Sine wave noise at different frequencies

[Ephant]

Supposed your audio bandwidth is set to 20000Hz. And the signal is 10mV and there is spec of 2mV noise at 20000Hz bandwidth. Does it mean if a function generator would produce constant 10mV with different frequencies between 20Hz to 20000Hz. The noises in the sine waves of each would be similar? Or would they vary and why?

 

[berkeman]

Supposed your audio bandwidth is set to 20000Hz. And the signal is 10mV and there is spec of 2mV noise at 20000Hz bandwidth. Does it mean if a function generator would produce constant 10mV with different frequencies between 20Hz to 20000Hz. The noises in the sine waves of each would be similar? Or would they vary and why?

Sorry, this does not make sense to me. I think you are asking how to model noise in a bandwidth, but it's hard to tell. Can you try again? Thanks.

 

[Ephant]

Sorry, this does not make sense to me. I think you are asking how to model noise in a bandwidth, but it's hard to tell. Can you try again? Thanks.

Noise is over a bandwidth. So there is certain noise at 20kHz. i mean for example the referred to input noise of 2mV at 20kHz spec. Does this mean the noise at 5kHz and 15kHz sine wave has similar 2mV noise? or does 15kHz have more noise given higher frequency, but then the noise is 2mV spec is at 20kHz.

 

[DaveE]

Supposed your audio bandwidth is set to 20000Hz. And the signal is 10mV and there is spec of 2mV noise at 20000Hz bandwidth. Does it mean if a function generator would produce constant 10mV with different frequencies between 20Hz to 20000Hz. The noises in the sine waves of each would be similar? Or would they vary and why?

Normally you wouldn't assume any correlation between the signal and noise. What "noise" actually is needs to be further defined. IRL it's often over the entire band (i.e. many/all frequencies), like white noise, 1/f noise, etc. Discrete signals (wrt frequency) that you don't want are often called interference, not noise. But without a description of "noise" we just don't know.

If I had to guess, I'd model it as 1/f noise below 100 - 1KHz or so, and white noise above that.

PS: This is why people buy spectrum analyzers...

 

[DaveE]

There's lots of stuff on the web about electronic noise, like these:

https://www.ti.com/lit/ab/sboa345/s...18776&ref_url=https%3A%2F%2Fwww.google.com%2F

https://www.ti.com/lit/an/slva043b/...70774&ref_url=https%3A%2F%2Fwww.google.com%2F

https://www.analog.com/media/en/training-seminars/tutorials/MT-047.pdf

Plus about a million others...

 

[Ephant]

Normally you wouldn't assume any correlation between the signal and noise. What "noise" actually is needs to be further defined. IRL it's often over the entire band (i.e. many/all frequencies), like white noise, 1/f noise, etc. Discrete signals (wrt frequency) that you don't want are often called interference, not noise. But without a description of "noise" we just don't know.

If I had to guess, I'd model it as 1/f noise below 100 - 1KHz or so, and white noise above that.

PS: This is why people buy spectrum analyzers...

I'm not referring to interference. Noise is defined over a bandwidth like 20kHz. I was just asking whether the signal has identical noise amplitudes at 5kHz or 15kHz sine waves or whether 15kHz has more noise amplitude given the high pass filter after the op amp is set to 20kHz.

 

[DaveE]

Most noise sources aren't best thought of as sine waves. It's more like signals spread out over a range of frequencies. Like the spectrum of a delta function, for example. Read about white noise if you're not familiar with it yet.

It is likely that above about 100-1KHz the noise is mostly white noise.

 

[Ephant]

Most noise sources aren't best thought of as sine waves. It's more like signals spread out over a range of frequencies. Like the spectrum of a delta function, for example. Read about white noise if you're not familiar with it yet.

It is likely that above about 100-1KHz the noise is mostly white noise.

I'm talking of 10mV 5kHz and 15kHz signal coming from a signal generator, If the op-amp has 20kHz filter set after it. Would the 10mV 5khz and 15kHz signal have similar white noise amplitudes or would the 15khz signal be noisier?

