Rayleigh vs. Nyquist

Started by RichD December 12, 2017
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

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 > -- > Rich
https://svi.nl/NyquistRate