1.5D DFT

Hello
Suppose you have sensors regularly laid out in a cross shape. with each
sensor sampling a time series.  Is there any meaningful way to look at the
frequency spectrum of this data?  

>Hello
>Suppose you have sensors regularly laid out in a cross shape. with each
>sensor sampling a time series.  Is there any meaningful way to look at
the
>frequency spectrum of this data?  
>
"define","compute", etc are better than "look at" here.

On May 21, 5:20&#4294967295;pm, "alexryu" <ryu.a...@gmail.com> wrote:

Yes, the results could be very meaningful, if you consider the array
and its subsequent processing to be a beamformer.

Consider the cross shaped array to be lying on the x-y plane.  Then
consider a planar pressure wave of a single frequency arriving
perpendicular to the array from the z direction.  If you were to
repeatedly take FFTs of each sensor, you'd find that the results out
of all the '0' bins over time are a replica of the waveform impinging
on the 'broadside' direction of the array. If the waveform were
arriving from a different direction, then one or another of the FFT
bin outputs would give you a replica of that waveform.  So you can
interpret outputs as being 'spatial' frequencies.

That's the 'easy' answer, but it's really a lot more complicated than
that.  I would suggest you look at just the 1D case first (i.e.: a
line array) to see how you can get 'spatial' frequencies that depend
on various look directions.  Furthermore, if the arriving waveform
consists of more than one frequency, then you'll get look directions
that are a function of frequency.  This is highly undesirable in many
sonar systems.  There are several ways of dealing with the problem,
such as using phase shifts (i.e.: time delays) to modify beam
direction, or splitting the input data into narrow frequency bins and
then beamforming each frequency separately, etc.

You might want to look into some beamforming papers, such as:

L. J. Rennie, &#4294967295;The TAP III Beamforming System,&#4294967295; IEEE J. Oceanic
Engineering, vol. OE-6, no. 1, Jan. 1981, pp. 18-25.

Kevin

Oops. I meant to write: take the FFT of the line array in the 'x'
direction, and the FFT of the line array in the 'y' direction.

As I said, I think it's a lot easier to understand if you start with
just one line array and figure out how and why it will give you
spatial frequencies when you repeatedly FFT the inputs to the line
array (bin '0' will give you the waveform impinging from the broadside
or perpendicular direction to the array over time).

Kevin