Kilohearts Plug-ins (My Misunderstanding)

[Tj Shredder]

I can easily quote Wacky, as I am blocked anyway…; - )

I'm shocked how few users here understand how summing works. It doesn't take many instances of those plugins to end up with a noise floor that ruins even a 16 bit integer signal.

To put it simple you need more than 256. If the end result sounds good for human ears, a 16-bit integer delivers 96 dB of dynamics.
Each doubling of a signal in a DAW of 16-bit signals could add 6 dB of noise…
Thus if you use 24-bit integer signals, you can have 256 Tracks without getting audible noise, even if all these tracks are on full level and carry only dither noise.
(If they carry a zero signal instead of dither noise, you can boost it easily by 600 dB without changing it…)
Beside that, this scenario is not of a real production where the majority of tracks don‘t play at the same time, its still not an issue even with 1024 tracks…
If the mixing is in 32-bit float, you get a 24-bit Mantissa and the exponent is scaling the noise. That means if you lower the level of a track, the noise is lowered as well.
If you can‘t get a clean signal out of a 32-bit mixing environment. You need to go back to school and learn the basics…
Of course there are processes which will sound better if you do it in double precision. Those are done in that precision as long the complete application is a 64-bit application.
Yes the DAW and the plugins need to be coded in 64-bit. But that are programming details which normal users don‘t need to get into.
Then you need to know about mathematical rounding errors. If you type into a gain plugin +3dB, and then -3dB it is not precise what you think it is. You would need to set it to a binary equivalent, which no DAW will give you. You can do experiments like that in Max/MSP to find out what is going on. There are tons of threads about that. Of course the rounding errors are way lower in 64-bit precision, and they add up like anything. But you need at least 256 times to do those calculations in the worst case scenario to loose 8-bit of precision…
And the worst case is purely theoretical !

[limitlesssss]

Then you need to know about mathematical rounding errors. If you type into a gain plugin +3dB, and then -3dB it is not precise what you think it is. You would need to set it to a binary equivalent, which no DAW will give you.

That's why I also tried to cut/boost exactly 6.0205999132796239042747778944899dB which was not possible. Kilohearts Gain gave me only 4 digits after the decimal point and I ended up with 6.0206dB.

[Tj Shredder]

The dB value will be converted into an level. That already will have a rounding error, and those will be different for positive and negative numbers.
There you go…

[SamDi]

All I'm asking is, why should there be a noise floor to begin with in a purely digital signal that is being operated in a 64-Bit FP DAW environment? Is it dithering noise? I doubt it. In a floating point environment dithering is odd. What is it? Why can I perfectly null a duplicated track when I flip the polarity of one of the tracks, but as soon as I insert even *one* Kilohearts Gain plug-in (untouched) on one of the tracks, all of a sudden the noise floor of the null raises to -150dBFS? Why? What is it? I want to know. What is going on behind the scene of these plug-ins? How about when I insert two Kilohearts Gain plug-ins on one of the tracks, one of which is cutting exactly 3dB and the other is boosting exactly 3dB? Shouldn't the result of the null be absolute silence instead of -129dBFS? Why isn't it absolute silence? What is going on behind the scene?

Is that nitpicking? Okay, I understand. Those who don't care because they're busy releasing hit records after hit records are welcome to ignore this thread.

I think, that your conclusions from your observations are wrong:

1.) When you chaining 32bit plugins, up- and downscaling shouldn't introduce any additional errors aka noise unless dithering is used, what I doubt.
2.) Further it seems to me, that the noise, you observed is just the rounding error of the +- 3dB operations, you perform. This would exactly match to the -150dB (shouldn't it be -144dB rather?), which is the smallest bit in the fraction of the float.

You could the the following tests to proove or disproove my statements:
1.) Make your tests again with your DAW set to 32bit. Also there you should have these rounding errors. It would be strange, if not.
2.) Make the same tests with 64 and 32 bit, but with +-20dB. Since this is a factor of exactly 10 no rounding errors should occur on both bit depths.

So at least you get clarity.

