How can one see the noise in the Fourier Domain (Nyquist Frequency)?

[AlphaCrucis]

TL;DR Summary

How can one see the noise in the Fourier Domain if line profile extends passed Nyquist Frequency.

Say we have a transform of a line profile that extends out to the Nyquist frequency such that you cannot see the noise level, what could you change in your spectrograph arrangement that would allow you to see the noise level in the Fourier domain?

My thought is that we can apply a filter, P(s), to remove the high-frequency noise. To do this, we assume that the stellar spectrum and the noise have distinctly different transforms so the stellar signal is concentrated toward lower frequencies whereas the amplified noise signal occurs at higher frequencies and in ideal situations can be readily identified. This works because the instrumental profile was narrow enough to compare to the stellar lines so only modest alterations are involved in the stellar signal AND the signal-to-noise ratio of the observations is high.

Is choosing such a filter, P(s), how we "change the spectrograph arrangement" that allows us to see the noise level in the Fourier Domain? Or is there another way?

 

[BvU]

Hello @AlphaCrucis ,

!
​

A rather late welcome, that is. I see that so far in PF you have started four threads. All have been responded to. All three previous replies out of four have not seen any reaction whatsoever from you, even though two politely ask you clear questions (this is the fourth thread and it will ask questions too).

From your post it appears to me that you know quite a bit about FT and signal processing.
You know about the Nyquist frequency and I suppose you know that anything beyond gets folded back (aliased) into the reconstructed signal. But I don't see terms like windowing, Hamming, Hann function, etc..

SInce you don't describe your spectrograph arrangement nor the signals handling, we are compltely in the dark (pardon the pun ). I gather you don't neccesarily want to improve the reconstructed signal, but instead you want to get a feeling for the noise level.

So a simple reply would be: Repeat the whole thing without a stellar signal present.

But I can imagine that is not what you expected to get as an answer.

Another suggestion might be that you change the sampling frequency (preferably up ) and see what it does to the tails, then try to estimate noise levels from that dependency.

Is choosing such a filter, P(s), how we "change the spectrograph arrangement" that allows us to see the noise level in the Fourier Domain? Or is there another way?

$\$

 

[AlphaCrucis]

Hello @AlphaCrucis ,

!
​

A rather late welcome, that is. I see that so far in PF you have started four threads. All have been responded to. All three previous replies out of four have not seen any reaction whatsoever from you, even though two politely ask you clear questions (this is the fourth thread and it will ask questions too).

From your post it appears to me that you know quite a bit about FT and signal processing.
You know about the Nyquist frequency and I suppose you know that anything beyond gets folded back (aliased) into the reconstructed signal. But I don't see terms like windowing, Hamming, Hann function, etc..

SInce you don't describe your spectrograph arrangement nor the signals handling, we are compltely in the dark (pardon the pun ). I gather you don't neccesarily want to improve the reconstructed signal, but instead you want to get a feeling for the noise level.

So a simple reply would be: Repeat the whole thing without a stellar signal present.

But I can imagine that is not what you expected to get as an answer.

Another suggestion might be that you change the sampling frequency (preferably up ) and see what it does to the tails, then try to estimate noise levels from that dependency.
$\$

Thanks for the reply! I will try to be more responsive on these forums when posting and replying; and thank you for the answer. I am looking for a way to change something in the spectrograph setup, physically whatever it may be, to amplify the noise so i am able to see the noise in the Fourier Domain. I will think more on this,

 

[DaveE]

Thanks for the reply! I will try to be more responsive on these forums when posting and replying; and thank you for the answer. I am looking for a way to change something in the spectrograph setup, physically whatever it may be, to amplify the noise so i am able to see the noise in the Fourier Domain. I will think more on this,

You will have a better response from people if you can distill your questions down to a more general form. Try to identify the fundamental issues in you question and describe it in a way that doesn't require us to guess about the specific set up, or have special knowledge in your field. I suspect that there are a bunch of people here that can help with signal processing questions that don't know much about astronomical equipment.

You will scare people away if they think they either have to work hard to understand your question, or if they think they need highly specific knowledge to answer.

 

[AlphaCrucis]

You will have a better response from people if you can distill your questions down to a more general form. Try to identify the fundamental issues in you question and describe it in a way that doesn't require us to guess about the specific set up, or have special knowledge in your field. I suspect that there are a bunch of people here that can help with signal processing questions that don't know much about astronomical equipment.

You will scare people away if they think they either have to work hard to understand your question, or if they think they need highly specific knowledge to answer.

Noted. Thank!

 

[DaveE]

I am looking for a way to change something in the spectrograph setup, physically whatever it may be, to amplify the noise so i am able to see the noise in the Fourier Domain.

Most would leave the noise as it is (or reduce it) and work on getting a detector with better noise performance. Whatever your noise is, with enough thought, time, and money, you can see it. Increasing noise may be problematic, it may be easy to add noise, but is it the same as the noise that you care about?

Also, I can pretty much guarantee that your noise comes from multiple sources (light, optics, electronics, digitizers, ...). If you haven't already, try to identify each one, it's magnitude and characteristics, so you can focus your effort in the right place.

 

[andrew s 1905]

What type of spectrograph is it? Increasing noise is normally easy. Is that what you really want to do?
Regards. Andrew