input signal x(n) to an output signal y(n) through a system transformation T{.}.The definition of a system is very broad . without some restrictions ,the characterization of a system requires a plete inputoutput relationship knowing the output of a system to a certain set of inputs dose not allow us to determine the output of a system to other sets of inputs . Two types of restrictions that greatly simplify the characterization and analysis of a system are linearity and time invariance, alternatively referred as shift invariance . Fortunately, many system can often be approximated by a linear and time invariant system . The linearity of a system is defined through the principle of superposition: T{ax1(n)+bx2(n)}=ay1(n)+by2(n) (7) 3 Where T{x1(n)}=y1(n) , T{x2(n)}=y2(n), and a and b are any scalar constants. Time invariance of a system is defined as Time invariance T{x(nn0)}=y(nn0) (8) Where y(n)=T{x(n)} and 0n is a integer linearity and time inva riance are independent properties, ,a system may have one but not the other property ,both or neither . For a linear and time invariant (LTI) system ,the system response y(n) is given by y(n)= ?????? ??k nhnxknhkx )(*)()()( (9) where x(n) is the input and h(n) is the response of the system when the input is δ(n).Eq(9) is the convolution sum . As with continuous time convolution ,the convolution operator in Eq(9) is mutative and associative and