- , , () , .
, , s(t) = a(t)+jb(t), (t) b(t) - , (instantaneous power) :
w(t) = s(t) s*(t) = [a(t)+jb(t)] [a(t)-jb(t)] = a2(t)+b2(t) = |s(t)|2, (2.2.1)
.. , - .
:
wn = sn s*n = [an+jbn] [an-jbn] = an2 + bn2 = |sn|2, (2.2.1')
( ) . :
s = w(t)dt = |s(t)|2dt. (2.2.2)
Es = wn = |sn|2. (2.2.2')
w(t) , :
w(t) = (1/Dt) |s(t)|2dt.
. , , - ( , ). . .
, , - , (average power) :
WT(t) = (1/T) w(t) dt = (1/T) |s(t)|2 dt. (2.2.3)
, . :
Ws = w(t) dt. (2.2.3')
() (root mean sqare, RMS).
, . , s(t) , R . , , ( -):
w(t) = |s(t)|2/R,
w(t) s(t) R. s(t) R. s(t) R=1 (2.2.1). s(t) , - , , . .
|
|
(2.1.2) (2.2.2) , :
Es = ||s(t)||2, ||s(t)|| = (2.2.4)
. s(n) = {0,1,2,3,4,5,4,3,2,1,0,0,0,0....}.
: Es = s2(n) = 1+4+9+16+25+16+9+4+1 = 85. : ||s(n)|| = 9.22
u(t) v(t):
E = [u(t)+v(t)]2 dt = Eu + Ev + 2 u(t)v(t) dt. (2.2.5)
, ( ), , . u(t)+v(t), , :
Euv = 2 u(t)v(t) dt. (2.2.6)
, :
Euv = 2 áu(t), v(t)ñ. (2.2.6')
x(t) y(t):
wxy(t) = x(t) y*(t), (2.2.7)
wyx(t) = y(t) x*(t),
wxy(t) = w*yx(t).
:
wxy(t) = wyx(t) = x(t) y(t). (2.2.8)
(2.2.7-8) .