. 18.1.1. |
. P P>1. , , . . , , . : , (t - ), ( - ).
, , (, ):
s(x,y) = sin(x2+y2), - < x,y < (18.1.1)
( ) . 18.1.1.
( ) - , Dx Dy. , x y, Dx Dy :
sn,m = s(nDx,mDy), - < n,m < . (18.1.1')
sn,m s (x=nDx,y=mDy), x y () . 1 ( ) s(n,m) º sn,m. - : - (x,y), - ( - ). , , , , . , , , , - , .. - , , .
(18.1.1) , , . . , , .
(, ), .
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. 18.1.2. |
d(nDx,mDy) = dn,m :
dn,m = 1, n = m = 0.
= 0, n 0, m 0.
dn,m = dn dm,
dn, dm - ( ) n m. . 18.1.2.
n1, m1 : d((n-n1)Dx,(m-m1)Dy) = dn-n1,m-m1. , , , ().
. 18.1.3. |
: s(n,m) = d(n) s(n,m) = d(m).
. 18.1.3 , - m = 0: s(n,m) = d(m), n = 2: s(n,m) = d(n-2).
, P- P- , P- , P- .., , , .
. 18.1.4. |
u(n,m), . 18.1.4, :
u(n,m) = 1, n 0 m 0,
= 0, .
u(n,m) = u(n) u(m),
u(j) n m: u(j)=1 j 0, u(j)=0 j<0. (n,m)- .
: s(n,m) = anbm, - < n,m < , b . = exp(jw1), b = exp(jw2), ||=1, |b|=1:
s(n,m) = exp(jnw1+jmw2) = cos(nw1+mw2)+jsin(nw1+mw2).
, , , .
. , . , :
s(n,m) = s(n) s(m).
. :
s(n,m) = si×n(n) si×m(m),
N- . , s(n,m) :
s(n,m) = s(n,i) d(m-i). (18.1.2)
. 18.1.5. |
. , , . .18.1.5 , -3 n 2, -2 m . , . .
. 18.1.6. |
. , . , :
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s(n,m+M) = s(n,m),
s(n+N,m) = s(n,m), (18.1.3)
, n m. N m n ( ). ( .18.1.6) , .
(18.1.3) :
s(n+N1, m+M1) = s(n,m), (18.1.4)
s(n+N2, m+M2) = s(n,m),
D = N1M2 - N2M1 0.
. 18.1.7. |
(N1,M1) (N2,M2) N M, . D, |D|. (4,4) (3,-5) . 18.1.7.
. P- s() P- , P P- N - , :
s() = s( + ), i = 1,2,3,...,P.
N i N P P. . . s() N. s() N, s( + ) = s(), PN s(). , .