Consider the Nyquist criterion for sampling a continuous=20 waveform - 2x bandwidth - then the Rayleigh resolution=20 principle - peaks must separate by at least 1 wavelength. =20 Don't these look much analogous? =20 Especially as =CE=BB =3D 1/f Ruminating a bit more... Nyquist sampling can be=20 viewed as a mandate to sample each period, at least=20 twice. And, Rayleigh mandates that the image be=20 'sampled' twice, in the sense of a peak and trough. It strikes me they may be equivalent, in some deeper=20 sense. Has anyone ever tried to derive such a result,=20 mathematically? I can't be the first to ever conjecture this - =20 -- Rich

# Rayleigh vs. Nyquist

Started by ●December 12, 2017

Posted by ●December 12, 2017

On Wednesday, December 13, 2017 at 12:40:53 PM UTC+13, RichD wrote:> Consider the Nyquist criterion for sampling a continuous=20 > waveform - 2x bandwidth - then the Rayleigh resolution=20 > principle - peaks must separate by at least 1 wavelength. =20 >=20 > Don't these look much analogous? =20 > Especially as =CE=BB =3D 1/f >=20 > Ruminating a bit more... Nyquist sampling can be=20 > viewed as a mandate to sample each period, at least=20 > twice. And, Rayleigh mandates that the image be=20 > 'sampled' twice, in the sense of a peak and trough. >=20 > It strikes me they may be equivalent, in some deeper=20 > sense. Has anyone ever tried to derive such a result,=20 > mathematically? >=20 > I can't be the first to ever conjecture this - =20 >=20 > -- > Richhttps://svi.nl/NyquistRate