B Sine wave noise at different frequencies

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The discussion centers on the relationship between signal frequency and noise amplitude in audio systems. It is clarified that noise is typically modeled as a broadband signal, often approximated as white noise, which remains relatively constant across different frequencies within the specified bandwidth. The noise amplitude at different frequencies, such as 5kHz and 15kHz, is expected to be similar, assuming the same conditions, including temperature and resistance. However, variations in noise characteristics can occur due to the nature of the noise source and the system's response. Ultimately, understanding noise in audio amplifiers requires careful consideration of bandwidth, temperature, and the specific noise model being applied.
  • #61
Ephant said:
... (the reason it's multiply by 2 is because the differential input needs the noise multiply by 2 according to one designer).
When you add or subtract two equal independent noise sources, the RMS sum of the noise amplitudes, rises by only √2.
At the same time, the differential signals are dependent, so the signal doubles, and the S/N ratio improves by 2/√2 = √2.
 
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  • #62
Baluncore said:
When you add or subtract two equal independent noise sources, the RMS sum of the noise amplitudes, rises by only √2.
At the same time, the differential signals are dependent, so the signal doubles, and the S/N ratio improves by 2/√2 = √2.

Yes. That was why I was taught the following formula in computing for the noises in my equipment.

10k Source resistance: 0.13 * Sqrt (10000 Hz) * Sqrt (1000Hz) = 411 nV rms
2x 5k input stage gain settings resistors: Sqrt(2) * 0.13 * Sqrt (5000) * Sqrt (1000Hz) = 411 nV rms

The second above is composed of two 5k resistors and has same noise as the 10k in first. Sqrt (2) was used.

I own 2 amplifiers. One is the above with 5nV/Sqrt (Hz) AMP01 main amp with OPA2132P input stage (with 8nV/Sqrt (Hz) noise). The second is the $16750 gUSBamp used by major R&D research centers worldwide. I read of a Sigma 5 discovery where it was used. That was why I bought it second hand for $1000 plus.
It has this spec.

https://www.gtec.at/product/gusbamp-research/

Sensitivity 85,7 nV / +/- 250 mV
Noise level < 0.4 µV rms 1-30 Hz

A physicist told me it has no amplifier but only ADC where the signal is directly mapped into it.

At 1000Hz. Let's say the noise is 0.8µV rms. If there is a 0.1µV (100nV) signal. Can you see the 0.1µV (100nV) signal with the 0.8µV rms noise at 1000Hz using FFT or Power Spectrum Accumulate?

It doesn't use the technology or use the concept of lock-in amplifier or has no stand alone gain amplifier. Without using lock-in amplifier. How deep can you go beneath the noise floor and still see the signal? With its sensitivity or resolution of 85.7nV. Can you see a 95nV signal using FFT? Or not?








 
  • #63
Ephant said:
At 1000Hz. Let's say the noise is 0.8µV rms. If there is a 0.1µV (100nV) signal. Can you see the 0.1µV (100nV) signal with the 0.8µV rms noise at 1000Hz using FFT or Power Spectrum Accumulate?
Yes, but you must have sufficient samples. You will also benefit from amplification of the signal before the A-D converter.
 
  • #64
Baluncore said:
Then try a lock-in-amplifier.
https://en.wikipedia.org/wiki/Lock-in_amplifier

Note that switching CMOS analog gates have very low noise when being used as a mixer, to down-convert a noisy signal to DC. Follow that with a 1 Hz LPF to remove most of the noise, then a chopper stabilised CMOS amplifier.

I read about Lock-in-amplifier but I don't know why my dozens of electronic experts/advisors at PSE didn't suggest it. Maybe I didn't tell them what I was searching for.

Can lock-in-amplifier be used when you don't know the specific frequency you are looking for? Can it be used broadband? Specifically I'm scanning the dark matter sector in the 0 to 2400 Hz. Can a lock-in-amplifier help? Can it sweep through the 0 to 2400 Hz frequency with reference frequency that can move from 0 to 2400 Hz?
Or lock-in-amplifier not applicable in my application?
 
  • #65
Ephant said:
Can it be used broadband?
No. You would need to know what you are looking for.

FFT ± PSA does not need to know the signal.

If the signal pattern repeats, then use an FFT to do autocorrelation, which will detect the repeat period.
 
  • #66
Baluncore said:
No. You would need to know what you are looking for.

FFT ± PSA does not need to know the signal.

If the signal pattern repeats, then use an FFT to do autocorrelation, which will detect the repeat period.

Power Spectrum or Power Spectral Density software can also be used to navigate below the noise floor. Is it not? (which one is appropriate for my case)? I need to know the power of each frequency that FFT alone can't. There is a distinction between FFT and PSD and PS.

