# Beam Forming and sampling Frequency

The beam former works using time delay to focus the beam pattern on a especific direction, a time delay represents a sample delay in the discrete dominium, that means that is necesary to use a greater sampling frequency to get more resolution. I would like to know, a very common ultrasound frequency for ultrasound echography is 1.5MHz and imagin that in an especific case we are using an array of 8 ultrasound sensors, what would be the sampling frequency for each sensor in order to get HD imaging???
Is time delay the only option to steer the beam pattern??

• This is a digital signal processing (DSP) question. I don't think beamforming is generally done by simply by whole numbers of samples. Each signal (series of real samples) would probably be converted to an analytical signal (series of complex numbers) and then a small phase shift would be applied to form the beam. But I am not a DSP person. Mar 3 '17 at 16:52
• 1) What transducer dimensions? 2) What transducer spacing? 3) What, exactly, is HD? 4) Why do you think resolution is entirely dependent on sample frequency? (It's not.) Mar 3 '17 at 17:23
• by now I am using 8 40KHz transducers, 5mm of spacing, I tougth that spatial filtering depends on the delays that are used to steer a beam, more angles to steer mean smaller time delays, that is where de Fs comes as a limitation, for me. You are saying that it is not a limitation, can you explain me why? my sampling frequency is 125KHz Mar 3 '17 at 17:52
• I am saying that signal processing techniques can effectively add any desired delay independent of the sampling rate. Mar 4 '17 at 5:29

You can produce an I/Q pair representing the real valued sample with any desired phase shift just by multiplying it with the cosine (I component) and sine (Q component) of the desired phase shift, this is your classic multiply a real signal by a vector to the unit circle in analytic space.

Re = Sample * cos theta

Im = sample * sin theta

Theta will obviously vary across the array.

You then sum up all the Real and Imaginary components before converting back into an amplitude by Pythagoras.

If you want to amplitude shade the array to reduce side lobes, this can be done by scaling the sine and cosine values.

Notice that at no point has sample rate or frequency entered the considerations (Frequency and array spacing will matter for calculating the required sine and cosine values for each element of each beam, sample rate will matter for calculating range).

I would note that this setup for beam forming relies on the pulse being long compared to the array bandwidth (So that the energy is arriving at all elements simultaneously, just with different phases, a safe assumption with 40KHz in air, not so much with a 5 cycle pulse in an imaging sonar, or a towed array or such), if this is a problem in your application I suggest some reading around hilbert transforms may be useful.