qfunc

Q function

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Syntax

y = qfunc(x)

Description

example

y = qfunc(x) returns the output of the Q function for each element of the real-valued input. The Q function is (1 – f), where f is the result of the cumulative distribution function of the standardized normal random variable. For more information, see Algorithms.

Examples

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Open Live Script

Calculate the Q function values for a real-valued input vector.

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

Plot the results.

plot(x,y)
grid

Open Live Script

Calculate the QPSK error probability at an Eb/N0 setting of 7 dB by using the Q function.

Convert the Eb/N0 in dB to its linear equivalent.

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

Using the Q function, calculate the QPSK error probability, Pb=Q(2EbN0).

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

Input Arguments

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Input, specified as a real-valued scalar, matrix, or array.

Data Types: double

Output Arguments

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Q function output, returned as a scalar, matrix, or array. y has the same dimensions as input x. Output values are in the range [0, 1].

Algorithms

For a scalar x, the Q function is (1 – f), where f is the result of the cumulative distribution function of the standardized normal random variable. The Q function is defined as

Q(x)=12π∫x∞exp(−t2/2)dt

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

Q(x)=12erfc(x2)

See Also

Functions

Introduced before R2006a

Communications Toolbox Documentation

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