Page 1 of 2

Re: Spectrum Recorder PCI-E Card?

Posted: Tue Jan 29, 2019 4:33 pm
by Rich Feldman
>> I see,measurement technology is unbelievable expensive in comprehension to other electronic equipment.

Did you overlook digital multimeters that cost less than $5, and are often given away free for buying something at a Harbor Freight store?
Light bulbs and magnetrons are relatively inexpensive, because the technology is mature and millions are made every day.
Same goes for smart phones and large TV sets. Technically not too challenging, and the makers get revenue from tracking you long after the original purchase.
Super digitizers, like you originally asked for, are expensive because they are technically cutting-edge, and the quantities are too low to justify high volume production methods and cost reduction. I bet the $3500 IC's that Chris pointed to don't use a plain old xx-nanometer digital CMOS process, on plain silicon, through mainstream 12-inch wafer fab lines.

First exercise for you, Harald:
Find out and explain the meaning of 6 GHz and 20 Msps in the same software-defined radio spec. Front-end downconverter? Undersampling, with sampler aperture size and jitter very small compared to repetition rate?

As for how to separate nearly-coincident pairs of 20 ns analog-voltage pulses,
here are some guesses (without research) about what might be good enough for your interest.
How about one good sample every 2 nanoseconds? (500 Msps) You know the pulse shape, and should be able to fit the data samples no matter how the sample clock phase is aligned to any given pulse location.
Analog 3db bandwidth 200 MHz? (sub 2 ns risetime)
Digitized to render 10 or 12 bit numbers for your largest expected coincident-pulse voltage?
I think this is getting into mainstream oscilloscope territory, except maybe for the bit count.
Another critical consideration is voltage noise.

What fraction of the pulses will overlap, if they have ordinary random statistics and the average rate is 60,000 cpm?

Re: Spectrum Recorder PCI-E Card?

Posted: Tue Jan 29, 2019 10:36 pm
by Steven Sesselmann
Harald_Consul wrote: Tue Jan 29, 2019 9:33 am Meanwhile I have figured out, that the signal amplitude of a (negative voltage) scintillation tube typically is in the range of
~20 mV with a pulse length of ~20 ns.
What exactly are you trying to achieve with GHz sampling?

Can you amplify and stretch the pulse so you can sample at a lower rate?

This is how I achieve pulse height analysis from PMT's with only 48 Khz sampling and a few software tricks.

Steven

Re: Spectrum Recorder PCI-E Card?

Posted: Wed Jan 30, 2019 8:48 am
by Harald_Consul
Well, yes I thought it would require 100 or maybe even 1000 samples to disassemble a multiple signal voltage amplitude (of 20 ns in this case) into its originals properly. This is to some degree also a statistical/ mathematical question I have not researched fully, this time.

However I can say,
  • the more single event amplitudes are contained in a cumulated measured amplitude,
  • the more easily the amplitudes of two or more low energy events do exactly pile up to the amplitude of a higher energy event and
  • the more individual the curvature of each single event amplitude is
the (much) more samples will be required to properly decompose a multiple signal into its origins.

List above last edited on Thu 2019-01-31 12:06 pm

Richard, I will "do my homework" and come back.

Steven, is there a turn key solution for pulse stretching?

Re: Spectrum Recorder PCI-E Card?

Posted: Wed Jan 30, 2019 5:29 pm
by John Myers
A rule of thumb is to sample at a rate of 2.5 times the frequency of the signal. In order to avoid aliasing you need to sample above the Nyquist rate (2x the freq).
So to accurately reproduce a 20ns pulse you would sample at 125Msps.

It may be possible to use a slower rate (undersampling) if there were no other longer pulses that would alias with the faster ones.

Re: Spectrum Recorder PCI-E Card?

Posted: Wed Jan 30, 2019 7:20 pm
by Andrew Seltzman
Some things to think about:

You are trying to digitize a stochastic, non-repetitive signal. Frequency domain methods (eg a spectrum analyzer) will not be of much use.
The Nyquist rate is the BARE MINIMUM frequency that is theoretically required to reconstruct a REPETITIVE signal.
20 points per period of a sine wave will give you nice looking plot.
10 points per pulse will generally be ok to fit a gaussian pulse nicely if you have a shaping amplifier.
If you don't have a shaping amplifier, the best you can localize the time location of the edge is on the order of sampling period of the digitizer.
In this case, if you are looking to capture pulse height, capturing the peak value with an analog peak detector circuit and then using a slower ADC will be much more useful. As Steven said, using a shaping amplifier to slow down the pulse is another valid alternative.