Anyway, be aware that no matter, where it comes from it has no practical impact since:

1.) Much higher noise is already in any physical recorded signals
2.) When chaining plugins there are much more artefacts introduced by digital calculations, think of aliasing, other errors from DSP optimizations, means algorithms exchanging performance with precisions, interpolation errors, introduced distortions everywhere, etc., etc, a noise starting at -150dBFS, even when accumulated is by far the least problem, you have
3.) Think of all the emulating plugins, which add intentional noise to mimic analog sound. Much higher noise signal then
4.) What about guys, using analog gear in their signal path? What do you think, how much noise is there introduced and amplified in the signal path?
5.) And last but not least you talk about noise in zero signal, which is barely there in music. As soon as you have a wanted signal, a noise, even beeing just -20 - -30 db under this signal, you are not able to hear it, since your ear is masking it. So even if you would reach a noise level around of -50dbFS, it wouldnt be perceived, assumed that your gain staged loudness during production is somewhere around -20 LUFS
6.) Don't forget, there are really people out there, who are convinced, that vinyl is the much more audiophile medium. What is the s/n ratio there? 50-60db or so?

The most ridiculous argument, which one stated here, is that professional productions with 32bit are a big catastrophe with this huuuuge noise. With 90% of today's plugin running with 32 bit and running digital productions since decades, reality just prooves him wrong.

[EfreetiSultan]

Im very very curious aswell, what could be causing it.

[Jac459]

All I'm asking is, why should there be a noise floor to begin with in a purely digital signal that is being operated in a 64-Bit FP DAW environment? Is it dithering noise? I doubt it. In a floating point environment dithering is odd. What is it? Why can I perfectly null a duplicated track when I flip the polarity of one of the tracks, but as soon as I insert even *one* Kilohearts Gain plug-in (untouched) on one of the tracks, all of a sudden the noise floor of the null raises to -150dBFS? Why? What is it? I want to know. What is going on behind the scene of these plug-ins? How about when I insert two Kilohearts Gain plug-ins on one of the tracks, one of which is cutting exactly 3dB and the other is boosting exactly 3dB? Shouldn't the result of the null be absolute silence instead of -129dBFS? Why isn't it absolute silence? What is going on behind the scene?

Is that nitpicking? Okay, I understand. Those who don't care because they're busy releasing hit records after hit records are welcome to ignore this thread.

I think, that your conclusions from your observations are wrong:

1.) When you chaining 32bit plugins, up- and downscaling shouldn't introduce any additional errors aka noise unless dithering is used, what I doubt.
2.) Further it seems to me, that the noise, you observed is just the rounding error of the +- 3dB operations, you perform. This would exactly match to the -150dB (shouldn't it be -144dB rather?), which is the smallest bit in the fraction of the float.

You could the the following tests to proove or disproove my statements:
1.) Make your tests again with your DAW set to 32bit. Also there you should have these rounding errors. It would be strange, if not.
2.) Make the same tests with 64 and 32 bit, but with +-20dB. Since this is a factor of exactly 10 no rounding errors should occur on both bit depths.

So at least you get clarity.

Anyway, be aware that no matter, where it comes from it has no practical impact since:

1.) Much higher noise is already in any physical recorded signals
2.) When chaining plugins there are much more artefacts introduced by digital calculations, think of aliasing, other errors from DSP optimizations, means algorithms exchanging performance with precisions, interpolation errors, introduced distortions everywhere, etc., etc, a noise starting at -150dBFS, even when accumulated is by far the least problem, you have
3.) Think of all the emulating plugins, which add intentional noise to mimic analog sound. Much higher noise signal then
4.) What about guys, using analog gear in their signal path? What do you think, how much noise is there introduced and amplified in the signal path?
5.) And last but not least you talk about noise in zero signal, which is barely there in music. As soon as you have a wanted signal, a noise, even beeing just -20 - -30 db under this signal, you are not able to hear it, since your ear is masking it. So even if you would reach a noise level around of -50dbFS, it wouldnt be perceived, assumed that your gain staged loudness during production is somewhere around -20 LUFS
6.) Don't forget, there are really people out there, who are convinced, that vinyl is the much more audiophile medium. What is the s/n ratio there? 50-60db or so?

