0.3 Table of formulas

Information and signal theory Page 1 / 1

Lists important formulas, both analog and time discrete.

Analog	Time Discrete
Delta function	Unit sample
$δ t 0$ for $t 0$ , $t$ ∞ ∞ δ t 1	$δ n 1 n 0 0$

Unit step function	Unit step function
$u t 1 t 0 0$	$u n 1 n 0 0$

Angular frequency	Angular frequency
$2 F$	$2 f$

Energy $E_{a} t$ ∞ ∞ x t 2	Energy $E_{d} n$ ∞ ∞ x n 2

Power $P_{a} 1 T_{0} t T_{0} 2 T_{0} 2 x t 2$	Power $P_{d} 1 N n N_{1} N_{1} N 1 x n 2$

Convol. $y t τ$ ∞ ∞ x τ h t τ	Convol. $y n k$ ∞ ∞ x k h n k

Fourier Transformation	Discrete Time Fourier Transform
$X Ω t$ ∞ ∞ x t Ω t	$X ω n$ ∞ ∞ x n ω n

Inverse Fourier Transform	Inverse DTFT
$x t 12 Ω$ ∞ ∞ X ω Ω t	$x n 12 ω X ω ω n$

Fourier coeffecients	Discrete Fourier Transform
$α_{k} 1 T_{0} t 0 T_{0} x t k Ω_{0} t$	$X k n 0 N 1 x n 2 N k n$

Series expansion	Inverse DFT
$x t k$ ∞ ∞ α k k Ω 0 t	$x n 1 N k 0 N 1 X k 2 N k n$

Parseval	Parseval
$t T_{1} T_{0} x t 2 k 1$ ∞ k 2	$1 N k 0 N 1 X k 2 n 0 N 1 x n 2$

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Source: OpenStax, Information and signal theory. OpenStax CNX. Aug 03, 2006 Download for free at http://legacy.cnx.org/content/col10211/1.19

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