# Help understanding the “Nyquist Criterion”

I am researching the split-step parabolic equation and its split step solution as in:

Ozgun, Ozlem & Apaydin, Gokhan & Kuzuoglu, Mustafa & Sevgi, Levent. (2011). PETOOL: MATLAB-based one-way and two-way split-step parabolic equation tool for radiowave propagation over variable terrain.

The idea is to solve equation:

where $$F$$ is a Fourier transform, $$x$$ is the horizontal range, $$z$$ is the vertical range, $$k=2\pi/\lambda$$ is the wavenumber, $$n$$ the refractive index of air and $$p=k\text{sin}(\theta)$$ is the Fourier transform variable in spectral domain, and $$\theta$$ is the angle propagation angle from horizontal

The idea is that we have an antenna which propagates in $$(x,z)$$ direction like shown in the image below

We need to choose the $$\Delta z$$ that is the altitude increment in a way that avoids alliasing. What I don't understand from the link I pasted is that authors say, that there is a "Nyquist Criterion" such that:

$$z_{max}\times p_{max}=\pi N$$

where $$N$$ is the Fourier transform size, $$z_{max}$$ is the maximum vertical height as shown above and $$p_{max}$$ is the maximum value of the spectral variable. Could anyone try and derive this for me? Tell me where it comes from? Thank you.