: : 1 : ,

.

: .

:4 . , ( , ), , .

-- $x(t)$, $t$. . ( ) . , , , (, , ), , .. .

$x(t)$ - . -- x(t) $t$ -- $x(t_i)$ $t_1$, $t_2$, ..., $t_i$, ...( $\Delta t = t_i - t_{i-1}$ ). , , . $x(t)$ $\Delta t$ , $x(t_i)$ $x(t_{i-1})$ , $x(t)$ $t_i$ $t_{i-1}$ ( $x(t_{i-1})$ $x(t_i)$). $f > 1/\Delta t$ .

-- $t_i$ , . t , , , $t_1$, $t_2$, ..., $t_i$, ... -- , , x. $x_1$, $x_2$, ..., $x_n$, ... $x(t_i)$ .

:

$x(t)$ , $x(t) = \sqrt{t}$, $\Delta t = 0.1$ (.. $t = 0, 0.1, 0.2, \dots$), $x$ (.. $x = 0, \pm 0.01, \pm 0.02, \dots$).

$x$ = 0. 0.3162... 0.4472... 0.5477... 0.6324... ...
$t$ = 0 0.1 0.2 0.3 0.4 ...

x,

$x$ = 0. 0.32... 0.45... 0.55... 0.63... ...
$t$ = 0 0.1 0.2 0.3 0.4 ...

( $f > 1/\Delta t$) , ( $\Delta x = x_n - x_{n-1}$) . , $x_n(t_i)$ ( ) $x(t_i)$ ( ) $\Delta x$. , .

, ,

$x(t_i)$ = 0. 0.3162... 0.4472... 0.5477... 0.6324... ...
$x_n(t_i)$ = 0. 0.32... 0.45... 0.55... 0.63... ...
$t_i$ = 0 0.1 0.2 0.3 0.4 ...
$\approx$ 0. 0.00377 0.00279 0.00228 $-$0.00246 ...

, , , $\Delta x = x_n - x_{n-1}$ ( ). , $\Delta x$ , ( /) $x$. , $\Delta x = \varepsilon x$, $\varepsilon$ - ( ). ( ).

-- - (). $f$ ( $f = 1/\Delta t$) ( , $x$, $2^N$, $N$ - ). , ($\Delta x$ ), ( $\Delta t$).

, ( - (, , ..)) - (). ( [1]).

CD: $f = 44.1~{\rm }$, , 16 .

. , , . , . , .. , 1 0. , , . ( , - .).

[1] .., .., .., , - : , , 1990, 160 .: . - ( , . 1153).

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: : 1 : ,
baldin@inp.nsk.su
1999-05-25