The most ridiculous argument, which one stated here, is that professional productions with 32bit are a big catastrophe with this huuuuge noise. With 90% of today's plugin running with 32 bit and running digital productions since decades, reality just prooves him wrong.

I agree so much.

[limitlesssss]

All I'm asking is, why should there be a noise floor to begin with in a purely digital signal that is being operated in a 64-Bit FP DAW environment? Is it dithering noise? I doubt it. In a floating point environment dithering is odd. What is it? Why can I perfectly null a duplicated track when I flip the polarity of one of the tracks, but as soon as I insert even *one* Kilohearts Gain plug-in (untouched) on one of the tracks, all of a sudden the noise floor of the null raises to -150dBFS? Why? What is it? I want to know. What is going on behind the scene of these plug-ins? How about when I insert two Kilohearts Gain plug-ins on one of the tracks, one of which is cutting exactly 3dB and the other is boosting exactly 3dB? Shouldn't the result of the null be absolute silence instead of -129dBFS? Why isn't it absolute silence? What is going on behind the scene?

Is that nitpicking? Okay, I understand. Those who don't care because they're busy releasing hit records after hit records are welcome to ignore this thread.

I think, that your conclusions from your observations are wrong:

1.) When you chaining 32bit plugins, up- and downscaling shouldn't introduce any additional errors aka noise unless dithering is used, what I doubt.
2.) Further it seems to me, that the noise, you observed is just the rounding error of the +- 3dB operations, you perform. This would exactly match to the -150dB (shouldn't it be -144dB rather?), which is the smallest bit in the fraction of the float.

You could the the following tests to proove or disproove my statements:
1.) Make your tests again with your DAW set to 32bit. Also there you should have these rounding errors. It would be strange, if not.
2.) Make the same tests with 64 and 32 bit, but with +-20dB. Since this is a factor of exactly 10 no rounding errors should occur on both bit depths.

So at least you get clarity.

Anyway, be aware that no matter, where it comes from it has no practical impact since:

1.) Much higher noise is already in any physical recorded signals
2.) When chaining plugins there are much more artefacts introduced by digital calculations, think of aliasing, other errors from DSP optimizations, means algorithms exchanging performance with precisions, interpolation errors, introduced distortions everywhere, etc., etc, a noise starting at -150dBFS, even when accumulated is by far the least problem, you have
3.) Think of all the emulating plugins, which add intentional noise to mimic analog sound. Much higher noise signal then
4.) What about guys, using analog gear in their signal path? What do you think, how much noise is there introduced and amplified in the signal path?
5.) And last but not least you talk about noise in zero signal, which is barely there in music. As soon as you have a wanted signal, a noise, even beeing just -20 - -30 db under this signal, you are not able to hear it, since your ear is masking it. So even if you would reach a noise level around of -50dbFS, it wouldnt be perceived, assumed that your gain staged loudness during production is somewhere around -20 LUFS
6.) Don't forget, there are really people out there, who are convinced, that vinyl is the much more audiophile medium. What is the s/n ratio there? 50-60db or so?

The most ridiculous argument, which one stated here, is that professional productions with 32bit are a big catastrophe with this huuuuge noise. With 90% of today's plugin running with 32 bit and running digital productions since decades, reality just prooves him wrong.

Thank you. This was a great answer.

• I changed the mixing bit depth to 32-Bit FP.
• I then created a track containig 1000Hz, 977Hz, 944Hz sine wave, and then a sine sweep @ -3dBFS.
• Duplicated the track and flipped its polarity and unsurprisingly it nulled.
• I then inserted one instance of Kilohearts Gain not touching it.
• And lo and behold, it nulled to negative infinity. So the person who said “even at 0dB it may not be exactly 0dB” was wrong.
• Unfortunately when cutting and boosting the same amount (yes even -/+ 20dB) it doesn't null at either precision single or double.
• Interestingly the 1000Hz shows aliasing, 977Hz doesn't show aliasing but something like dither, 944Hz is strange, and sine sweep doesn't show aliasing but dither-like noise.

[limitlesssss]

The dB value will be converted into an level. That already will have a rounding error, and those will be different for positive and negative numbers.
There you go…

I suspect TJ also has a point: I tested it again in a different way so that I don't have to do cutting and boosting simultaneously.

