# Documentation

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# qfunc

## Syntax

• y = qfunc(x)
example

## Description

example

y = qfunc(x) returns the output of the Q function for each element of the real array x. The Q function is one minus the cumulative distribution function of the standardized normal random variable.

## Input Arguments

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Input, specified as a real scalar or array.

## Output Arguments

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Q function output, returned as a real scalar or array having the same dimensions as input x.

## Examples

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Determine the values of the Q function for an input vector.

x = -4:0.1:4; y = qfunc(x); 

Plot the results.

plot(x,y) grid 

Convert an input Eb/No in dB to its linear equivalent.

ebnodB = 7; ebno = 10^(ebnodB/10); 

Determine the QPSK error probability, , given that:

 
Pb = qfunc(sqrt(2*ebno)) 
Pb = 7.7267e-04 

## More About

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### Algorithms

For a scalar x, the formula is

$Q\left(x\right)=\frac{1}{\sqrt{2\pi }}\underset{x}{\overset{\infty }{\int }}\mathrm{exp}\left(-{t}^{2}/2\right)dt$

The Q function is related to the complementary error function, erfc, according to

$Q\left(x\right)=\frac{1}{2}\text{erfc}\left(\frac{x}{\sqrt{2}}\right)$

## See Also

#### Introduced before R2006a

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