Also look into something called a "baseline restoration circuit" which can help at high count rates.

Re: Spectrum Recorder PCI-E Card?

Posted: Wed Jan 30, 2019 7:48 pm
by Steven Sesselmann
Harald_Consul wrote: Wed Jan 30, 2019 8:48 am Steven, is there a turn key solution for pulse stretching?
What I use is just a fast rail to rail opamp as a current amplifier with a high impedance drain, so when a pulse comes in via the coupling, it takes time to filter through.

Obviously this only works when the pulse count rate is slow, otherwise you get pulse pile up (PPU).

Thousands of people around the world are now doing gamma spectrometry with sound card sampling which everyone here said would be impossible when it was first suggested 10 years ago.

Steven

Re: Spectrum Recorder PCI-E Card?

Posted: Thu Jan 31, 2019 1:57 am
by Rich Feldman
Bit of clarification about continuous-time and discrete-time functions, and the Nyquist rate.

Consider a continuous-time function x(t) that has the important property of being bandlimited. It has no frequency content at or above the limiting frequency Fb. Periodicity doesn't matter. Frequencies that we don't care about do matter.

Suppose we generate a discrete time signal X(n) by sampling x(t) at regular intervals -- times separated by exactly 1/2Fb.
Then x(t) can be perfectly reconstructed from X(n)
, using the interpolation method called sin(x)/x or "sinc" or Whittaker-Shannon.
https://en.wikipedia.org/wiki/Whittaker ... on_formula

Digital storage oscilloscopes often support horizontal scale factors that have more pixels than samples. Then they render the waveforms using sin(x)/x interpolation, which is not fakery. It actually eliminates real errors that would appear if they drew straight lines to connect the sample dots.

Of course the key to lossless sampling is having a bandlimited signal to start with.
If you start with an arbitrary function y(t), you can generate x(t) with a low-pass filter ("anti aliasing filter") that passes no frequencies at or above Fb. Information lost at that point is gone. Whatever gets through into x(t), there's no fidelity benefit from using a sample rate higher than 2Fb.
In practice, designers need some room for the anti-alising filter to roll off between 100% passing with constant delay (in frequency range of interest) to 100% stopping (at and above half the sampling rate).

Re: Spectrum Recorder PCI-E Card?

Posted: Thu Jan 31, 2019 5:15 am
by Harald_Consul
For my understanding. Do you or don't you agree with:
Harald_Consul wrote: Wed Jan 30, 2019 8:48 am However I can say,
  • the more single event amplitudes are contained in a cumulated measured amplitude,
  • the more easily the amplitudes of two or more low energy events do exactly pile up to the amplitude of a higher energy event and
  • the more individual the curvature of each single event amplitude is
the (much) more samples will be required to properly decompose a multiple signal into its origins.

List above last edited on Thu 2019-01-31 12:06 pm
?

Especially did I forget a characteristic of the mathematical problem, which determines the necessary number of samples (data points) to decompose properly?

Further questions to the mathematical problem:
  • Is the amplitude/duration relation among the amplitudes of singular high energy particles and singular low energy particles approximately constant?

Intermediate result of mathematical part of the problem:

From the first research into this topic it looks like mixed distribution models aka mixture models from the free statistical software R might be suitable to decompose complex amplitudes.

Re: Spectrum Recorder PCI-E Card?

Posted: Thu Jan 31, 2019 12:16 pm
by Rich Feldman
Harald,
Some of your particle detector questions need to be answered before we can properly tackle the pile-up problem.
If you can't find them by reading, or asking on forums, how about finding them by experiment?

First please help your helpers stay engaged.
* Clarify whether the goal is real-world spectrum measurements by you, or thought experiments, or something else.
* What is the maximum average count rate you need to deal with?
* What's the approximate numerical probability that any event will have another event close enough to make a combined pulse?
* How low must the probability be, to not interfere with your application?

* Why don't you reduce the overlap probability by using a detector that makes shorter pulses, as suggested by others in this thread? Or by moving the detector to reduce the maximum count rate?