What is best Power Spectrum or Power Spectral Density software available? I just read that REW RTA is not accurate. It is only good for pink noise. I used it the past months and was wrong using it thinking its FFT was so accurate.

https://www.hometheatershack.com/threads/spectrum-rta-feature.9872/
 
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  • #67
When talking about noise in a signal, as in your example, it represents some random component that can be caused by various factors, such as electromagnetic interference or thermal movement of electrons in the device. This noise can be represented as a random signal with a certain spectral characteristic. When you change the frequency of a signal, its spectral content, including noise, also changes.

In your example, if the function generator produces a signal with different frequencies from 20 Hz to 20000 Hz, then the noise in each of these frequency regions may be different. For example, at higher frequencies the signal may be more susceptible to electromagnetic interference and other sources of noise, which may result in increased noise levels compared to lower frequencies.
 
  • #68
Baluncore said:
Given sufficient time and samples, it is possible to dig anything out of the noise.
Whether it is there or not!
 
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  • #69
AlexisBlackwell said:
When talking about noise in a signal, as in your example, it represents some random component that can be caused by various factors, such as electromagnetic interference
If the noise in a system is from external EMI coupling in, it is almost by definition not random.

AlexisBlackwell said:
This noise can be represented as a random signal with a certain spectral characteristic. When you change the frequency of a signal, its spectral content, including noise, also changes.
Changing the frequency of a desired signal does nothing to the spectral content of the noise in a channel. Please take care not to post misinformation.
 
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  • #70
Ephant said:
Power Spectrum or Power Spectral Density software can also be used to navigate below the noise floor. Is it not? (which one is appropriate for my case)? I need to know the power of each frequency that FFT alone can't. There is a distinction between FFT and PSD and PS.

What is best Power Spectrum or Power Spectral Density software available? I just read that REW RTA is not accurate. It is only good for pink noise. I used it the past months and was wrong using it thinking its FFT was so accurate.

https://www.hometheatershack.com/threads/spectrum-rta-feature.9872/

I can't find any information in google what is the difference between using Power Spectral Density or Power Spectrum in looking for signal under the noise floor. What is the difference between Power Spectral Density and Power Spectrum? What would be more effective in navigating the noise floor?

I can't ask in the digital signal processing forums directly because I can't tell them I'm scanning the dark sector. If one just wants to seek some broadband peaks. Is Power Spectral Density more useful? For example. If I want to search for the peaks in the Dark Spectrum like the following. IS PSD more useful? This was the result of using Matcad N-ways Parallel Factor Analysis using Power Spectral Density in toy model or simulations.

dark sector spectrum.jpg
 
  • #71
Ephant said:
looking for signal under the noise floor.
So far, despite having posted a number of screen shots, you haven't yet said what you mean by noise floor.
Ephant said:
I can't tell them I'm scanning the dark sector.
What does that mean in grown up language?
 
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  • #72
Yeah, what's a dark sector?
Ephant said:
I can't ask in the digital signal processing forums directly because I can't tell them I'm scanning the dark sector.
 
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  • #73
I was beginning to wonder about Ephant. I was thinking tinfoil hats etc..
 
  • #74
sophiecentaur said:
So far, despite having posted a number of screen shots, you haven't yet said what you mean by noise floor.

In Audacity, I was taught days after this thread was started that I could add noises in Audacity and see how they mixed up. So I was able to visualize the earlier question why 50Hz has more jagged edge vs 900Hz. .

This is 50Hz signal with 1000Hz noise.

white noise 1000khz and 50hz signal.JPG


This is 900Hz signal with 1000Hz noise.

white noise 1000khz and 900hz signal.JPG



Before I used the 1000 Hz software low pass filter in Audacity on the following 30,000 Hz signal. I didn't know what would happen. I thought if you didn't put any low pass filter on the hardware itself (like a 2nd order Butterworth filter). The noises would overwhelm the lower frequency increasing its noise. After I ran it. It became clear to me what it means the frequency spectrum of white noise is flat. And how white noise is characterized by a flat spectrum, i.e. the variance is approximately the same at all frequencies. And it is retained even after passing via an ADC. That's why you can do digital filtering like brick wall

audacity 30000 to 1000hz software loss pass.JPG


And with your descriptions in the following. How can I not understand Noise Floor already. Of course Noise Floor doesn't mean there is a floor at the circuit where noise collects. It's like Sky is the Ceiling. There is no actual ceiling.

"The Noise we are discussing is a totally random fluctuation of a signal. Forget the sine wave ideas - that's just Maths and comes later. There is nothing in a hot resistor (or a transistor etc.) that consists of a sine wave oscillator there's just random fluctuations of charge carriers in there. When you look at a signal on a wire with an oscilloscope you will see a fuzz around the wanted signal that fuzz / grass is at a level that depends on the bandwidth that's been admitted by the input filter. "


sophiecentaur said:
What does that mean in grown up language?

