Q_func

Q_func - 1 Q-function Handout c Keith M Chugg 1 Definitions...

This preview shows pages 1–2. Sign up to view the full content.

1 Q -function Handout – c ± Keith M. Chugg 1 Deﬁnitions The Q -function is tail integral of a unit-Gaussian pdf, and is deﬁned as Q ( z ) Δ = Z z 1 2 π e - x 2 2 dx. The Q -function has the following properties: lim z →∞ Q ( z )=0 lim z →-∞ Q ( z )=1 Q (0)=1 / 2 Q ( - z - Q ( z ) . There are several other common notations used to denote this integral function or a close relative. The Q -function is sometime referred to as the “Gaussian Integral Function” and denoted GIF( z ). Other functions which are closely related are the erf( · ) (error function) and erfc( · ) (complementary error function): erf( z ) Δ = Z z 0 2 π e - x 2 dx z 0 erfc( z ) Δ = Z z 2 π e - x 2 dx =1 - erf( z ) z 0 The Q -function is related to these functions by Q ( z )= 1 2 " 1 - erf ˆ z 2 !# = 1 2 erfc ˆ z 2 ! z 0 . It is clear that if X ( u ) is a mean zero, unit variance Gaussian random variable, that Q ( z - F X ( u ) ( z ) . A useful relation is that if Y ( u ) is Gaussian with mean m and variance σ 2 , then Pr { Y ( u ) >a } = Q ± a - m σ .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 4

Q_func - 1 Q-function Handout c Keith M Chugg 1 Definitions...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online