Forums

Spatial Aliasing in Beamformers

Started by Tom June 7, 2004
I have been reasing a paper that says that for acoustic beamformers (I
suppose the same applies to EM beamformers), the distance between
microphones must be

d<Lmin/2

where Lmin is the minimum wavelength.For 8kHz sampling frequency this makes

d<0.0425metres or 4.25cm. This seems a little on the small side and others
are using microphones (say two microphones) much further apart at the same
sampling freq -say 20cm. What effect does spatial aliasing have and is this
right?

Thanks

Tom


"Tom" <somebody@knowherex.netgx> wrote in message news:<1086593292.556900@radsrv1.tranzpeer.net>...
> I have been reasing a paper that says that for acoustic beamformers (I > suppose the same applies to EM beamformers), the distance between > microphones must be > > d<Lmin/2 > > where Lmin is the minimum wavelength.For 8kHz sampling frequency this makes > > d<0.0425metres or 4.25cm. This seems a little on the small side and others > are using microphones (say two microphones) much further apart at the same > sampling freq -say 20cm. What effect does spatial aliasing have and is this > right? > > Thanks > > Tom
I think the scale of your numbers may be right, although I suspect you forgot to divide by 2. Spatial sampling works completely analugous to temporal sampling. You need to sample dense enough to get a unique representation of your signal. The only exception is when you can use prior knowledge of what you are going to sample. If, for instance, a microphone array is mounted on a PC screen to record spoken commands from somebody using the terminal, one can assume that the sound source is going to be located within a very small space in front of the monitor. In that case, one might get away with using an array that is sparser than the Nyquist density. The effect of the aliasing is that the array has several lobes or "beams" of high sensitivity, as opposed to only one if the spatial Nyquist criterion is fulfilled. Rune
Tom wrote:
> I have been reasing a paper that says that for acoustic beamformers (I > suppose the same applies to EM beamformers), the distance between > microphones must be > > d<Lmin/2 > > where Lmin is the minimum wavelength.For 8kHz sampling frequency this makes > > d<0.0425metres or 4.25cm. This seems a little on the small side and others > are using microphones (say two microphones) much further apart at the same > sampling freq -say 20cm. What effect does spatial aliasing have and is this > right? > > Thanks > > Tom > >
There are some situations where spatial aliasing is irrelevant. If you know the arrival times of a pulse at three sensors, you can uniquely determine the location of transmission. They do this with sonobouoys.
"Tom" <somebody@knowherex.netgx> wrote in message news:<1086593292.556900@radsrv1.tranzpeer.net>...
> I have been reasing a paper that says that for acoustic beamformers (I > suppose the same applies to EM beamformers), the distance between > microphones must be > > d<Lmin/2 > > where Lmin is the minimum wavelength.For 8kHz sampling frequency this makes > > d<0.0425metres or 4.25cm. This seems a little on the small side and others > are using microphones (say two microphones) much further apart at the same > sampling freq -say 20cm. What effect does spatial aliasing have and is this > right? > > Thanks > > Tom
Spatial undersampling creates grating lobes, an optical term. In practice, it means that in receive mode you will pick up interference from directions where there is no signal, and in transmit mode you send signals in directions you do not wish to. If you are in a "quiet" room with good absorbing walls then you may not have much problem with spurious signals hitting you and receiving them from unexpected directions. The problem is quite severe for direction finding and radar where the environment is not under control. You may think of the grating lobes as the aliased spatial (actually angular) frequencies aliased in to the "baseband" by spatial undersampling.
Stan Pawlukiewicz wrote:

> Tom wrote: > >> I have been reasing a paper that says that for acoustic beamformers (I >> suppose the same applies to EM beamformers), the distance between >> microphones must be >> >> d<Lmin/2 >> >> where Lmin is the minimum wavelength.For 8kHz sampling frequency this >> makes >> >> d<0.0425metres or 4.25cm. This seems a little on the small side and >> others >> are using microphones (say two microphones) much further apart at the >> same >> sampling freq -say 20cm. What effect does spatial aliasing have and is >> this >> right? >> >> Thanks >> >> Tom >> >> > > There are some situations where spatial aliasing is irrelevant. If you > know the arrival times of a pulse at three sensors, you can uniquely > determine the location of transmission. They do this with sonobouoys.
Loran works that in reverse. Simultaneous pulses from three transmitters uniquely locate the receiver. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
"Rune Allnor" <allnor@tele.ntnu.no> wrote in message
news:f56893ae.0406070521.4a4a06d5@posting.google.com...
> "Tom" <somebody@knowherex.netgx> wrote in message
news:<1086593292.556900@radsrv1.tranzpeer.net>...
> > I have been reasing a paper that says that for acoustic beamformers (I > > suppose the same applies to EM beamformers), the distance between > > microphones must be > > > > d<Lmin/2 > > > > where Lmin is the minimum wavelength.For 8kHz sampling frequency this
makes
> > > > d<0.0425metres or 4.25cm. This seems a little on the small side and
others
> > are using microphones (say two microphones) much further apart at the
same
> > sampling freq -say 20cm. What effect does spatial aliasing have and is
this
> > right? > > > > Thanks > > > > Tom > > I think the scale of your numbers may be right, although I suspect > you forgot to divide by 2. > >
That's straight out of the paper. The max freq is 4kHz (Nyquist freq),speed of sound 330m/s hence wavelengh (min) = 330/4000 = 0.0825m. Clearly d<half this or 0.04125m- about 4cm. As you sample higher to get more bandwidth the siuation gets even worse! Sampling at 22kHz for instance gives Lmin = 330/10000=0.033m and d<1.65cm which is pretty darned close!! How do you get time-difference of arrival with mics that close. Also there are numerous papers where they put the mics about the same distance as the humad ears apart - maybe 18cm? This would give aliasing too no doubt - are they all wrong? Tom
"Tom" <somebody@knowherex.netgx> wrote in message news:<1086659732.33742@radsrv1.tranzpeer.net>...
> "Rune Allnor" <allnor@tele.ntnu.no> wrote in message > news:f56893ae.0406070521.4a4a06d5@posting.google.com...
> > I think the scale of your numbers may be right, although I suspect > > you forgot to divide by 2. > > > > > That's straight out of the paper. The max freq is 4kHz (Nyquist freq),
You're right. I short-cirquited the sampling frequency and Nyquist. Rune