Before speculating on samplers, you need to declare your expectations about the PMT output when mixed radiation is present.
* What is the pulse waveform for one representative particle? Please draw or point to a picture, with x-axis time units given.
* What is the range of pulse shapes for particles of the same energy, interacting at different places within the scintillator?
* How about the range of pulse shapes for all particles of a different energy? Repeat for other energies in the range of interest.
* Do you trust that the detector system is linear? That means that when two events happen at about the same time, their respective output voltages for each instant are simply added.

Each pulse shape (the real continuous-time waveform) has a frequency content, and that drives the required sampling rate.
If the typical pulses are smooth and well-behaved, they may be naturally sort of bandlimited. If faster-edge risetime were on the order of 2 ns, that suggests not much going on above 200 MHz, and high fidelity sampling might be done at 500 Msps.

The key to reconstruction (to get pulse locations much more precisely than the sample interval, or to resolve overlapping pulses)
is to do the interpolation properly. Connecting sample dots with straight lines is simplistic, and significantly wrong, unless you oversample by an unnecessarily large ratio. Fine if oversampling is cheap. Foolish if your money is better spent on good samples at a lower rate, with proper front end filter, as found in practical oscilloscopes.

Re: Spectrum Recorder PCI-E Card?

Posted: Thu Jan 31, 2019 2:14 pm
by Richard Hull
Rich makes a fabulous point. GM counters have a dead time that must be accounted for with 60 usec being one of the best and 200 usec being the norm in many older tubes. True random events like radioactivity have issues with detection just not being counted due to a GM tube's dead time.

Moving the detector farther away with a GM set up might not allow for the inverse square law to compute back to the actual radiation emission rate!
This is especially true with mica windowed tubes as a tremendous amount of alphas just will not be counted due to their MFP in air! This can amount to, often, 50% of the total radiation. Add to this, the fact that many low energy betas can scatter before being counted in a more distant mica windowed detector.

For neutron tubes, especially like the 3He tubes and PMT gamma detectors, the pulses are very short compared to the gas amplification scenario within a GM detector. Moving a neutron detector can result in fairly accurate back figuring using the inverse square law provided you are not so far away from the source that scattering and reflections from nearby moderators do not significantly interfere.

It all comes back to......

1. Knowing what you are measuring and all of its oddball characteristics and gotchas.
2. Knowing what you are measuring with (detector and all of its electronics), and its limitations and gotchas.
3. Trying like the devil to stay out of statistics that grasp at straws where the statistics becomes like a drunk at a lamp post at night....Using it more for support that illumination.

Rich touched on all of this in a wise and steady manner above.

Richard Hull

Re: Spectrum Recorder PCI-E Card?

Posted: Thu Jan 31, 2019 3:04 pm
by Harald_Consul
Thank you guys. All those pitfalls in the electronic pathway of the analog signal beginning with the PMT and ending with analog preprocessor part before the A/D converter have been very insightful.

I have figured out, that 50 samples/ observations may be a good start for applying mixed distribution models, as 30 observations is the bottom to test a normal distribution. As the amplitude is about 20 nano-seconds long, that would make 2.5G Sample/s.

However, at the moment 2.5 MSample/s is the maximum of data acquisition cards (DAQ cards) at Ebay. Thus, I am postponing the acquisition of the DAQ card to wait for higher sampling rates in 1 or 2 years. For bridging I have to use my 200MHZ digi osci, meanwhile, which however is pretty limited in the total number of samples. But I am not willing to pay 5000 USD for a 2.5 GS/s card.

Re: Spectrum Recorder PCI-E Card?

Posted: Thu Jan 31, 2019 3:56 pm
by Rich Feldman
Sorry, can't stay away.
Harald, I think you are missing the main point. Let's try again using one specific example.

Suppose your 20 ns pulses (with arbitrary alignment to sampling clock, and arbitrarily overlapping neighbors) are smooth and have minimum risetimes on the order of 2 ns, hypothetically. So that after a linear, continuous-time lowpass filter that stops everything above 250 MHz, very little was lost. Example continues with the assumption that in continuous-time filtered waveform, you could accurately get the location and size of each pulse, even when they partly overlap.

