Special symbols
Notation
Function
Rectangle
Triangle
Heaviside unit step
Sign (signum)
Impulse symbol
Sampling or replicating symbol
Even impulse pair
Odd impulse pair
Filtering or interpolating
Asterisk notation for convolution
Asterisk notation for serial products
Pentagram notation
Various two-dimensional functions
O(x) = { Ixl <!
Ixl >!
A(x) = { - Ixl Ixl < 1
Ixl > 1
H(x) = { x > 0
x < 0
sgnx = {1 x > 0
x < 0
5(x)
00
III(x) = :L 5(x - n)
-00
n(x) = !5(x + !) + !5(x - !)
..(x) = !5(x + !) - !5(x - !)
sin TTX .. J t( 7Tr)
sinc x = , J lnc r =
7TX 2r
f(x) * g(x) tJ(u)g(x - u) du
{f,} * {g,} { fJg,-,}
f(x) * g(x) tj(U)g(x + u) du
20(X,y) = O(x)O(y)
25(x,y) = 5(x) 5(y)
2III(x,y) = III(x)III(y)
2 s inc (x,y) = sinc x sinc y
Guide to reference data
Summary of special symbols
Oddness and evenness
Conjugates
Fourier transforms
Theorems for Fourier transform
Correspondences in the two domains
Laplace transforms
Two-dimensional Fourier transforms
Three-dimensional Fourier transforms
Hankel transforms
Mellin transforms
z transforms
Abel transforms
Hilbert transforms
70, 71
13, 15
16
107, 131, 265, 573
130, 206, 268
190, 199
385,388
333-335
342
338
345-346
350-351
354
365
