k-Wave User Forum » Topic: Fourier analysis of the signals
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Bradley Treeby on "Fourier analysis of the signals"
http://www.k-wave.org/forum/topic/fourier-analysis-of-the-signals#post-7656
Sat, 27 Jun 2020 13:31:38 +0000Bradley Treeby7656@http://www.k-wave.org/forum/<p>Hi Anastasiia,</p>
<p>It is not possible to model a circular piston transducer in a 2D cartesian coordinate system, period. This is because the 2D wave equation inherently assumes that everything is infinitely repeated in the third dimension.</p>
<p>I pointed to the new functions as they give some examples for modelling circular transducers in 3D or in an axisymmetric coordinate system.</p>
<p>Alpha 0.1 just means the codes are in an alpha state (early version), and this is the first release (hence 0.1).</p>
<p>Hope that helps,</p>
<p>Brad.
</p>Anastasiia on "Fourier analysis of the signals"
http://www.k-wave.org/forum/topic/fourier-analysis-of-the-signals#post-7635
Tue, 23 Jun 2020 11:26:39 +0000Anastasiia7635@http://www.k-wave.org/forum/<p>Hi Bradley, thanks for your reply!<br />
One small question. What is alpha 0.1?</p>
<p>And, just to make sure, so previously, before this new set of functions you recently wrote, it was not possible to model a circular source/receiver in 2D?</p>
<p>Thanks!
</p>Bradley Treeby on "Fourier analysis of the signals"
http://www.k-wave.org/forum/topic/fourier-analysis-of-the-signals#post-7556
Sat, 06 Jun 2020 14:26:46 +0000Bradley Treeby7556@http://www.k-wave.org/forum/<p>HI Anastasiia,</p>
<p>It depends on which analytical model you're referring to, but many results are derived for continuous wave excitation. In this case, to match the results, you need to drive your piston with a sine wave, run the simulation until steady state (including the edge waves), and then extract the harmonic amplitude from the last few cycles (taking care to record exactly and integer number of cycles). Note, if you are performing a simulation in 2D with a line, you will need to compare with the analytical solution for an infinite rectangular source (maybe you are doing this already).</p>
<p>I've just posted a <a href="http://www.k-wave.org/forum/topic/alpha-version-of-kwavearray-off-grid-sources">new array class</a> for k-Wave that has some examples of comparing to analytical solutions for circular transducers, which might help.</p>
<p>Let me know if you're still stuck on something.</p>
<p>Brad.
</p>Anastasiia on "Fourier analysis of the signals"
http://www.k-wave.org/forum/topic/fourier-analysis-of-the-signals#post-7507
Tue, 19 May 2020 10:52:24 +0000Anastasiia7507@http://www.k-wave.org/forum/<p>Hi Bradley,<br />
I recently got to testing my function that extracts the Fourier components of the received pulse. In my linear simulation (2D, 3D) i transmit with a circular transducer and receive with a circular transducer. I was curious what conditions give me the best fit to the predicted analytical profile of the fundamental and also how i should analyze the received signals (specifically the Fourier transform). I was wondering if you could give me few tips? I have a couple of questions below.<br />
1) When I look at some simulated data of the pressure fields in publications (e.g. demonstrating the diffraction pattern), i wonder if they analyze the whole signal (with the edge wave or without it?). If the pulse is short enough these components can be separated.<br />
In my case, analyzing the central part of the first signal gave decent results, however, the fundamental profile is still somewhat far from the theoretically predicted one, even though i can see the main crests and valleys. On the other hand, If I give the whole signal to the Fourier function in matlab, the profile is much sharper, shows a very nice shape correspondence to the prediction, but, strangely, has a lag in it. Do you have an idea why this lag could occur? And when analyzing the received signal at a sensor point, would you advise selecting a part of it? Or taking the whole thing with/without the edge wave in the analyzed signal?<br />
2) Another observation is that a shorter pulse gives a sharper fundamental profile, very close to the theoretically predicted one. I suppose that makes, sense since then we have better resolution. However, when the diffraction correction integral is derived, i never saw a mention that it can depend on the number of pulses in the sent signal. I suppose they assume a delta plane wave pulse? Do you perhaps know works when the number of cycles is also accounted for when deriving the diffraction pattern?<br />
P.S. even for the 1 cycle pulse simulation the pressure profile is somewhat lagging for a small receiver, compared to the analytical solution. I was wondering if any comparison has been performed in you publications between the solutions offered by k-wave and the analytical solutions for the fundamental (Rayleigh integral or with the multigaussian beam model) for plane piston circular transducers?</p>
<p>Thank you in advance!
</p>