I am reading about noise reduction techniques using arrays and I came across both these terms, I tried googling it up to find the difference between them. It would be so nice if someone can help me with this... :) --------------------------------------- Posted through http://www.DSPRelated.com
Difference between sperically isotropic noise and spatially white noise
Started by ●July 21, 2015
Reply by ●July 21, 20152015-07-21
"maheshwarS" <107292@DSPRelated> writes:> I am reading about noise reduction techniques using arrays and I came > across both these terms, I tried googling it up to find the difference > between them. It would be so nice if someone can help me with this... > :)Hi, I don't know authoritatively, e.g., from a textbook, but the following are my best educated guesses. "Isotropic" means equal power in all directions, so spherically isotropic noise is a noise source that emits equal power in all directions. Spatially white noise is noise that is uncorrelated from element to element or as a function of direction. -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●July 21, 20152015-07-21
On Tue, 21 Jul 2015 12:26:54 -0400, Randy Yates <yates@digitalsignallabs.com> wrote:>"maheshwarS" <107292@DSPRelated> writes: > >> I am reading about noise reduction techniques using arrays and I came >> across both these terms, I tried googling it up to find the difference >> between them. It would be so nice if someone can help me with this... >> :) > >Hi, > >I don't know authoritatively, e.g., from a textbook, but the following >are my best educated guesses.I'll add some guesses as well,>"Isotropic" means equal power in all directions, so spherically isotropic >noise is a noise source that emits equal power in all directions.Or, for a terminal or array, the received noise is isotropic. This might apply to a beamforming system.>Spatially white noise is noise that is uncorrelated from element to >element or as a function of direction.Or, for a mobile or portable system, the noise is consistently white regardless of location. So, just based on our guesses, there may be a difference in that "spherically isotropic" just means it's the same in every direction from a particular location, and "spatially white" means it's white regardless of location in space. Maybe somebody has more authoritative definitions, then we can see how well we guessed. ;)>-- >Randy Yates >Digital Signal Labs >http://www.digitalsignallabs.comEric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by ●July 21, 20152015-07-21
On Tue, 21 Jul 2015 17:01:05 +0000, Eric Jacobsen wrote:> On Tue, 21 Jul 2015 12:26:54 -0400, Randy Yates > <yates@digitalsignallabs.com> wrote: > >>"maheshwarS" <107292@DSPRelated> writes: >> >>> I am reading about noise reduction techniques using arrays and I came >>> across both these terms, I tried googling it up to find the difference >>> between them. It would be so nice if someone can help me with this... >>> :) >> >>Hi, >> >>I don't know authoritatively, e.g., from a textbook, but the following >>are my best educated guesses. > > I'll add some guesses as well, > >>"Isotropic" means equal power in all directions, so spherically >>isotropic noise is a noise source that emits equal power in all >>directions. > > Or, for a terminal or array, the received noise is isotropic. This > might apply to a beamforming system. > >>Spatially white noise is noise that is uncorrelated from element to >>element or as a function of direction. > > Or, for a mobile or portable system, the noise is consistently white > regardless of location. > > So, just based on our guesses, there may be a difference in that > "spherically isotropic" just means it's the same in every direction from > a particular location, and "spatially white" means it's white regardless > of location in space. > > Maybe somebody has more authoritative definitions, then we can see how > well we guessed. ;)This is just so hugely dependent on context that we may as well stare at blots of ink and tell each other what they look like. Howe'r: in signal processing domains where the signal has a spatial as well as a temporal component (like video), "spatial noise" refers to the amount of random variation from one position to another, as opposed to random variation from one time (or, with video, frame) to another. My specific experience is video, where if one says "spatially white noise" then one means that the variation from pixel to pixel on the screen is independent of position (this is as opposed to bias or gradient or some sort of repetitive pattern). Nearly all image sensing devices these days are focal plane arrays, with a whole lot of reverse-biased diodes arranged in a grid: focal plane arrays can exhibit just about every sort of spatial noise that you can imagine, in addition to temporal (frame-frame) noise that, on a good day, is independent of the pixel, but that's on a good day. I strongly suggest that the OP go back to the original source material and see if what it means can be deduced from context. If not, post some links and maybe someone here will feel motivated to take a look. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●August 11, 20152015-08-11
I looked at this a while back, if we're assuming the discussion is in the context of antenna (sensor) arrays. For spatially white noise, there is no correlation between elements. This generally refers to amplifier shot noise etc. and not noise in the environment. The covariance matrix is found as R = sigma^2 I where I is the identity matrix, sigma^2 is the noise power (variance) For spherically isotropic *narrowband* Gaussian white noise, the covariance between elements i and j can be approximated as cov(i, j, k, d) = sigma^2 sin (kd) / kd where k = 2.pi.f / c is the wave number and d is the distance between the elements. I can dig out a source that dealt with this, if that would be helpful. It is possible to approximate the covariance matrix for cylindrically isotropic narrowband white noise, too.
