. :
s(n,m) = sa(nDx,mDy),
Dx Dy - sa(x,y) x y. Dx Dy, , 1.
, , . . - .
Wx Wy:
Sa(Wx,Wy) = sa(x,y) exp(-jWxx-jWyy) dxdy. (18.4.1)
sa(x,y) = Sa(Wx,Wy) exp(jWxx+jWyy) dWxdWy. (18.4.2)
:
S(k,l) = s(n,m) exp(-jn2pk/N-jm2pl/M), (18.4.3)
S(k,l) = exp(-jn2pk/N) s(n,m) exp(-jm2pl/M), (18.4.3')
s(n,m) = S(k,l) exp(-jn2pk/N-jm2pl/M). (18.4.4)
s(n,m) = exp(-jn2pk/N) S(k,l) exp(-jm2pl/M). (18.4.4')
(18.4.3') (18.4.4') , . s(n,m) S(k,l) n k , - m l. , s(n,m) S(k,l) ( ), - ( ).
. sa(x,y) , :
Sa(Wx,Wy) = 0 |Wx| p/Dx, |Wy| p/Dx,
, , sa(x,y) -:
sa(x,y) = Sn Sm s(n,m) . (18.4.5)
, , , , "", , . "" , .
. 18.4.1. |
. v1 = (v11,v21)T v2 = (v12,v22)T, T - (. 18.4.1). (x,y):
|
|
x = v11n + v12m,
y = v21n + v22m.
:
=
= (x,y)T, =(n,m)T, =(v1 | v2)- . , v1 v2 . sa(x,y) :
s() Ü sa( ).
= (W1,W2)T:
Sa() = sa() exp(-j T ) d , (18.4.6)
sa() = Sa() exp(j T ) d , (18.4.7)
, d d .
:
S() = Sn s() exp(-j T ), (18.4.8)
s() = S() exp(j T ) d . (18.4.9)
: = (w,w)T .
s() sa() (18.4.7):
s() = sa( ) = Sa() exp(j T ) d .
= T, :
s() = Sa( / T) exp(j ) d .
, :
s() = Sa(( -2p )/ T) exp(j ) d , (18.4.10)
- w w. (18.4.9), :
S() = Sa(( -2p )/ T),
S( T) = Sa( - ), (18.4.11)
- :
= 2p , (18.4.12)
, - 2 2. (18.4.11) .
. 18.4.2. |
, Dx Dy wx wy : wxN = p/Dx wyN = p/Dy. . ( ) . . 18.4.2 Dx=1 Dy=1.
:
, det = DD, (18.4.13)
. (18.4.14)
. , (18.4.11) . T (18.4.11) :
S( T) = Sa() / |det |. (18.4.15)
Sa() = |det | S( T) = |det | S(), Î . (18.4.16)
(18.4.16) , |det | . , (18.4.16), ( -):
sa() = s() exp(j T ( - )) d .
sa() = s() f( - ), (18.4.17)
f(..) :
f( - ) = exp(j T ( - )) d . (18.4.18)
|
|
- 4p2 , , (2p)P.
. , . , .. |det |, .
, , - . (18.4.13-14). , . 18.4.1, Dt = D , :
, .
, , wr:
Sa(w,w) = 0 w2+w2 > wr2.
2wr 2wr/ . :
= , det = p2/wr2,
= , det = 2p2/(wr2 ).
1/|det |, , 13.4% . "" . , 4- "" 2 , "".