 

[DaveE]

I'm talking of 10mV 5kHz and 15kHz signal coming from a signal generator, If the op-amp has 20kHz filter set after it. Would the 10mV 5khz and 15kHz signal have similar white noise amplitudes or would the 15khz signal be noisier?

IDK. What do I win if I guess right? My guess is white noise.
Take a short time-out and read about noise in audio amplifiers. Read the data sheets for your instruments, amplifiers, devices, etc.
It probably looks something like this:

 

[Ephant]

IDK. What do I win if I guess right? My guess is white noise.
Take a short time-out and read about noise in audio amplifiers. Read the data sheets for your instruments, amplifiers, devices, etc.
It probably looks something like this

I

IDK. What do I win if I guess right? My guess is white noise.
Take a short time-out and read about noise in audio amplifiers. Read the data sheets for your instruments, amplifiers, devices, etc.
It probably looks something like this:
View attachment 342638

I have read it previously already. The above is at 5nV/Sqrt(Hz). This means if the bandwidth is 20kHz. the noise rms is 5n/Sqrt(Hz) x Sqrt (20Khz BW) = 5 x 141.42 = 707nV rms or 0.707 uV rms noise at 20kHz bandwidth. My question is supposed the function generator would produce a 1mV signal at 5kHz and 15 Khz. Would they have similiar noise amplitude at 5kHz and 15kHz given the noise is 0.707uV rms at 20kHz?

 

[DaveE]

I


I have read it previously already. The above is at 5nV/Sqrt(Hz). This means if the bandwidth is 20kHz. the noise rms is 5n/Sqrt(Hz) x Sqrt (20Khz BW) = 5 x 141.42 = 707nV rms or 0.707 uV rms noise at 20kHz bandwidth. My question is supposed the function generator would produce a 1mV signal at 5kHz and 15 Khz. Would they have similiar noise amplitude at 5kHz and 15kHz given the noise is 0.707uV rms at 20kHz?

1) IDK, ask the signal generator manufacturer.
2) I bet the noise is essentially the same. This is the last time I'll say it... probably white noise.
3) Your signal generator probably outputs noise over a wide frequency range, regardless of what the signal frequency is set to. My guess is that the noise density at any given frequency within a reasonable range is independent of the signal frequency.
4) In your example, the noise isn't 0.707uV at 20kHZ, it's 5nV/Sqrt(Hz). In your example, it's 0.707uV over the 20kHZ band. I know it sounds like pedantic nitpicking, but it's an important point in dealing with noise, and communicating with other engineers. It is most common, in my experience, for engineers to discuss noise density at a frequency (eg. ##\frac{nV}{\sqrt{Hz}}##) and use spectrum analyzers, as opposed to noise voltages (power, current, etc.) over a frequency band. In either case the words, units, and models must match each other.

edit:
5) Why don't you measure it if it's important?

 

[Baluncore]

My question is supposed the function generator would produce a 1mV signal at 5kHz and 15 Khz. Would they have similiar noise amplitude at 5kHz and 15kHz given the noise is 0.707uV rms at 20kHz?

The noise of the signal generator output amplifier continues independently of the signal. If you turn the signal generator down to zero volts output, it will still produce the same 5 nV/√Hz in the 20 kHz bandwidth.

Unlike noise, Total Harmonic Distortion, THD, appears as integer harmonics of the signal frequency, with amplitude related to the signal amplitude.

 

[Ephant]

The noise of the signal generator output amplifier continues independently of the signal. If you turn the signal generator down to zero volts output, it will still produce the same 5 nV/√Hz in the 20 kHz bandwidth.

Unlike noise, Total Harmonic Distortion, THD, appears as integer harmonics of the signal frequency, with amplitude related to the signal amplitude.

And the noises of the main audio amplifier occurs independently of the signal also? This means a signal injected to the audio amplifer will have same noise amplitudes from 20Hz to 20,000Hz (let's say it's 8nV/Sqrt (Hz) in the 20 kHz bandwidth) and the waveforms will all look like the following if you can zoom them in and out in Audacity?

So if the above is 2kHz.. it will look like that at 19kHz if you can zoom out the 19kHz sine waves at Audacity?

