pub fn spectral_lines(sf: u32, n_max: usize) -> Result<Vec<(f64, f64)>>Expand description
The lines of the power spectrum, (f, P) at $f = nB/M$ for $|n| \le$ n_max (in
units of $B$), $P = |\sum_{\ell} X(nB/M; \ell)|^{2}/(T_{s}^{2} M^{2})$ (Chiani and
Elzanaty 2019, eq. (21)); they hold $1/M$ of the power (Property 4).
At $f = n/M$, $w = 1$ and the sum over the symbols is the quadratic Gauss sum $\sum_{\ell = 0}^{M - 1} e^{-j\pi(\ell - c)^{2}/M} = \sqrt{M} e^{-j\pi/4}$ ($c$ an integer, $M$ even), so that
$$ P_{n} = \frac{1}{2M^{2}} \left|K\left(\sqrt{2/M}\,(M/2 - n)\right) + K\left(\sqrt{2/M}\,(M/2 + n)\right)\right|^{2}, $$
two Fresnel evaluations per line.
ยงErrors
As ser.