Beamforming

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if i have an aperture size of 8 and i have to apply them on 50 transducer elements, then i apply beamforming to 8 transducers and then shift my aperture by one and then apply Beamforming again and thus we keep on doing this till we shift aperture 42 times to cover whole 50 elements of the transducer.

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Ah, so the confusion here is the use of the same term in two different applications; apertures (receiver elements) and apodization (windowing or weighting).

If you are only applying your weighting function to 8 elements, then your windowing function has only 8 non-zero values.

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Please explain the sinc function like response thing again? I have a linear array of 50 transducers with 8 as my aperture size to calculate the beamforming.

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The beampattern of a single receiver element is the Fourier transform of its illumination function. Assuming each receiver element receives sound uniformly across its surface, you can think of it as being a rect() function in units of distance. The Fourier transform of this rect() function is a sinc() function beam response.

The beampattern or an array of receiver elements is the Fourier transform of its illumination function multiplied by that of the individual receiver response. So if you sum up all your receivers with equal weighting, you get a much narrower sinc function multiplied by the wide sunc function of the receiver element. You can steer the narrow beam within the large beam by delaying before summing.

But you should know this already, right?

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Also, does equal weight means no weight, or there is some weight calculation to be performed? If yes, how will i have to determine the algorithm for that?

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Equal weight means a weight of 1. In your 8 element case, you could model it as a window function with 50 weights (one for each receiver element), of which 42 are zero, and 8 are 1.

The design algorithm you are looking for is a window design algorithm. The same algorithm you would design an FIR filter with.

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I have some issues regarding the DC offset removal, but i just thought to implement the beamformer in verilog first and then go for the filtering after the ADCs.

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DC removal can be done in the FPGAs. However, since you are sampling so much higher than your ultrasonic signal bandwidth, your digital filters can be designed to remove DC.

Cheers,

Dave