 

[Baluncore]

That will depend on the temperature.
https://en.wikipedia.org/wiki/Johnson–Nyquist_noise#Noise_voltage_and_power

 

[Ephant]

That will depend on the temperature.
https://en.wikipedia.org/wiki/Johnson–Nyquist_noise#Noise_voltage_and_power

What you mean? usually the temperature is the same for the bandwidth of 20Hz to 20kHz, Is it not? So the result is the same. If same, then why will it depend on the temperature?

 

[Baluncore]

Because thermal noise depends on temperature.
Did you not look at the link?
If you turn off the signal generator, it will still generate thermal noise.

 

[Ephant]

Because thermal noise depends on temperature.
Did you not look at the link?
If you turn off the signal generator, it will still generate thermal noise.

Yes I looked at the link. I know both signal generator and main audio amplifier create thermal noises. I was just asking that since as you describe "The noise of the signal generator output amplifier continues independently of the signal.". Then the signal is independent of the noises background (right?) So just focusing on the main amplifier. The noises at 2kHz and 19Khz is similar and if you looked at the waveforms like in following, then the noises from 100Hz to 20,000Hz are identical if zoomed out *given* the same condition (or temperature) of the signal generator? My question is not about the signal generator but whether the noises in the waveforms at 2kHz and 19kHz would be similar. Why did you mention about temperature when my question is the difference in 2kHz and 19kHz with the same input conditions.

 

[Baluncore]

Why did you mention about temperature when my question is the difference in 2kHz and 19kHz with the same input conditions.

Because the noise voltage is a function of temperature, resistance and bandwidth. You asked if the noise would be the same under some condition. If I had said yes, you would later claim that I should have warned you about changes in temperature and resistance, two critical things you have been ignoring.

My question is not about the signal generator but whether the noises in the waveforms at 2kHz and 19kHz would be similar.

That sentence is meaningless.
There is almost no noise at 2 kHz or 19 kHz because spot frequencies have zero bandwidth. Or do you mean the noise voltage while there is a signal at 2 kHz or 19 kHz, in the same 20 kHz channel?

We assume a linear system. It does not matter how many signals there are, each signal is independent of all other signals. The noise will still be there without any signals, since the circuit continues to have resistance and temperature.

Noise is just a broadband signal in the channel.

 

[Ephant]

Because the noise voltage is a function of temperature, resistance and bandwidth. You asked if the noise would be the same under some condition. If I had said yes, you would later claim that I should have warned you about changes in temperature and resistance, two critical things you have been ignoring.

That sentence is meaningless.
There is almost no noise at 2 kHz or 19 kHz because spot frequencies have zero bandwidth. Or do you mean the noise voltage while there is a signal at 2 kHz or 19 kHz, in the same 20 kHz channel?

We assume a linear system. It does not matter how many signals there are, each signal is independent of all other signals. The noise will still be there without any signals, since the circuit continues to have resistance and temperature.

Noise is just a broadband signal in the channel.

Someone made a plot of the noises at 50Hz vs 900Hz using 1kHz bandwidth. Why do the noises not look the same? The 50Hz is rough, the 900Hz is smooth.

 

[Baluncore]

Someone made a plot of the noises at 50Hz vs 900Hz using 1kHz bandwidth.

Please stop referring to noise at spot frequencies. In both cases, the noise fills the available 1 kHz bandwidth. It is the signals being plotted, that are at 50 Hz and 900 Hz.

Why do the noises not look the same? The 50Hz is rough, the 900Hz is smooth.

Because the horizontal axis is different, by a factor of 16.67 between the plots. Each shows about 10 cycles of the signal.

 

[Ephant]

Please stop referring to noise at spot frequencies. In both cases, the noise fills the available 1 kHz bandwidth. It is the signals being plotted, that are at 50 Hz and 900 Hz.

In the top screenshot. Isn't the noise also appearing in the plots in the form of the jagged edges?

Because the horizontal axis is different, by a factor of 16.67 between the plots. Each shows about 10 cycles of the signal.

