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# qfunc

y = qfunc(x)

## 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, ${P}_{b}$, given that:

${P}_{b}=Q\left(\sqrt{2\frac{Eb}{No}}\right).$

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

## 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

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