Beamforming

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Could you explain this again?

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Lets say the signal from receiver n, sample m is called r[n,m], then the output of your beam-former without any delay (no steering) is

out[m] = sum_n w[n] r[n.m]

which says that each receiver r has a weighting function w. This weighting function is exactly like a FIR filter coefficient response, but it is described in terms of spatial units, eg. 50 receivers of width D are used to create an array of receivers of width 50*D. If 8 of those receivers are summed to create a beam, then the synthesized receiver has a width 8*D. The beampattern of that 8 element response is the Fourier transform of the weighting function, eg., if all the weights are 1, then the beam is a sinc() function, or if all the weights are those of a Hanning window, then the beam is that of the Fourier transform of a Hanning window, with sidelobes down at the level of a Hanning window.

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I understand that why are we actually applying the window. As the narrower the window is the more we can capture the area.

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The narrower the window or the fewer receivers you use, the wider the beam. You're better off to as as many receivers as you can, and control the beam shape using the window function.

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The FIR filter you discussed is the one that we would need for the DC removal, right? So we first have to apply the FIR filter and then the beamforming and both follows the same window based design. right?

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Right, you can use the same window design software. For the receiver elements, you can indicate that you have 50 elements and that you want a specific radiation sidelobe level, and design a window function. For the samples you would design an FIR filter to preserve the signal spectrum of interest.

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I think i am pretty much sure of the design. I should specify it exactly first.

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Yes. Document the design, and upload the PDF.

Cheers,

Dave