Метрология, стандартизация и сертификация. Акмайкин Д.А. - 23 стр.

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23
 S
0
!&) &!#$$ . '0" #& (/)
,+!) y = y
0
+ S
0
(!
1
!
0
)(1
t/T
),  , ()) "!. ,
/) ( #$ ,! y(t) (! !!&" (&"
*!!, &  0,63  "! !. #$! (-
/ (+ '# #- ! !" (#!#$ (!, (-
2" !*"!) &!. &* ") (!) t
y
= (3
÷
4)T.
! !*"!! #!&!, !*").0!/) (!" ( !!-
#$" *, /) #!&! !*")) ( * x(t)=Xsin
ω
t.
2" #&  / y(t) = S(
ω
)X sin [
ω
t+
ϕ
(
ω
)].
'0" #& #) & !"!& (1!
!
= y(t) Sx(t) = y(t) y

/ !# (#). ! !-
# !:
( ) ( ) ( )
d66h6txty
0
=
,  h(
τ
) !"(#$) ,+!).

( ) ( ) ( )
)(txd66h6txt
0
*+
=
.
! !(t) "&#" (! r, *(!1" x(t
τ
) !
( ) ( ) ( )
(
)
( )
(
)
r
r
r
r
txtx
txtxtx
ττττ
!
1...
!
2
)(
2
++
+
=
.
! (#& *#-! ( 0. ,"#, (-
#&!"
( ) ( ) ( ) ( ) ( )
(
)
( ) ( ) ( )
++
=
0 0 0
rr
r
*+
txd66h6tx
r!
1
...d66htxd66htxt7
)(
τ
.
 #$ -! ! 2,,!+! (! 5" (-
#). ' !# ! #) (& ,+!!.
'*&! ( #$ -!) &* 2,,!+!
:
( )
ττ
dhC
x
=
0
;
( )
τττ
dhC
x
=
1
; …;
( )
τττ
dhC
x
rr
r
= )1(
, (#&!"
(
)
(
)
(
)
(
)
(
)
(
)
txCtxCtxCt7
rr
r*+
++
+= ...
10
.
2,,!+! .
0
, .
1
, .
r
* . 2,,!+!"! 1!',
 /) &* (&. ,+!. W(P). !)
P=j
ω
=0, !,,+!) ( ! &!) =0, !* ,+!! (&-
 * /) 2,,!+! :
   S0  !&     )&      ! #$       $ .     '0 " # & ( /       )
, +!) y = y0 + S0(!1 – !0)(1 − −t/T),  ,−(      ) ) " !. ,
 / ) (         #$            ,! y(t) ( ! ! !& "      ( & "
 *    !!, &          0,63        " !         !.    #$  !( -
 /     ( + ' # # - ! !"                 ( # ! #$   (   !, ( -
2 " !*"    !) &! . & *      ") (     !)ty = (3÷4)T.
      ! !*"   !! #!&! , !*" ).0!/ ) ( !"      ( !                                                                        !-
    #$ " *                      , /          ) #!&!               !*" )          )( *                   x(t)=Xsinωt.
    2 " #&                         / y(t) = S(ω)X sin [ωt+ϕ(ω)].
         '0 "                     #&    #)     &       ! "!&                                        (         1          !
∆   !   = y(t) – Sx(t) = y(t) – y                    /                 !    #(                 #).            !      ! -
                                         ∞

          #              !: y (t ) = x(t − 6 )h(6 )d6 ,                    h(τ) – !"( #$                ),          +!).
                                         0

                            ∞
            ∆   *+ (t ) =       x(t − 6 )h(6 )d6 − x(t ) .
                            0

                            ! !(t) "             &#          "         ( ! r, * (!1 " x(t − τ)                       !
                               x ′′(t ) 2             r x
                                                          (r )
                                                               (t )τ r
x(t − τ ) = x(t ) − x ′(t )τ +         τ + ... + (− 1) ⋅               .
                                 2!                        r!
                        ! ( #&                           *# - !             (               0 . , " #, ( -
                                  ∞                  ∞
                                                                               (− 1)r           ∞

                *+ (t ) = x(t ) h(6 )d6 − x (t )         τ ⋅ h(6 )d6 + ... +            x ( r ) (t ) 6 r ⋅ h(6 )d6 − x(t ) .
# &!" 7                                    ′
                                  0                  0
                                                                                 r!             0

                                 #$               - ! !                    2,,!+!   ( ! 5" (                              -
        #).   ' !                        #          ! #)(                      &  , +!!.
           ' * &! (                               #$                       - !) & *   2,,!+!
                ∞                            ∞                                          ∞

    : C 0 = h(τ )dτ ; C1 = − τh(τ )dτ ; …; C r = (−1) τ h(τ )dτ , ( # &!"
                                                     r r

                x                            x                                          x

7    *+   (t ) = C0 x(t ) + C1′x′ (t ) + ... + C r(r ) (r )
                                                         x    (t ) .
                2,,!+!  .0, .1, ….r *  .                                         2,,!+!    "! 1!' ,
                   / ) & * (        & . ,                                        +!. W(P).    !  )
P=jω=0, !,,                       +! )(              ! &! ) =0, !* ,                        +!! (                   & -
  *      / )                       2,,!+!               :

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