So instead of inserting two Kilohearts Gain plug-ins on *ONE* track (cutting and boosting simultaneously), I inserted only one Kilohearts Gain on each track, both doing the exact same amount of cutting or boosting. And they nulled to negative infinity in both 32-Bit FP and 64-Bit FP. So I think TJ's point about rounding error is also correct. Thank you.

[FrogsInPants]

2.) Make the same tests with 64 and 32 bit, but with +-20dB. Since this is a factor of exactly 10 no rounding errors should occur on both bit depths.

You can get rounding errors in floating point operations when multiplying or dividing by 10. This should be especially easy to see with dividing, as 1/10 does not itself have an exact floating point representation.

[limitlesssss]

Anyway, be aware that no matter, where it comes from it has no practical impact since:

1.) Much higher noise is already in any physical recorded signals

No doubt.

3.) Think of all the emulating plugins, which add intentional noise to mimic analog sound. Much higher noise signal then

Of course, but that's not what you expect when you're using a “transparent” plug-in.

4.) What about guys, using analog gear in their signal path? What do you think, how much noise is there introduced and amplified in the signal path?

A lot and it probably sounds good to them. And good for them. But then again, this discussion was/is about plug-ins that are supposed to be as transparent as possible.

5.) And last but not least you talk about noise in zero signal, which is barely there in music. As soon as you have a wanted signal, a noise, even beeing just -20 - -30 db under this signal, you are not able to hear it, since your ear is masking it. So even if you would reach a noise level around of -50dbFS, it wouldnt be perceived, assumed that your gain staged loudness during production is somewhere around -20 LUFS

I never claimed I could hear the noise by the way. This discussion is not about that (at least you won't hear that argument from me).

6.) Don't forget, there are really people out there, who are convinced, that vinyl is the much more audiophile medium. What is the s/n ratio there? 50-60db or so?

And good for them. More power to them.

[Jac459]

Anyway, be aware that no matter, where it comes from it has no practical impact since:

1.) Much higher noise is already in any physical recorded signals

No doubt.

3.) Think of all the emulating plugins, which add intentional noise to mimic analog sound. Much higher noise signal then

Of course, but that's not what you expect when you're using a “transparent” plug-in.

4.) What about guys, using analog gear in their signal path? What do you think, how much noise is there introduced and amplified in the signal path?

A lot and it probably sounds good to them. And good for them. But then again, this discussion was/is about plug-ins that are supposed to be as transparent as possible.

5.) And last but not least you talk about noise in zero signal, which is barely there in music. As soon as you have a wanted signal, a noise, even beeing just -20 - -30 db under this signal, you are not able to hear it, since your ear is masking it. So even if you would reach a noise level around of -50dbFS, it wouldnt be perceived, assumed that your gain staged loudness during production is somewhere around -20 LUFS

I never claimed I could hear the noise by the way. This discussion is not about that (at least you won't hear that argument from me).

6.) Don't forget, there are really people out there, who are convinced, that vinyl is the much more audiophile medium. What is the s/n ratio there? 50-60db or so?

And good for them. More power to them.

... And I can only agree with your answers. I mean, I don't think this SN ratio thing is important but I am sure there is a ton of things I find important and don't matter for you. So if you find it important and want to lobby about it, good for you...

I am a bit less comfortable on some people going on your side by arguing it is a professional vs amateur things... Like The prodigy doing ultra sophisticated songs in 12bit samplers aren't professional, or the number of ultra successful beat makers using FL studio and fab filters...
That's a pretty assholish argument...

Anyway, the funny things is that in the war, "CPU consumption" vs "64bits sound" defenders, both parties arguments are exactly transposable.

"SN of 150db does matter" vs "worry about noise when you actually hear it" and
"CPU consumption does matter" vs "worry about CPU consumption when you actually have issue with it".

[limitlesssss]

Anyway, be aware that no matter, where it comes from it has no practical impact since:

1.) Much higher noise is already in any physical recorded signals

No doubt.

3.) Think of all the emulating plugins, which add intentional noise to mimic analog sound. Much higher noise signal then

Of course, but that's not what you expect when you're using a “transparent” plug-in.

