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LP = {s(t); s(t+kT) = s(t), -∞ < t < ∞, kÎI}.
(), :
s(t) = A×sin (2pft+f) = A×sin (wt+f), s(t) = A×cos(wt+j), (1.1.1)
. 1.1.5. . |
, fo, wo, j, f - , : - , f - , w = 2pf - , j f- . T = 1/f = 2p/wo. j = f-p/2 . f ( t = 0).
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s(t) = An sin (2pfnt+jn) ≡ An sin (2pBnfpt+jn), Bn ∈ I, (1.1.2)
s(t) = y(t kTp), k = 1,2,3,..., - y(t), . fp =1/Tp .
. 1.1.6. . . 1.1.7. . |
(f=0) ( - ) An jn, , fp. , fp, , , . , - ( ).
. 1.1.6 , . :
s(t) = Ak×cos(2×p×fk×t+jk),
: Ak = {5, 3, 4, 7} - ; fk = {0, 40, 80, 120} - ; jk = {0, -0.4, -0.6, -0.8} - ; k = 0, 1, 2, 3. 40 .
( ) . 1.1.7. , s(t), , .
, f = 1/. , Df = fp:
s(t) = (ak cos 2pkDft + bk sin 2pkDft), (1.1.3)
ao = (1/T) s(t) dt, ak = (2/T) s(t) cos 2pkDft dt, (1.1.4)
bk = (2/T) s(t) sin 2pkDft dt. (1.1.5)
K = kmax fmax , fmax < Kfp. fmax ¥, s(t).
:
s(t) = Sk cos (2pkDft-jk), (1.1.3')
Sk = , jk = argtg (bk/ak). (1.1.6)
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. . 1.1.10 , (0, ¥):
s(t) = exp(-a×t) - exp(-b×t),
a b , a = 0.15, b = 0.17.
. 1.1.11. . |
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[0, ¥]. , (1.1.3) Df 0 kDf f.
s(t) = (a(f) cos 2pft + b(f) sin 2pft) df = S(f) cos(2pft-j(f)) df. (1.1.7)
a(f) = s(t) cos 2pft dt, b(f) = s(t) sin 2pft dt, (1.1.8)
S(f) = , j(f) = argtg (b(f)/a(f)). (1.1.9)
a(f), b(f) S(f) , . (1.1.8-1.1.9) , (1.1.7) .
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s(t) = u(t) cos(2pfot+jo).
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L2 = {s; |s(t)|2 dt < ∞}.
s(t) , . , , : s(t) → 0.
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(. 1.2.1) . 1.2.2. Dt = const ( ) y(n). , - y[t]. - {s(ti)}, ti. ( ) : s(ti) = {a1, a2,..., aN}, t = t1, t2,...,tN. - ( ), , ..
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H = log2 N = log2 16 = 4.
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3. 9- ? = 0. 4. 8- ? = 1.
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H = log 2 N + log 2 M = log 2 16 + log 2 4 = 6 º log 2 (N ´ M) = log 2 64 = 6,
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, , U = {u1, u2,..., uN} {(u1), (u2),..., (uN)} , 1. , U, . 1946 :
H(U) = - pn log2 pn. (1.4.2)
. , , (1.4.2) pn p=1/N . H(U) , .
, , , , 2 .
ui | pi | ui | pi | ui | pi | ui | pi | ui | pi |
.064 | .015 | .096 | .009 | .003 | |||||
.015 | .064 | .024 | .004 | .007 | |||||
.039 | .010 | .041 | .013 | .019 | |||||
.014 | .029 | .047 | .006 | - | .124 | ||||
.026 | .036 | .056 | .003 | ||||||
, | .074 | .026 | .021 | , | .015 | ||||
.008 | .056 | .020 | .016 |
. 32 . . , .
:
H(u) = log 32 = 5
:
H(u) = - 0.064 log 0.064 - 0.015 log 0.015 -.................. - 0.143 log 0.143 4.42.
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