Now you want to do the processing using discrete-time methods (and discrete voltage resolution, but that's an independent detail).
You want 50 points per 20 ns pulse, which is 2.5 Gs/s (0.4 ns sample spacing). OK so far.
I claim that capturing 10 points per pulse ( 0.5 Gs/s, 2.0 ns spacing) in the filtered signal is enough.
Because you can compute the missing 40 points, without error, by proper multi-point interpolation from the sparser samples.
You could interpolate to a time resolution of 500 points per pulse if you wanted -- practically continuous-time. It works because of the properties of bandlimited signals. Wish there were time to make an illustrated demonstration, to overcome intuitive resistance to the concept.

Re: Spectrum Recorder PCI-E Card?

Posted: Fri Feb 01, 2019 6:47 am
by Harald_Consul
Thanks Rich!

First of all it is absolutely common when two or more scientists from different disciplines talk together in some kind of interdisciplinary communication, that they do not understand each other fully, simply due to different education and different wording. This sometimes requires a lot of patience on both sides. ;-)

When a mixed distribution model is applied to distinct between a multiple particle amplitude and single particle amplitude this is only based on the shape respectively the curvature of the signal amplitude.

Any interpolation between two samples will not exactly meet the true curvature of the amplitude. On the contrary the interpolation always pushes the curvature towards the one, that has been assumed for the interpolation. As any interpolation must be based on some curvature assumption, the interpolation can produce further data points, but no additional information about the true distribution/ true curvature of the signal.

Thus, the only possibility to decompose a piled up multi particle signal into singular particle events would be a better mathematical approach than the one I mentioned, that would require less than 50 samples/ data points per amplitude.

Re: Spectrum Recorder PCI-E Card?

Posted: Fri Feb 01, 2019 11:20 am
by Rich Feldman
Harald,
Would you mind sending, as lists of numbers, one or more realistic-looking PMT pulses with 0.4 ns between samples? You can draw them yourself, and they could even be piecewise linear if that simplifies your task.

I want to whip up, or at least threaten to whip up, a numerical demonstration.
We will resample at 1/5 of the rate, then see how sin(x)/x interpolation perfectly reconstructs all points along curves between the "sparse" samples.

Of course we will put an anti-aliasing filter before the sparse sampling. All interpolated points will exactly match the full-rate signal after the filter.
You need to be content with the fidelity of the full-rate filtered pulses
, which is like having front end electronics with a useful but not excessive analog bandwidth. Let's see how that looks when the original pulses are designed by you. Piecewise-linear shapes would get their sharp corners rounded by the filter, and excessively fast risetimes would be knocked down a bit.

The demo will have knobs to choose the time shift between two superimposed PMT pulses, and the phase of the sparse sampling.
Addition of the two time-shifted pulses can happen before or after the filtering, before or after the sparse sampling, and before or after the interpolation. We will see that they all give the same answer.

Respectfully,
Rich

Re: Spectrum Recorder PCI-E Card?

Posted: Fri Feb 01, 2019 1:41 pm
by Harald_Consul
Rich, currently I do not have any real scintillation data, as I am still working on figuring out the electrical pin allocation of my "brand new" second hand scintillator tube.

Compare
viewtopic.php?f=20&t=12635&p=82261#p82261
viewtopic.php?f=13&t=12581&start=10

Re: Spectrum Recorder PCI-E Card?

Posted: Fri Feb 01, 2019 1:56 pm
by John Myers
One way to separate peaks is with deconvolution.

Harald, do you just want to precisely measure the number of particles or do you also want to measure the energy of the particle?
If you only want to count the particles it seems to me that you wouldn't need such a high sample rate. You would only need enough to distinguish between different types.

Re: Spectrum Recorder PCI-E Card?

Posted: Fri Feb 01, 2019 2:07 pm
by Harald_Consul
I want to count them seperately by energy.

E.g.:
#127 x 2.3 keV
#245 x 3.5 keV
# 87 x 7.1 keV

Deconvolution looks good. There are three R-Packages for deconvolution:
- dtangle
- deconvolveR
- decon

I do not have any experience in deconvultion, yet. How many samples (measurements) would deconvolution require per amplitude?

Re: Spectrum Recorder PCI-E Card?

Posted: Fri Feb 01, 2019 3:09 pm
by John Myers
When the time-domain function of each type of pulse, F(x), is known you then use FFT math to convert it to its frequency-domain representation, G(x).
Then when you measure a signal with multiple peaks squashed together you can use deconvolution on the G(x)'s to separate the peaks.

The number of samples needed will depend on how similar each pulse type is. You need a greater sample rate to distinguish between 2.3 keV and 3.5 keV then you would need between 2.3 keV and 7.1 keV. We need to know what each pulse looks like first to give a definitive answer.

