1、3.1.3 所涉及公式1212()()Taxnbaynb(3-1-1)Linear transformation open brace, a Multiplies x sub one open parenthesis n close parenthesis plus b Multiplies x sub two open parenthesis n close parenthesis close brace equals a multiplies y sub one open parenthesis n close parenthesis plus b multiplies y sub two
2、 open parenthesis n close parenthesis .where , and and are any scalar constants.11(),Txny22()()Txnb00(3-1-2)Linear transformation open brace, x open parenthesis n minus n sub zero close parenthesis close brace equals y open parenthesis n minus n sub zero close parenthesis.*kynxhnkxhn(3-1-3)y open pa
3、renthesis n close parenthesis equals capital sigma the quantity x open parenthesis k close parenthesis h open parenthesis n minus k close parenthesis from k approaches negative infinity to k approaches positive infinity, equals x open parenthesis n close parenthesis convolution sum h open parenthesi
4、s n close parenthesis.xnyx(3-1-4)x open parenthesis n close parenthesis convolution sum y open parenthesis n close parenthesis equals y open parenthesis n close parenthesis convolution sum x open parenthesis n close parenthesis.*nywxywn(3-1-5)Open bracket x open parenthesis n close parenthesis convo
5、lution sum y open parenthesis n close parenthesis close bracket convolution sum w open parenthesis n close parenthesis equals x open parenthesis n close parenthesis convolution sum open bracket y open parenthesis n close parenthesis convolution sum w open parenthesis n close parenthesis close bracke
6、t.*xywxynxw(3-1-6)x open parenthesis n close parenthesis convolution sum open bracket y open parenthesis n close parenthesis plus w open parenthesis n close parenthesis close bracket equals x open parenthesis n close parenthesis convolution sum y open parenthesis n close parenthesis plus x open pare
7、nthesis n close parenthesis convolution sum w open parenthesis n close parenthesis.nh(3-1-7)Capital sigma the quantity of the absolute value of h open parenthesis n close parenthesis from n approaches negative infinity to n approaches positive infinity is less than infinity.0hnfor (3-1-8)h open pare
8、nthesis n close parenthesis equals zero for n is less than zero.3.2.3 所涉及公式(3-2-1)()()jnnHheThe signal equals capital sigma the signal times to the power of )(hneminus j times omega times from equals minus infinity to equals plus n ninfinity.(3-2-2)1()()2jnhnHednThe signal equals one over 2 times pi
9、 times the integral from minus pi to pi hof the signal times to the power of j times omega times with respect to )(e nw, where is from Negative infinity to positive infinity.n(3-2-3)01()()cos,0hHdnThe signal equals one over pi times the integral from 0 to pi of the signal htimes cosine of omega time
10、s with respect to w, where is greater than )( nnor equal to zero.(3-2-4)(),0hnnThe signal equals the signal , where is greater than or equal to zero.)-(h)(hnn(3-2-5),(0nMnhoterwisThe signal equals the signal , where is from minus to plus , )(h )(hnnMequals 0 ,where is otherwise.n(3-2-6)()()MnHzhzThe
11、 signal equals capital sigma the signal times to the power. )(hnznth-(3-2-7)(),0,1.2lbhlThe signal equals the signal , where is numbers from 0 to 2 times l )(hMll.M(3-2-8)10(),0,1.2LllBzbMThe signal equals capital sigma the signal times to the power, )(z blzlth-where is numbers from 0 to 2 times .l
12、M(3-2-9)()()MBzHzThe signal equals the quantity to the power times the signal .zMth- )z(H(3-2-10)()()jMeThe signal equals to the power of minus j times omega times times Be Mthe signal .)(H(3-2-11)()BThe signal equals the signal )(B )(H(3-2-12)()(),hnwnThe signal equals the signal times the signal ,
13、 where is from h )(hn)(wnnnegative infinity to positive infinity.(3-2-13)1,()0MnwnotherwisThe signal equals 1, where n is numbers from minus to .)( M(3-2-14)1()()()2HWHdThe signal equals the signal times the signal equals one over 2 )(H)(Wtimes pi times the integral from minus pi to pi of the signal times the signal H.)-(3-2-15)2()WThe signal equals 2 times pi times .-)-(3-2-16)()1,wnThe signal equals 1,where the absolute value of is less than infinity.)(n n