 

[sophiecentaur]

I was just asking whether the signal has identical noise amplitudes at 5kHz or 15kHz sine waves or whether 15kHz has more noise amplitude given the high pass filter after the op amp is set to 20kHz.

That sentence is meaningless.

Exactly. Noise is random fluctuations. The noise Power depends on the bandwidth over which it's measured. If you are interested in a particular narrow band (wanted) signal then the Signal to Noise Ration can be improved by reducing the bandwidth of the receiver / detector.

 

[Ephant]

Exactly. Noise is random fluctuations. The noise Power depends on the bandwidth over which it's measured. If you are interested in a particular narrow band (wanted) signal then the Signal to Noise Ration can be improved by reducing the bandwidth of the receiver / detector.

There seems to be some analogy between the white noise where all frequency spectrum occurs and the quantum vacuum/fluctuations. How does noise differs to the vacuum fluctuations? Do they have the same behavior? just want to know differences between them or how they are similar.

 

[sophiecentaur]

How does noise differs to the vacuum fluctuations?

You are making a rather big leap here. Perhaps we should sort out conventional noise processes first?

Noise is a very general term and can include systematic additional signals as well as totally random ones. but randomness is not an obvious thing. Post #9 has the spectrum of a 'typical' noise signal. Different parts of that signal are caused by different mechanisms. The easiest (ideal) noise signal is caused by random thermal fluctuations of the charges in a conductor. @DaveE 's quoted noise spectrum shows that , at the lower end of the EM spectrum, noise levels increase.

Some signals contain noise that is actually systematic and dependent on the wanted signal. The so-called quantisation noise that's generated during sampling and digitisation is actually more of a distortion because the same noise can occur when a signal is repeated - that's not random but can often be treated that way.

It's usually more productive to read round a topic before expecting to ask useful questions about it. Start with Wiki and follow some llinks.

 

[Ephant]

Please stop referring to noise at spot frequencies. In both cases, the noise fills the available 1 kHz bandwidth. It is the signals being plotted, that are at 50 Hz and 900 Hz.


Because the horizontal axis is different, by a factor of 16.67 between the plots. Each shows about 10 cycles of the signal.

Do you know what signal processing techniques where they remove the jagged edges at the say 50Hz signal that is there at the original? Because in the BCI2000 software at a center. The output at 50Hz doesn't have any jagged edges noises.

 

[Baluncore]

For a sinewave, lower frequency noise causes the baseline to wander up and down. Higher frequency noise looks like small jagged pulses added to the sinewave.

Both plots have 1 kHz BW limiting.

The 900 Hz shows a very short block of time that stretches the noise horizontally, and so makes it look smooth. There is little noise between 900 Hz and 1 kHz, so most of the noise is lower frequency, that appears to make the baseline for 900 Hz wander more than that for the 50 Hz.

The 50 Hz has lots of time on the display, and plenty of higher frequency noise between 50 Hz and 1 kHz. That higher frequency noise looks jagged. The baseline of the 50 Hz does not wander as much as the 900 Hz because there is not much noise below the 50 Hz signal.

 

[Ephant]

For a sinewave, lower frequency noise causes the baseline to wander up and down. Higher frequency noise looks like small jagged pulses added to the sinewave.

Both plots have 1 kHz BW limiting.

The 900 Hz shows a very short block of time that stretches the noise horizontally, and so makes it look smooth. There is little noise between 900 Hz and 1 kHz, so most of the noise is lower frequency, that appears to make the baseline for 900 Hz wander more than that for the 50 Hz.

The 50 Hz has lots of time on the display, and plenty of higher frequency noise between 50 Hz and 1 kHz. That higher frequency noise looks jagged. The baseline of the 50 Hz does not wander as much as the 900 Hz because there is not much noise below the 50 Hz signal.

How often do you think signal conditioning is done to smoothen the jagged edges in the lower frequency signal like in the following? How do they remove the jagged edges? Would it affect the baseline and make it bounce up and down, like perhaps converting high frequency noise to low frequency noise?

 

[Baluncore]

How often do you think signal conditioning is done to smoothen the jagged edges in the lower frequency signal like in the following?