Re: Spectrum Recorder PCI-E Card?

Posted: Fri Feb 01, 2019 6:48 pm
by Chris Mullins
Harald,

I'm not sure those deconvolution functions in R are what you are looking for. If the pulse shape is dominated more by the impulse response of the amplifier, then if you know the amplifier transfer function you can undo the time-domain effect of the amp by a deconvolution, which can be done in the time or frequency domain. This would restore the original, much narrower pulses that excited the amp, and presumably would undo the overlap if there are multiple closely spaced pulses. This is a time series analysis approach to undo a (presumably) linear transformation that smeared the original narrow pulse into a much wider one, not a statistical approach.

Like Rich said, if the amplifier naturally bandlimits the original pulse to say, 250 MHz (which it does if it's linear, and is limiting the rise time to ~2ns), then there is no loss of information in sampling at ~500Ms/s. If you sample faster, you're not gaining any information in a signal processing sense, because that information has already been removed by the bandlimiting amplifier. The deconvolution technique would work just as well at 500Ms/s as it would at 5Gs/s or even 50Gs/s

I think there's some confusion here because some of these terms used in discrete time series signal processing seem to be used in statistical analysis, but with different meanings. E.g. convolution, sampling, etc. Those R deconvolution functions don't seem to be related at all to the time-series deconvolution John was talking about (e.g. as demonstrated here with MATLAB: https://terpconnect.umd.edu/~toh/spectr ... ution.html)

An electrical engineering/signal processing approach would be to simulate this in something like MATLAB (or a free analog, Octave), which is geared more towards time-series analysis, and develop your basic algorithm there. Then, you could use a function generator with dual outputs to generate narrow pulses (that sometimes are closely spaced enough that the amp output would overlap), combine them, run them through a typical PMT amp filter (or equivalent), sample with a digital scope, and try your algorithm on it. That would give you some repeatable data to work with before you have your real scintillator working with real sources.

Re: Spectrum Recorder PCI-E Card?

Posted: Sat Feb 02, 2019 3:05 pm
by John Futter
Again
What Harald wants to do is exactly what an MCA does-- pulse height into bins
and no a computer or microcontroler is not the way to go if you want to count fast
I have already given the answer

Re: Spectrum Recorder PCI-E Card?

Posted: Sun Feb 03, 2019 7:45 am
by Harald_Consul
You're absolutely right John, if I wanted to count in real time.

But that's not the case! Instead I want to record a longer period to a fast PC hard disk (a SSD) and to analyze the recorded data much more sophisticated by a statistical software for hours, days and weeks to solve the piled up amplitudes problem fully (thus to count 100% correctly).

John, why should I invest 800 USD for a multichannel analyzer or even much more USD for a more universal spectrum analyzer now, that count piled up amplitudes wrong,

when the HackRF software defined radio costs about 200 USD and most possibly its next generation will be 1GSample/s and I can record terrabytes of amplitude data with it and I could do nearly any known analysis with it using a statistics software like R?

Re: Spectrum Recorder PCI-E Card?

Posted: Sun Feb 03, 2019 12:13 pm
by Chris Mullins
Harald,

Focusing on just a couple small issues in this response - I think there are still some large terminology gaps causing some misunderstanding. In the US, a "spectrum analyzer" is a specific tool used mostly for RF work in the frequency domain. None of the hits in your ebay search for "spectrum analyzer" would be well suited for what you're trying to accomplish, or will be counting any pulses at all. Rich hit on this in his first reply in this thread - your use of the word "spectrum" here is a bit confusing, and when he asked about "radiation energy spectrum", that use of the word "spectrum" is completely different than how it's used in the phrase "spectrum analyzer" in the US.

Rich also tried to guide you to realize why that HackRF software-defined radio isn't going to be useful for your use. SDRs use special sampling techniques optimized for their purpose - take Rich's advice to learn about undersampling, and RF down-conversion to understand why that makes them unsuitable for baseband pulse sampling.

If you're trying to develop novel pulse analysis algorithms on a small budget, your best approach with real hardware is to get a cheap scope with a PC interface, and dump triggered waveforms to get some raw data. Looks like you can get a 500MHz, 1-2Gs/s scope used on ebay starting around $500 (in the US). If you don't already have a scope with those specs, you're going to need one anyway to get your hardware working. If you dump captured waveforms to a PC at the maximum rate of the scope, those won't be a continuous 2Gs/s trace, but still gives you data to work with. Statistically, does it matter if you only have a small percentage of the entire dataset, if the waveforms you do have are captured in an unbiased manner?

