2,5 Mhz seem to me an adequate sampling rate for AE. What low sampling effect are you refering to exactly? Do you have low frequency components in your signal?

If you know that the spectrum of your target signal is relatively sparse, for example in Fourier domain, then you may have a better reconstruction of the original signal through L1 optimization techniques. You may take a look into 'compressive sampling' theory, alternatively the paper 'Signal reconstruction from the undersampled signal samples' by Kamalesh may give you some ideas that may fit your problem.

It depends what you realy want to do and also what kind of DAQ you are using. 2.5 MHz  for acoustic signal represents 6.25 times oversampling. Probably your sampling is some sort of DeltaSigma modulation with one or two bit resolution.

Hi Amro Elhelaly,

maybe you can interpolate your signal using suitable methods like linear or spline.

The sampling process itself misrepresents the frequency of any signal greater in magnitude than 1/2 the sampling.  Since such misrepresented ("aliased" frequencies are themselves always less than half the sampling rate, and they depend on the values of the sampling rate and the frequencies that were misrepresented, they can appear at virtually any frequency, even on top of other, legitimate, frequency components.  There is therefore no way to remove only the misrepresentations without affecting the legitimate frequency components.  That's why all signals are normally band-limited (i.e., low-pass filtered) BEFORE they are sampled.

In a word, no.  If any frequency components of an acoustic signal are greater in magnitude than 1/2 of the sample rate, they will be represented at incorrect frequencies by the sampling process itself.  For example, if the sampling rate is 1000 Hz, only frequencies with magnitudes less than 500 Hz can be correctly sampled.  I keep saying "magnitude" because negative frequencies are just fine, too.  So either a 400 Hz or a -400 Hz signal can be sampled just fine at 1000 samples per second.  But if you put in a frequency at, say, 600 Hz, the sampling process will "see" the same thing it would "see" if the signal were at 400 Hz, so, when it is converted from samples back into an acoustic signal, that 600 Hz component would come out at 400 Hz.  (Movies are visually sampled at 24 Hz, which is why wagon wheels sometimes appear to speed up, slow down, go backwards, etc., even though the movie just shows the wagon going faster and faster - same principle).

By the way, what do you mean by an "acoustic emission signal"?  The otoacoustic emissions that emanate from some people's ears?  Or any acoustic signal, like the sounds that allow bats to fly in completely dark caves?

Adhere to Nyquist sampling rate : if you sample at 2.5 MHZ, theoretically you can only reconstruct frequencies up to one-half of that 1.25 MHz, practically only one-third of that ~ 0.9 MHz.  As others have mentioned if there are higher frequencies then they will be aliased in weird ways, posing as lower freqs. You don't want that. Best bet is to filter analog signal at 0.75 MHZ 3 dB point.

In underwater acoustics, where long signal has to be acquired but short signals are desirable to increase computation time, it is common practice to bandbase the acquired signal. In a few word, band basing helps when the band you want to acquire is smaller than the sampling frequency. There are electronic components that are able to easily shift the desired band around zero and then they filter out the aliased components that raise up in the shifting process. Suppose the band of the signal you want to acquire is 100 kHz centered at 2 MHz, you will have problem with your 2.5 MHz sampling rate. But if you band base the signal, you could use a 150 KHz sampling rate without loosing anything of the information in the band of interest.

This technique can also be used if you have already a digital representation of your signal and you want to reduce the number of samples of the signal without loosing information.

Good luck

Gaetano Canepa mentions a technique that's worthy of consideration.  We haven't heard from you what the actual expected band and/or bandwidth of the signals of interest might be nor any prefiltering that might be done.  So it's not really possible to answer your question because we have no idea how 2.5MHz compares nor what you mean by "improve".  Maybe you mean to improve sampling noise levels (i.e. quantization noise) and not sample *rate*.

There are lots of answers about Nyquist and those are useful.  Just the same, it's important to recognize that we almost always violate the rule.  The real issue is in-band to out-of-band signal levels that will perturb your result.  There will always be some and we have to accept that most of the time.  Fortunately with prefiltering or just plain physics, one can live with it.  The real message is: "don't design for undersampling" which is another way of saying don't sample a signal at a low rate when you *know* there are constituents of the signal that will be aliased in the sampling process.

It's interesting to ask: "How do you *know*?"