special_fcts#

Convenience module for calculation of special mathematical functions useful for communications.

qampy.core.special_fcts.gauss(x, A, x0, w)#

Calculate the Gaussian function with a given amplitude, zero offset and width.

Parameters:

  • x (array_like) – Input array variable

  • A (float) – Amplitude

  • x0 (float) – Zero offset

  • w (float) – Width

Returns:

calculated array

Return type:

array_like

qampy.core.special_fcts.q_function(x)#

The Q function is the tail probability of the standard normal distribution see _[1,2] for a definition and its relation to the erfc. In _[3] it is called the Gaussian co-error function.

References

…[1] https://en.wikipedia.org/wiki/Q-function …[2] https://en.wikipedia.org/wiki/Error_function#Integral_of_error_function_with_Gaussian_density_function …[3] Shafik, R. (2006). On the extended relationships among EVM, BER and SNR as performance metrics. In Conference on Electrical and Computer Engineering (p. 408). Retrieved from http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4178493

qampy.core.special_fcts.rcos_freq(f, beta, T)#

Frequency response of a raised cosine filter with a given roll-off factor and width

qampy.core.special_fcts.rcos_time(t, beta, T)#

Time response of a raised cosine filter with a given roll-off factor and width

qampy.core.special_fcts.rrcos_freq(f, beta, T)#

Frequency transfer function of the square-root-raised cosine filter with a given roll-off factor and time width/sampling period after _[1]

Parameters:

  • f (array_like) – frequency vector

  • beta (float) – roll-off factor needs to be between 0 and 1 (0 corresponds to a sinc pulse, square spectrum)

  • T (float) – symbol period

Returns:

y – filter response

Return type:

array_like

References

..[1] B.P. Lathi, Z. Ding Modern Digital and Analog Communication Systems

qampy.core.special_fcts.rrcos_time(t, beta, T)#

Time impulse response of the square-root-raised cosine filter with a given roll-off factor and time width/sampling period after _[1] This implementation differs by a factor 2 from the previous.

Parameters:

  • t (array_like) – time vector

  • beta (float) – roll-off factor needs to be between 0 and 1 (0 corresponds to a sinc pulse, square spectrum)

  • T (float) – symbol period

Returns:

y – filter response

Return type:

array_like

References

..[1] https://en.wikipedia.org/wiki/Root-raised-cosine_filter

qampy.core.special_fcts.sech(x, A, x0, w)#

Calculate the hyperbolic secant function with a given amplitude, zero offset and width.

Parameters:

  • x (array_like) – Input array variable

  • A (float) – Amplitude

  • x0 (float) – Zero offset

  • w (float) – Width

Returns:

calculated array

Return type:

array_like

qampy.core.special_fcts.supergauss(x, A, x0, w, o)#

Calculate the Supergaussian functions with a given amplitude, zero offset, width and order.

Parameters:

  • x (array_like) – Input array variable

  • A (float) – Amplitude

  • x0 (float) – Zero offset

  • w (float) – Width

  • o (float) – order of the supergaussian

Returns:

calculated array

Return type:

array_like

qampy.core.special_fcts.ttanh(x, A, x0, w)#

Calculate the hyperbolic tangent with a given amplitude, zero offset and width.

Parameters:

  • x (array_like) – Input array variable

  • A (float) – Amplitude

  • x0 (float) – Zero-offset

  • w (float) – Width

Returns:

calculated array

Return type:

array_like