In grown up language. It means ordinarily, dark matter (we who tried to detect it call it the dark sector) shouldn't interact with ordinary matter, even down to the photons. But the Big Bang should logically produce some kind of relics that can bind them together, sort of a coupler (restoring higher symmetry state lower than the electroweak plasma). In the past. They tried to find equations that could produce all the constants of nature, but couldn't. So the universe is more complicated than simple minded idea of it. And the idea is just slowing coming around the corner, and CERN is still transitioning to the idea the universe is more complicated than their rigid ideas as Sabine Hossenfelder kept saying.

Some of us believe ordinary and dark matter can be glued together. And we tried to detect it. No harm trying to detect it too for us civilians. But remember CERN are also composed of Civilians too, and very human.
 

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  • #75
Oh. I couldn't edit the above message anymore. In the attachments I forgot to delete. The 3rd image is the white noise not yet filtered to 1000Hz, so it is still causing jagged edge even to 900Hz signal. Also the noise amplitude is just 0.3 while the sine wave is 0.8.

noise not yet filtered signal 900hz.JPG


The noise and sine amplitude should be the same in the simulation, isn't it? The maximum is 1.0 but I used 0.8 to show the baseline better. I should have used 1.0 maximum amplitude white noise in the noise generator?

In the following I used 0.8 Noise with half right filtered to 1000Hz noise and a 50Hz signal

1000Hz noise and 50Hz signal.JPG


In the following I used 0.8 amplitude Noise with half right filtered to 1000Hz noise and a 900Hz signal.

1000Hz noise and 900Hz signal.JPG



Why do I share them? because it was when I saw them that I totally understand and visualize the reasons for jagged edges. You can let newbies try the Audacity noise generators who may not understand too.

About probing the noise floor using FFT. It is possible that many who didn't intend to probe the noise floor and using FFT just to view the signal above noise floor can unintentionally get signal from below the noise floor, is this right?

I need to know because if you show signals you acquired and didn't say some signal was below the noise floor. People who want to duplicate your result may only focus above the noise floor.

Also what would happen if you don't use FFT but just use Power Spectral Density analysis on the noises. Would you also be able to probe below the noise floor using PSD? This is my last question.

About my experiments to duplicate one done by a university. If I can't replicate it and it is faulty. Then the prospect of Particle Dessert for the next centuries is a possibility. But if I can replicate it. I'll share far and wide the findings of the University and all resources of CERN must be re-orient to the discovery instead of no major discoveries besides the Higgs. I'll update on the result months from now if I'm still here. I can't share the source now because it is not peer reviewed and may attract the wrath of the moderators. If I found sigma 5 results. I'll try to write or make other write a paper that can be peer reviewed and share here.
 
  • #76
Ephant said:
People who want to duplicate your result may only focus above the noise floor.
What exactly do you mean by this?
Ephant said:
About my experiments to duplicate one done by a university.
What form do your experiments take? Is there any hardware or is it all on a simulator (which someone else wrote)?
Ephant said:
CERN must be re-orient to the discovery instead of no major discoveries besides the Higgs.
So that's all they've achieved? They must be glad that you are around to put them on the right lines.
 
  • #77
sophiecentaur said:
What exactly do you mean by this?

I mean supposed a team used one hour sampling, and you use only 1 minute sampling and didn't know they used one hour to probe below the noise floor. Then you can't get the same data they have. I think this answers to my own question.


sophiecentaur said:
What form do your experiments take? Is there any hardware or is it all on a simulator (which someone else wrote)?

I'm just duplicating the experiment using room size Faraday cage (not yet built), very sensitive sensors and amplifiers, Matcad FFT/PSD/Paralac analysis etc.


sophiecentaur said:
So that's all they've achieved? They must be glad that you are around to put them on the right lines.

I mean the Large Hadron Collider major discovery was only the HIggs. Of course other accelerators/equipments before that confirmed the Standard Model like quarks, electroweak and others.

Since I'm getting some idea of the difference between FFT and Power Spectral Density. I googled a lot with some sites saying the spectrum looks the same, only the label varies, with the latter in W/Hz or other units. And will ask more in PSE, then I'll end up this thead with the following.

I think it may be more pessismistic to show them. 'll tell you why.
[Mentor Note: Several paragraphs of mystic nonsense deleted from this post]


Thank you guys for all the help. I have no futher questions about the subjects of this thread.
 
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  • #78
Ephant said:
I have no futher questions about the subjects of this thread.
Thread is closed then.
 

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