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
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