外文資料翻譯---信號與系統(tǒng)

1、1外文資料Signals and SystemSignals are scalar-valued functions of one or more independent variables. Often for convenience, when the signals are one-dimensional, the independent variable is referred to as “time” The independ

2、ent 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 commonly encountered in signal processing contexts.

3、 Discrete-time signals are typically associated with sampling of continuous-time signals. In a digital implementation of signal processing system, quantization of signal amplitude is also required . Although not precise

4、ly Correct in every context, discrete-time signal processing is often referred to as digital signal processing.Discrete-time signals, also referred to as sequences, are denoted by functions whose arguments are integers.

5、For example , x(n) represents a sequence that is defined for integer values of n and undefined for non-integer value of n . The notation x(n) refers to the discrete time function x or to the value of function x at a sp

6、ecific 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 discrete-time signal processing .These are summarized b

7、elow. 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 d

8、efined as U(n)=1 , n≧0 u(n)=0 ,otherwise (2)Exponential sequences of the form X(n)= (3) ?n APlay a role in discrete time signal processing similar to the role played by exponential 3T{ax1(n)+bx2(

9、n)}=ay1(n)+by2(n) (7)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 invarianceT{x(n-n0)}=y(n-n0)

10、 (8)Where y(n)=T{x(n)} and is a integer linearity and time inva riance are independent 0 nproperties, i.e ,a system may have one but not the other property ,both or neither .For a linear and time invariant (LTI) system

11、 ,the system response y(n) is given by y(n)= (9) ????? ?? ?kn h n x k n h k x ) ( * ) ( ) ( ) (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 c

12、ontinuous time convolution ,the convolution operator in Eq(9) is commutative and associative and distributes over addition:Commutative :x(n)*y(n)= y(n)* x(n) (10)Associative:[x(n)*y(n)]*w(n)= x(n)

13、*[ y(n)*w(n)] (11)Distributive:x(n)*[y(n)+w(n)]=x(n)*y(n)+x(n)*w(n) (12)In continuous time systems, convolution is primarily an analytical tool. For discrete time system ,the convolution su

14、m. In addition to being important in the analysis of LTI systems, namely those for which the impulse response if of finite length (FIR systems).Two additional system properties that are referred to frequently are the pro

15、perties of stability and causality .A system is considered stable in the bounded input-bounder output(BIBO)sense if and only if a bounded input always leads to a bounded output. A necessary and sufficient condition for a