Subhadip Saha

So, do I have to increase the total data length over 1 second ? since, sampling rate is ~100 MHz, even for 1 second oftotal data-length (or time series) there will be 10^8 to 10^9 data points to checked against threshold voltage. This is quite large, yet kindly let know if I have to run the simulation over 1 sec or not.

And, also in the programming, to calculate background rate (which is in Hz) the data length I am running my simulation is 1 second.

Sir, as I can see allen deviation minimizes ~100 sec. However, when a signal hits (even if it is noise signal) detector responses nearly instantaneously, right ? or will it wait for ~100 seconds ?

Yes, Sir your answer does explain totally. Thanks a lot.

ok. Thanks a lot for your valuable suggestion, one last thing I shall alter the value of n accordingly with sampling frequency to keep collection time conserved in all cases, right ?

yes sir,I am quite accustomed with scipy and numpy

Python

yes sir

ok sir. Thanks.

Thanks a lot.

Is there any methodological way to calculate value of n ?

and then I van compare the V_rms with V_TH to calculate Background Rate ?

like may be over 4-5 consecutive points ?

Sir, so I must take n-point average on square of the voltages ??

I amused to know that as I am changing the sampling frequency the total power (as well as standard deviation of Gaussian distribution) changes. This is because I have fixed "B" in expression of V_rms at all the sampling rate and hence used the same V_rms as standard deviation of Gaussian distribution in all the compilations (i.e., at different sampling frequencies). I have also rephrased the question with more information.

sir, if I understand this correctly, as I am trying to write a simulation on this and hence I am not applying any sort of filters, so background rate will increase as long as the sampling rate is chosen less than the bandwidth under consideration ? I mean the band-width (B) used in the expression of V_rms ? This is so ?

Sir, " and the thermal noise was amplified to be well above the quantization noise" - Pardon but I did not quite get this. Since, I am trying to estimate "Background Rate" for a Power Sensitive device and as you have mentioned that power essentially remains same with sampling frequency, right ? So for such a systems Background Rate must be independent of Sampling frequency, Right ? Kindly let me know whether I am on right track or not since I am merely a new learner. Thanks.

I may also use `np.fft.fftfreq(n, dt)' but here we can't ascertain whether the data has been taken for enough long t i.e $Ts$. So to precisely extract FFT data what shall be the most reliable way ? Thanks a lot.

in That case the way I defined freq array it has df =1 Hz, now actual df could have been far more smaller then will that not create any inconsistency in my fft data ?

we may have knowledge about $maximum frequency = Fs/2$.

but in real life implication we may not have any idea about df right

the input pulse is combination of sine wave of frequencies of dual bands

sir, here we know that

Thanks.Let me go through this.

Yes sir, the ifft of this rectangular fft data turns out to be similar as that of the original pulse. However, is "runge phenomenon " intrinsic artefact of np.fft.fft() module ? Or could we eliminate this sort of artefact ? as in a real pulse we may not know which of the frequencies are present hence this sort of artefacts may implant a wrong notion about frequency components. Right ?

Ok. I would like to request yout to suggest me some relevant illustrations or references on this as I would require this in my work and thus I am keener to learn these things in details and earnestly hope for your kind aid and coopertion. Thanks. And just to ascertain t = np.linspace(0, Ts, Ns+1)[:-1] + 1e-10 - Ts/2 shall be a better choice than t = np.linspace(0, Ts, Ns+1)[:-1] used earlier right ?

Okay, I got this now. Thanks. One last thing if you could explain, "The signal construction for the frequency spacing of df=0.001 is prohibitively expensive, it requires the evaluation of the sine 10000000000 times", How are you actually estimating that "10000000000" this number for df ?

Got it. Thanks a lot.

in your last code where you have mentioned about Riemann sums, Why have you chosen Ts so large ? Since,here df = is not so small !! And in the output there shall be values at 4 different frequencies i.e. 80, 30, 10, 1 Hz, Then why is not there only 4 peaks ? Kindly explain this.

so to keep both low frequency and high frequency components, How may I proceed ? since, in real lie the data I may receive may have dual band of frequencies. And, as I am keeping t_upper = 1/df the resulting fourier plot is far from rectangle. Kindly see here in the link, [link] (drive.google.com/file/d/1qjzd_eajFvrAowzuDtq0cehUdBuDr8Bt/…‌​)

But, np.concatenate() sort of concatenates two different arrays/tuples of same lengts rather than summing, Right ? whereas, y2 is thought to be a pulse which is superposition (sum of , may be coherent or incoherent ) of sine waves of dual frequency band. So, if you could kindly explain why are we chosing concatenate() rather than sum(). However, your code is running great. Thanks a lot.

As I am considering; 'f_g = np.arange(1, 10, 0.001) ; y2 = 0.0; y2 = sum(np.sin(2 * np.pi * f * t) for f in f_g) ; f_f = np.arange(30, 80, 0.001) ; y2 = sum(np.sin(2 * np.pi * f * t) for f in f_f)' . Then the low frequency components are missing from the frequency graph. Could you suggest me any way out?

Sir, one more thing that I have nocited just now, if, df = 1/1000 between 30 to 80 Hz, so we do expect a sort of uniform closely spaced amplitude (constant). Right ? If I use T_upper = 1/df I am not getting that sort graph, rather, if I chose T_upper >= 10*(1/df) then only I am getting uniform nearly continuous amplitude(sort of rectange) from 30 to 80 Hz. Please have your kind opinion this. Thanks a lot.

Sir, As you mentioned if df = 1/1000 then length of t shall be 1000. Right ? Is it the length or rather the upper limit such that t = np.linspace(0, 1001, Fs+1) ?

Sir, one more thing if you could kindly tell me, "[: -1]" Why is it used after linspace, what does it ensure ? Further, I understand that dt = 1/Fs. But, actually, didn't know about that upper time limit shall be set such that t_upper = 1/df ? Could you please explains why is it so required in our algorithm or may suggest me some study reference for that. Thanks