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Disser Ta Cao Liliane
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7/21/2019 Disser Ta Cao Liliane Silva
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T 2
T ∗2
&
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σ
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x(k) = As(k)
x(k)
A
A
y(k)
W
x(k)
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y(k)
p(y1, · · · , yn) =ni=1
pyi(yi)
E [g(y1), · · · , g(yn)] = E [g(y1)]E [g(y2)] · · · E [g(yn)]
g(.)
(y1, · · · , yn)
E [y1, · · · , yn] − E [y1]E [y2] · · · E [yn] = 0 y1 = y2 = · · · = yn
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(2×2)
(s1es2)
x1
x2
x1
x2
p(x) = 1
σ√
2πe−(x−µ)2
2σ2
µ
σ
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x(k)
E [x(k)]
x(k)
x(k)
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s(k)
W
s(k)
s(k)
x(k)
z (k)
z (k) = Qx(k)
Q
z (k)
Q
x(k)
z (k) = Qx(k)
E [x(k)x(k)T ] = M DM T
M
E [x(k)x(k)T ]
D
z (k)
z (k) = M D− 12 M x(k)
D− 12
D− 12 = diag(d
− 12
1 , · · · , d− 1
2n )
E [z (k)z (k)T ] = I
I
Ab
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z (k) = M D− 12 M x(k)
z (k) = M D− 12 M As(k)
z (k) = Abs(k)
Ab
Ab
A
n2
n(n−1)2
Ab A
s1(k) s2(k)
x1(k)
x2(k)
z 1(k)
z 2(k)
n = 2
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•
•
y(k)
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Kurt(y(k)) = E [y(k)4] − 3(E [y(k)2])2
y(k)
Kurt(y(k)) = E [y(k)4] − 3
E [y(k)4]
3E [[S 2(k)]2]
E [S 2(k)] = 1
• k > 0
• k < 0
• k = 0
• | Kurt |= 0
• | kurt |> 0
W
y(k)
•
x(k)
z (k)
•
W
•
y(k)
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•
x(k)
W
•
•
•
•
•
H
H (y) = −
P (y = ai)log(P (y = ai))
P (y = ai)
y(k) = y
ai
J
J (y) = H (ygauss) − H (y)
ygauss
y
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J (y) = 1
12
E [y3]2 + 1
48
Kurtosis(y)2
y
kurtosis
G(.)
J G(y) = α[E [G(y)] − E [G(b)]]
2
G(.)
b
G(.)
G1(u) = u3, G2(u) = tanh(a1 · u), G3(u) = u · exp(−a2·u
2
/2), G4(u) = u2
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U
U T U = I ,
I
X m×n
m ≥ n
U m×m
V n×n
X = U DV T
D =
σ1
σ2
σ3
σn
0 · · · · · · · · · 0
0 · · · · · · · · · 0
p = n
σ1 ≥ σ2 ≥ σ3 ≥ · · · ≥ σ p > σ p+1 = σn = 0
σi
X
U
V
D
X
XX T
X
V
X T X
U
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U
V
X
U
V
×
times
X = U DV T ,
σi 106
σ1 ≈ 5 × 104
σ512 ≈ 2 × 10−2
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X =512i=1
σiuivT i ,
uivT i
ui
vi
σiuivT i
×
u
v
50
×(1+512+512) = 51250
W T x(k)
J G(W )
J G(W ) = [E [G(W T
X (k)] − E [G(b)]2
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G(.)
b
E [.]
W
W n+1 = E [X · G(W T · X )] − E [G(W T · X )] · W
W = W n+1
||W n+1||
E [.]
•
•
•
•
•
•
•
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×
SN R = 10 logσ2
S
σ2R
= 20 log
σS
σR
σS
σR
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×
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G(.)
σ = 1
G1 G2 G3 G4
G1 G2 G3 G4
G(.)
G4
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G1
G2
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G3
G4
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G1
G2
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G3
G4
G(.)
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G1
G2
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G3
G4
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G1C 23
G1C 26
G2C 11
G2C 12
G3C 15
G3C 29
G4C 7
G4C 18
G4
C 7
G4
G4
o
×
×
×
G4
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G4
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G4
C 8
C 19
C 37
C 38
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