292

|

7 Appendix: Quantity- / Unit Symbols and Important Constants

Name of Quantity

Symbol

Domain / Value

Unit

Unitsymbol

z- transformed of f(n)

F(z)

ℝ

Sampled signal with

Dirac pulse

fT(t)

ℝ

Fourier-transformed of

fT(t)

FT(t)

ℝ

Sampled signal with

rectangular-pulse

f∆T(t)

ℝ

Fourier-transform of

f∆T(t)

F∆T(t)

ℝ

Short notation for

sampled signal at the

times fT(j ⋅T)

fT(j)

ℝ

Discrete signal after

undersampling

fTu(n)

ℝ

Discrete signal after

oversampling

fTü(n)

ℝ

Fourier matrix

W

ℝ

Circular cut-off frequency

ωg(t)

ℝ

Radiant

second

rad/s

Cut-off frequency

fg(t)

ℝ

Hertz

Hz

Averaged discrete signal

fM(k)

ℝ

Maximum signal duration

tg

ℝ

second

s

Complex frequency

p

ℂ

Periodic time

tp

ℝ

second

s

Periodic signal

fp(t)

ℝ

Periodic Sequence of

Dirac pulses in the fre-

quency domain

P(f)

Rectangular pulse

gF(t)

ℝ

Random variable x

X

ℝ

Expectation value X

E(X)

ℝ

Correlation function of X1

and X2

RX1X2

ℝ

Auto-correlation function

of x at time ti with a shift

of τj

RXX(ti, τj)

ℝ

Auto-correlation function

of RXX(ti, τj) averaged

over ti

RXX(j)

ℝ

Discrete Fourier-

transform of RXX(j) dis-

crete power spectral

density

SXX(j)

ℝ