There is a lot of good advice from everyone in this thread that I don't think you're fully digesting.

Re: Spectrum Recorder PCI-E Card?

Posted: Mon Feb 04, 2019 12:32 pm
by Harald_Consul
Just for info: I've got a 250 MHZ 1GSample/s digital oscilloscope with data export functionality. However the maximum #samples is very limited. 48k samples or so.

Ok, lets do some digestion of your advices now:
  1. You say, to sense a periodic signal (e.g. sinus signal) a sample rate of 2,5 times the frequency would be fine (2 times rate = nyquist rate = absolute minimum)
  2. However, scintillation tube amplitudes are not periodic. If the signal risetime were on the order of 2 ns, you consider the signal a 200 MHz signal and suggest "high fidelity sampling" at 500 Msps for it.
  3. The optimal sample rate might be even a little higher considering the antialising problem. "In practice, designers need some room for the anti-alising filter to roll off between 100% passing with constant delay (in frequency range of interest) to 100% stopping (at and above half the sampling rate)." Here I do not understand how much more sampling rate is effectively required for antialising.
  4. You do not refer to mathematical decomposition method of piled up amplitude. I say, a mathematical decomposition method for of piled up amplitude should be the basis to determine the necessary sampling rate.
  5. You say, piled up amplitudes do not occur this often, that this would justify analyzing them sophistacally. I say, I buy a measurement instrument, that I will most possibly used for many purposes in the future. Therefore it is better to have the option to decompose piled up amplitudes than not to have. Further, a lot of physics discoveries have been caused by new more sophisticated detectors. Maybe I've got the chance to make such discovery with a sophisticated measurement instrument.
  6. You say, the waveform/ curvature of an scintillation amplitude is highly system specific (starting with PMT and ending with last analog signal processing in front of the A/D converter) and will tremendously depend on the rise- and fall times of the whole analog electronic pathway. Thus, trying to decompose a highly individual signal is not possible, as some kind of signal map/ signal directory cannot exist. I say, the deformation of the signal does not matter for decomposing it statistically, as far the signal deformation from the system electronic is always the same (especially in the means of skewness and kurtosis).
  7. You say, a shaping amplifier to slow down the pulse is another valid alternative. You say yourself, that this is only possible when the scintillation analysis is in "single particle detection" condition. Otherwise two following amplitudes will pile up. As I do not know about my future measurement conditions, I am not too interested in this approach this time (which might change in future).

I will address your advices to the HackRf software defined radio in another digestion like this one.

Re: Spectrum Recorder PCI-E Card?

Posted: Tue Feb 05, 2019 12:45 am
by John Myers
  1. To avoid aliasing sampling needs to be greater then 2 times the signal frequency.
  2. ...
  3. Sampling too fast can also cause aliasing issues, so faster isn't necessarily better. The roll off rate of a filter isn't about the sample rate it has to do with how fast a frequency can be cutoff completely.
  4. Deconvolution is a mathematical method for separation(decomposition) of piled-up signals
  5. ...
  6. But it is possible to separate the pulses, it's just system specific because you need to know what each separate pulse looks like first before you try to 'decompose' a piled-up signal.
The HackRf is way too slow for the performance level you are looking for.

Re: Spectrum Recorder PCI-E Card?

Posted: Tue Feb 05, 2019 6:51 am
by Harald_Consul
  1. The following picture from wikipedia aliasing article shows a sine funtion, that is undersampled:
    AliasingSines.svg.png
    So, if I sampled a periodic sine function with 2 or 2.5 times its frequency (to avoid aliazing), would that also invoke, that there are enough samples (data points) to reconstruct any sine function by e.g. fourier transformation, as far the assumption of periodicity is met?
  2. If no. 1 is true, how is this reconstruction possibility then extended to non-periodic signals like scintillation amplitudes? By section-wise approximation by a sine function? If so, what mathematical method is used to this approximation? Afaik fourier transformation can only handle strictly periodic signals.
As I want to analyse the raw data in software, I have to explicitly rebuild the approximation/ interpolation logic, that may be applied by a digital scope implicitly on automatic.