When it is necessary.
It depends on the conversion rate of the A-D.

How do they remove the jagged edges?

They use a low-pass filter, or a band-pass filter.

Would it affect the baseline and make it bounce up and down, like perhaps converting high frequency noise to low frequency noise?

Low frequency noise would make the baseline jump up and down. If a band-pass filter was used, that would be reduced.

Linear signals are independent. Sine-wave signals are different to low-frequency noise, which is different to high-frequency noise. They can all be separated into different channels by using signal processing.

 

[Ephant]

When it is necessary.
It depends on the conversion rate of the A-D.


They use a low-pass filter, or a band-pass filter.

Low frequency noise would make the baseline jump up and down. If a band-pass filter was used, that would be reduced.

Linear signals are independent. Sine-wave signals are different to low-frequency noise, which is different to high-frequency noise. They can all be separated into different channels by using signal processing.

In white noise. the noises are all present in each frequency. So without any filter. the noises would be huge since all higher frequency noises would be present as well.

How does ADC sampling limit it? For example. Your ADC sampling is set to 4800 or 38400 without any low pass set in the setting. Does it mean the high frequency noises would be cut off at 4800 or 34800 respectively? or is it 2400 or 17400? or never at all?

 

[Baluncore]

In white noise. the noises are all present in each frequency. So without any filter. the noises would be huge since all higher frequency noises would be present as well.

The addition of random noise increases only as the root of the bandwidth.
Much noise is 1/f noise, so without a filter, the noise is limited.

Nyquist says that A-D sampling must be done at twice the rate of the highest frequency present in the signal. That usually requires a low-pass filter.
https://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem

 

[Ephant]

The addition of random noise increases only as the root of the bandwidth.
Much noise is 1/f noise, so without a filter, the noise is limited.

But what if the op amp or resistor would still produce white noise at 900 Gigaherz and so on. Or did you mean its like black body where when the frequency is so high the photons wont be emitted forever? what is the limit in the frequency when the noise would diminish so low?

Nyquist says that A-D sampling must be done at twice the rate of the highest frequency present in the signal. That usually requires a low-pass filter.
https://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem

What if no low pass filter setting is set and sampling is set to 38400? does it mean the the circuit can accept noise up to 38400 bandwidth?

 

[Baluncore]

I cannot teach you signal processing theory by a thousand questions.

What if, at this point, you learned to search for, and read, the easily and widely available literature.

 

[sophiecentaur]

@Ephant
Q and A is a hopeless way to learn any subject. You don't know which questions to ask, you don't know how to express them and you probably will not understand or appreciate the answers. You have to do your own finding out and learning.

 

[AlexisBlackwell]

Hello Ephant! The noise in sine waves will vary depending on the frequency at which the waves are generated. At higher frequencies, noise may be more noticeable due to the higher signal energy at those frequencies. Thus, the noise will vary depending on the frequency at which the sine waves are generated.

 

[Baluncore]

@AlexisBlackwell Welcome to PF.

The noise in sine waves will vary depending on the frequency at which the waves are generated.

The title of this thread is misleading. Fundamentally, sine waves do not have noise, by definition they are pure sine waves.

The noise is a separate broadband signal, present in the same channel as the sine wave signal. That noise will be amplified and attenuated with the sinewave, as it is processed. The sine wave is a narrowband signal, that can be detected or separated, from the broadband noise.

Distortion of sine waves, during generation or later signal processing, results in integer harmonics of the sine wave being present. If the distortion is symmetrical it will have odd harmonics only, if asymmetric, even harmonics will also be present. Each harmonic is another pure sine wave, at a higher frequency than the fundamental. The harmonic energy, resulting from distortion, may fall outside the band limited channel that carries the fundamental signal.

The noise, accompanying the sine wave, will depend on the bandwidth of the channel. The appearance of the noise, in the time domain, will depend on the position of the fundamental sine wave within the bandwidth of the channel. Noise at lower frequencies than the sinewave will appear as a wandering of the sine wave baseline, while noise at higher frequencies than the sine wave, will appear as jagged detail on the sine wave. That explains the problem with the title of this thread.