sI(t) cos (2πf0T

(1)

0��

��

0��

��

0�0 ��

� �� f0 ��

� �� Bw = �

0 2f0

��

�� f0�

s (t) = sI(t) cos (2πf0T )− sQ(t) sin (2πf0T ) . ��

�� sI(t)�� sQ(t)��

�� 0� ��

��

(2)

s (t) = Re{˜s(t) exp (j2πf0t)} , ˜s(t) = sI(t) + js_Q(t) . ��

�� ˜s(t) ��

s (t)� ��

��

�� f0� ��

��

0��

��

0��

�� s = a + jb � �� a, b ��

�� ^∗ �� s

�� s�

s^∗ = a− jb. ��

�� ^∗ ��

��

M =

� a + jb c + jd e + jf g + jh

�

→ M^∗ =

� a− jb c − jd e− jf g − jh

�

. ��

0��0 ��

�� M � �� ^T ��

��

(3)

M =

�

→ M^T =

� a + jb e + jf c + jd g + jh

�

. ��

0��

�� M � �� ^H ��

��

M =

�

→ M^H =

� a− jb e − jf c− jd g − jh

�

. ��

�� ^H ��

��

0��

�� M � �� M⁻¹��

�� M �� I�

M⁻¹M = I =







1 0 . 0 0 . 0 . . 0 . 0 0 . 0 1





. ��

0��

��

� �� n by n ��

��

M = M^T. ��

M �� O�

(4)

D =







λ1 0 0 0

0 . 0 0

0 0 . 0

0 0 0 λ_n





= O⁻¹MO. ��

�� O �� O^T = O⁻¹, O^TO = I� O ��

�� M�

0��

��

� �� n by n ��

��

M = M^H. ��

�� m ��

�� M�

M = mm^H. ��

��

m =

� a + jb c + jd

�

→ m^H =�

a− jb c − jd �

. ��

��

M = mm^H =

� a²+ b² (a + jb) (c− jd) (a− jb) (c + jd) c²+ d²

�

=

� a²+ b² a + jbc− jad + bd a− jbc + jad + bd c²+ d²

� . ��

(5)

� �� M �� U�

D =







λ1 0 0 0 0 . 0 0 0 0 . 0 0 0 0 λn





= U⁻¹MU. ��

�� U �� U^H = U⁻¹, U^HU = I� ��

�� ui �� Mui = λiui� ��

�� e^jΦ ��

Mui = λiui → Muie^jΦ = λiuie^jΦ. ��

�� (2.15) �� e^jΦ ��

��

0��

�� A� �� A ��

A = UDV^T, D =







λ1 0 0 0

0 . 0 0

0 0 . 0

0 0 0 λ_n





 ��

�� U,V �� 0� �� (2.16) ��

��

U^HAV^∗ = U^HUDV^TV^∗ = D. ��

0��

�� A �� (2.16) �� A^T = A� ��

��

(6)

A = UDU^T, D =







λ1 0 0 0

0 . 0 0

0 0 . 0

0 0 0 λ_n





 ��

�� λi ��

��

Ax = λx^∗. ��

0� �� A �� UDU^T �� (2.19)�

UDU^Tx = λx^∗. ��

0� �� U^H �� (2.20)�

U^HUDU^Tx = DU^Tx = U^Hλx^∗ ��

�� y = U^Tx� ��

Dy = λy^∗. ��

�� (2.19)� �� n ��

�� λi� y = ei, i = 1..n � �� ei ��

�� i^th ��

�� (2.19) �� λi �� x = U^∗ei� λi ��

�� U^∗ = [x1x2...xn]� ��

�� xi �� Axi = λix^∗_i� ��

�� e^jΦ ��

��

Axi = λix^∗i → Axie^jΦ = λie^j2Φ�

xie^jΦ�∗

= λie^j2Φxie^−jΦ = λixie^jΦ ��

�� (2.19) �� e^jΦ ��

(7)

��

0��

�� n� ��0��

��

SU(2 ) �� C² ��

S₁ =

� cos (ψ) − sin (ψ) sin (ψ) cos (ψ)

�

, S₂ =

� cos (τ ) j sin (τ ) j sin (τ ) cos (τ )

� ,

S3 =

� exp (jν) 0 0 exp (−jν)

� ��

�� Si =

� a c d b

�

, det (Si) = ad− bc� ��

�� (2.24) det (Si) = 1� ��

��

0��

��

(8)

0��

��

�� 0�

�� 0��

��

�� 0��

��

�� 0��

��

�� 0��

��

�� 0��

��

0��

��

�� ˆx×ˆy = ˆz �� ˆx^�×ˆy^� = ˆz^��

ˆ

x, ˆz, ˆx^�, ˆz^� ��

�� η� ��

η .

= 0 ��

(9)

ˆ

y^{F SA}^−Mono = ˆy^{�F SA−Mono}, ˆx^{F SA}^−Mono =−ˆx^{�F SA−Mono}, ˆz^{F SA}^−Mono =−ˆz^{�F SA−Mono}

��

0��0 ��

�� 0��

��

�� η = 0 ��

��

(ˆx× ˆy = ˆz)� �� 0��

�� ˆz^� �� ˆz�

��

�� 0��

��

(10)

�� 0�� 0��

�� 0��

��

0��

� ��

��

Aspect = �

φ θ Ψ �

��

�� φ �� θ ��

�� Ψ ��

��

�� ˆ

x” ˆy” ˆz” �

��

� ˆ

x ˆy ˆz �

��

(11)

��

� ˆ

x ˆy ˆz �

= R (Ψ) R (θ) R (φ)� ˆ

x” ˆy” ˆz” �

R (φ) =





cos (φ) 0 sin (φ)

0 1 0

− sin (φ) 0 cos (φ)





R (θ) =





1 0 0

0 cos (θ) sin (θ) 0 − sin (θ) cos (θ)





R (Ψ) =





cos (Ψ) sin (Ψ) 0

− sin (Ψ) cos (Ψ) 0

0 0 1





. ��

�� φ �� ˆy ��

θ �� ˆx �� Ψ ��

�� ˆz� ��

��

(12)

0��

��