B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

886 APPENDIX E: MISCELLANEOUS
E.4 Sums
k
r k +l - 1
L r m - -- - r --1
m= O
r
m - _,-N_ + _ l _-_,- M _
r - 1
m=M
r ,6 1
a I b
E.5 Complex Numbers
e ± jrr/2
= ±j
e ± jn rr
=
11 n even
e ±j e
- 1 n odd
= cos 0 ±j sin 0
a+ jb = rei 0
(reiel = /J k 0
(r1 ei 0 1 )(r2d 0 2 ) = r1 r2 ei< 0 1+0 2)
E.6 Trigonometric Identities
e ±jx = cosx ±j sinx
1 . .
COS X = -(ef X + e-J X )
2
1 . .
sinx = 2 / dx - e-1x)
cos ( x ± I) = =F sin x
sin ( x ± I) = ± cos x
2 sinx cosx = sin 2x
sin 2 x + cos 2 x = 1
cos 2 x - sin 2 x = cos 2x
1
cos 2 x = 2
(1 + cos 2x)
1
sin 2 x = 2
(1 - cos 2x)