comnum.theory_msk_psd

comnum.theory_msk_psd(ft)

The power spectral density of MSK at the normalised frequency fT, unit power and T = 1 (Proakis & Salehi, Sec. 3.4-3): S(f) = (16/π²) [cos(2πfT) / (1 - 16 f²T²)]², finite at fT = ±1/4, with nulls at fT = ±3/4, ±5/4, … and a 3 dB bandwidth of about 0.59/T.

Parameters:

ft (float | array_like) – normalised frequencies fT.

Returns:

the density, which integrates to one over all frequencies.

Return type:

float | numpy.ndarray

Raises:

ValueError – for values that are not real numbers.

Examples

>>> import comnum
>>> round(comnum.theory_msk_psd(0.0), 6)
1.621139
>>> comnum.theory_msk_psd([0.25, 0.75]).round(6).tolist()
[1.0, 0.0]