I always assumed that sensors for a beamformer had to be spaced at least lambda/2 (half a wavelength) apart else we get spatial aliasing. Is this true for acoustic arrays too? I have seen papers on small arrays (circular say) for mobiles and such like. Let us asume that the mics are 1cm apart giving a wavelenth of 0.02m and a frequency (min) of 16.5kHz. Not much use is it? Hardy
Acoustic Beamforming Question
Started by ●September 28, 2009
Reply by ●September 28, 20092009-09-28
HardySpicer wrote:> I always assumed that sensors for a beamformer had to be spaced at > least lambda/2 (half a wavelength) apart else we get spatial aliasing. > Is this true for acoustic arrays too? I have seen papers on small > arrays (circular say) for mobiles and such like. Let us asume that the > mics are 1cm apart giving a wavelenth of 0.02m and a frequency (min) > of 16.5kHz. Not much use is it?There is in general no lower limit to the spacing a directive array may have. Why do you think there is? The limit you have in mind may be on the overall extent of the array. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●September 28, 20092009-09-28
On 28 Sep, 22:41, HardySpicer <gyansor...@gmail.com> wrote:> I always assumed that sensors for a beamformer had to be spaced at > least lambda/2 (half a wavelength) apart else we get spatial aliasing.If the spacing is smaller than L/2, then there are few if any problems with spatial aliasing, but the array might be very expensive. If the spacing is larger than L/2, you can still get useful results, particularly with broad-bans signals: The lower frequencies are not aliased, so you can use information from the low-frequency bands to resolve aliasing at higher frequencies. Rune
Reply by ●September 28, 20092009-09-28
Rune Allnor wrote:> On 28 Sep, 22:41, HardySpicer <gyansor...@gmail.com> wrote: >> I always assumed that sensors for a beamformer had to be spaced at >> least lambda/2 (half a wavelength) apart else we get spatial aliasing. > > If the spacing is smaller than L/2, then there are few if > any problems with spatial aliasing, but the array might > be very expensive. If the spacing is larger than L/2, you > can still get useful results, particularly with broad-bans > signals: The lower frequencies are not aliased, so you can > use information from the low-frequency bands to resolve > aliasing at higher frequencies.That's just saying that a spacing greater than L/2 at high frequencies may not be greater than L/2 at low frequencies. It's a good point to keep in mind. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●September 28, 20092009-09-28
On 28 Sep, 23:08, Jerry Avins <j...@ieee.org> wrote:> Rune Allnor wrote: > > On 28 Sep, 22:41, HardySpicer <gyansor...@gmail.com> wrote: > >> I always assumed that sensors for a beamformer had to be spaced at > >> least lambda/2 (half a wavelength) apart else we get spatial aliasing. > > > If the spacing is smaller than L/2, then there are few if > > any problems with spatial aliasing, but the array might > > be very expensive. If the spacing is larger than L/2, you > > can still get useful results, particularly with broad-bans > > signals: The lower frequencies are not aliased, so you can > > use information from the low-frequency bands to resolve > > aliasing at higher frequencies. > > That's just saying that a spacing greater than L/2 at high frequencies > may not be greater than L/2 at low frequencies.Sure. The key is to remember that the spacing between elements is a fixed physical property of the array, while the wavelength varies across the frequency band.> It's a good point to > keep in mind.It is, but it can be surprisingly hard to remember. Rune
Reply by ●September 28, 20092009-09-28
On Sep 29, 10:00�am, Rune Allnor <all...@tele.ntnu.no> wrote:> On 28 Sep, 22:41, HardySpicer <gyansor...@gmail.com> wrote: > > > I always assumed that sensors for a beamformer had to be spaced at > > least lambda/2 (half a wavelength) apart else we get spatial aliasing. > > If the spacing is smaller than L/2, then there are few if > any problems with spatial aliasing, but the array might > be very expensive. If the spacing is larger than L/2, you > can still get useful results, particularly with broad-bans > signals: The lower frequencies are not aliased, so you can > use information from the low-frequency bands to resolve > aliasing at higher frequencies. > > RuneOk so I have it the wrong way round. Hardy
Reply by ●September 28, 20092009-09-28
On Mon, 28 Sep 2009 13:41:53 -0700 (PDT), HardySpicer <gyansorova@gmail.com> wrote:>I always assumed that sensors for a beamformer had to be spaced at >least lambda/2 (half a wavelength) apart else we get spatial aliasing.That's backwards. They have to be spaced at MOST half a wavelength apart to avoid spatial aliasing.>Is this true for acoustic arrays too?It is true for all arrays. Just remember that the shading coefficients and the beam pattern form a Fourier Transform pair (with an extra sin[theta] term, where theta is the angle from array-normal). If you think of a line array in "endfire" (theta equals 90 degrees) and a sinusoidal signal, then each element is sampling the sine wave as it passes by. If the elements are spaced farther than a half wavelength apart, it is like sampling a time domain waveform at less than twice the frequency of the sinusoid. At any theta less than 90 degrees, the elements are effectively closer together and spatial aliasing is less likely. Greg
Reply by ●September 29, 20092009-09-29
