Forma direct --> forma latice

, ,, , 1, 2, , , = : -1: 2, = 1:1:1

i j i i i jN j j i i i i j

i

a k aa a k a a i N j i

k

= = = -1

2, ,0

-1

,1

, , 1,N

N N i i k k k ik i

b c c b c a i N N= +

= = = " Forma latice --> forma direct

, ,0 , 1, 1,, 1, , = 2 :1: , = 1:1:i i i i i j i j i i i ja k a a a k a i N j i = = = + Decimare:

( ) ( )y n x nM= 110

1( )M

k MM

kY z X W z

M

=

= ( ) ( )11 2

0

1 yy M j kj Mk

Y e X eM

=

= Expandare:

, ,( )

0, i n rest

nx n kL kLy n

= =

L ( ) ( )LY z X z= j jy yY e X e =

Algoritmi rapizi de calcul TFD: ( ) ( )10

, 0,1, ,N

nkN

nX k x n W k N

=1= = 2j nknk NNW e =

In baza R cu decimare in timp: 1 2 1 2

1 2 1 2

, 0,1, , 1, 0,1, ,

, 0,1, , 1, 0,1, , 1;

Nn Rn n n n RR

N Nk k k k k RR R

1;= + = =

= + = =

In baza R cu decimare in frecventa 1 2 1 2

1 2 1 2

, 0,1, , 1, 0,1, , 1;

, 0,1, , 1, 0,1, , 1;

N Nn n n n n RR R

Nk Rk k k k RR

= + = =

= + = =

Q

cu baze mixte 1 2 1 2 2 2undeQ Q QN N N N N N N N N= = =" "