On 28 Sep., 23:00, Rune Allnor <all...@tele.ntnu.no> wrote:> On 28 Sep, 22:41, HardySpicer <gyansor...@gmail.com> wrote: > > > I always assumed that sensors for a beamformer had to be spaced at > > least lambda/2 (half a wavelength) apart else we get spatial aliasing. > > If the spacing is smaller than L/2, then there are few if > any problems with spatial aliasing, but the array might > be very expensive. If the spacing is larger than L/2, you > can still get useful results, particularly with broad-bans > signals: The lower frequencies are not aliased, so you can > use information from the low-frequency bands to resolve > aliasing at higher frequencies.Rune, that's intersting. If I read you correctly, you are suggesting to use correlation (if it exists) between low- and high-band to resolve spatial aliasing. Let us assume that low- and high-band of a signal from a desired direction are somehow correlated. How would you proceed to use this correlation to split the high-band into desired signal and undesired noise (ie. input from aliased beams)? Regards, Andor
Reply by ●September 29, 20092009-09-29
On 29 Sep, 10:52, Andor <andor.bari...@gmail.com> wrote:> On 28 Sep., 23:00, Rune Allnor <all...@tele.ntnu.no> wrote: > > > On 28 Sep, 22:41, HardySpicer <gyansor...@gmail.com> wrote: > > > > I always assumed that sensors for a beamformer had to be spaced at > > > least lambda/2 (half a wavelength) apart else we get spatial aliasing. > > > If the spacing is smaller than L/2, then there are few if > > any problems with spatial aliasing, but the array might > > be very expensive. If the spacing is larger than L/2, you > > can still get useful results, particularly with broad-bans > > signals: The lower frequencies are not aliased, so you can > > use information from the low-frequency bands to resolve > > aliasing at higher frequencies. > > Rune, that's intersting. If I read you correctly, you are suggesting > to use correlation (if it exists) between low- and high-band to > resolve spatial aliasing. Let us assume that low- and high-band of a > signal from a desired direction are somehow correlated. How would you > proceed to use this correlation to split the high-band into desired > signal and undesired noise (ie. input from aliased beams)?You can't separate out noise coming from an aliased beam by this method, so it doesn't work quite as well as a directional noise filter as one might have wanted it to. But you can use the broad-band property of the signal to resolve directional amgiguities at high frequencies, so you can do directional processing of broad-band transient signals. This kind of technique is used all over seismics, where one deploy sensors bundeled up in cables. Once upon a time there were practical limitations to both the density of sensors along the cable and to how many many cables one could deploy [*], so the sampling theorem was almost never satisfied in the spatial dimensions. Rune [*] There still are such limitations, but I suspect the numbers have changed to the point that spatial aliasing is not quite as big an issue these days, as it used to be.
Reply by ●September 29, 20092009-09-29
Rune Allnor wrote:> On 29 Sep, 10:52, Andor <andor.bari...@gmail.com> wrote: >> On 28 Sep., 23:00, Rune Allnor <all...@tele.ntnu.no> wrote: >> >>> On 28 Sep, 22:41, HardySpicer <gyansor...@gmail.com> wrote: >>>> I always assumed that sensors for a beamformer had to be spaced at >>>> least lambda/2 (half a wavelength) apart else we get spatial aliasing. >>> If the spacing is smaller than L/2, then there are few if >>> any problems with spatial aliasing, but the array might >>> be very expensive. If the spacing is larger than L/2, you >>> can still get useful results, particularly with broad-bans >>> signals: The lower frequencies are not aliased, so you can >>> use information from the low-frequency bands to resolve >>> aliasing at higher frequencies. >> Rune, that's intersting. If I read you correctly, you are suggesting >> to use correlation (if it exists) between low- and high-band to >> resolve spatial aliasing. Let us assume that low- and high-band of a >> signal from a desired direction are somehow correlated. How would you >> proceed to use this correlation to split the high-band into desired >> signal and undesired noise (ie. input from aliased beams)? > > You can't separate out noise coming from an aliased beam by > this method, so it doesn't work quite as well as a directional > noise filter as one might have wanted it to. But you can use > the broad-band property of the signal to resolve directional > amgiguities at high frequencies, so you can do directional > processing of broad-band transient signals. > > This kind of technique is used all over seismics, where one > deploy sensors bundeled up in cables. Once upon a time there > were practical limitations to both the density of sensors along > the cable and to how many many cables one could deploy [*], so > the sampling theorem was almost never satisfied in the spatial > dimensions. > > Rune > > [*] There still are such limitations, but I suspect the numbers > have changed to the point that spatial aliasing is not quite > as big an issue these days, as it used to be.Antenna patterns are frequently lobed. Beamforming puts the main lobe at the desired direction, but sidelobes can confuse. Low-frequency components can help to identify whether higher components could come from the same source. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