4.) What about guys, using analog gear in their signal path? What do you think, how much noise is there introduced and amplified in the signal path?

A lot and it probably sounds good to them. And good for them. But then again, this discussion was/is about plug-ins that are supposed to be as transparent as possible.

5.) And last but not least you talk about noise in zero signal, which is barely there in music. As soon as you have a wanted signal, a noise, even beeing just -20 - -30 db under this signal, you are not able to hear it, since your ear is masking it. So even if you would reach a noise level around of -50dbFS, it wouldnt be perceived, assumed that your gain staged loudness during production is somewhere around -20 LUFS

I never claimed I could hear the noise by the way. This discussion is not about that (at least you won't hear that argument from me).

6.) Don't forget, there are really people out there, who are convinced, that vinyl is the much more audiophile medium. What is the s/n ratio there? 50-60db or so?

And good for them. More power to them.

... And I can only agree with your answers. I mean, I don't think this SN ratio thing is important but I am sure there is a ton of things I find important and don't matter for you. So if you find it important and want to lobby about it, good for you...

I am a bit less comfortable on some people going on your side by arguing it is a professional vs amateur things... Like The prodigy doing ultra sophisticated songs in 12bit samplers aren't professional, or the number of ultra successful beat makers using FL studio and fab filters...
That's a pretty assholish argument...

Anyway, the funny things is that in the war, "CPU consumption" vs "64bits sound" defenders, both parties arguments are exactly transposable.

"SN of 150db does matter" vs "worry about noise when you actually hear it" and
"CPU consumption does matter" vs "worry about CPU consumption when you actually have issue with it".

To be fair, it wasn't the noise per se that I had an issue with. It was the fact that I didn't know what exactly was causing it. In my head, I was thinking: “if this plug-in is causing noise that it's not supposed to cause, what else is going on that I'm not aware of?”. Because in my mind when I entered -6.0205999dB on the first Gain plug-in and +6.0205999dB on the second, my assumption was that the plug-ins were using those exact numbers without any rounding error being involved. So in my mind, they were supposed to null, but they didn't and there was a noise floor at around -150dBFS. Even if the noise floor was around -600dBFS, I still would've wanted to find out why. Not that I could ever hear the noise floor obviously.

But as soon as TJ mentioned rounding error in the numbers, it immediately clicked. So I think TJ's answer that positive and negative numbers have *different* rounding errors is a very compelling case as to why I wasn't able to null them. It's at least the best possible answer so far.

Having said that, I'm still waiting for the folks at Kilohearts to reply to my email. I'm sure they have useful information to share. And if they're okay with it I'll definitely share it here.

By the way, you may not believe it, but I like the aesthetics of 12-Bit recordings.

[Jac459]

Anyway, be aware that no matter, where it comes from it has no practical impact since:

1.) Much higher noise is already in any physical recorded signals

No doubt.

3.) Think of all the emulating plugins, which add intentional noise to mimic analog sound. Much higher noise signal then

Of course, but that's not what you expect when you're using a “transparent” plug-in.

4.) What about guys, using analog gear in their signal path? What do you think, how much noise is there introduced and amplified in the signal path?

A lot and it probably sounds good to them. And good for them. But then again, this discussion was/is about plug-ins that are supposed to be as transparent as possible.

5.) And last but not least you talk about noise in zero signal, which is barely there in music. As soon as you have a wanted signal, a noise, even beeing just -20 - -30 db under this signal, you are not able to hear it, since your ear is masking it. So even if you would reach a noise level around of -50dbFS, it wouldnt be perceived, assumed that your gain staged loudness during production is somewhere around -20 LUFS

I never claimed I could hear the noise by the way. This discussion is not about that (at least you won't hear that argument from me).

6.) Don't forget, there are really people out there, who are convinced, that vinyl is the much more audiophile medium. What is the s/n ratio there? 50-60db or so?

And good for them. More power to them.

... And I can only agree with your answers. I mean, I don't think this SN ratio thing is important but I am sure there is a ton of things I find important and don't matter for you. So if you find it important and want to lobby about it, good for you...

I am a bit less comfortable on some people going on your side by arguing it is a professional vs amateur things... Like The prodigy doing ultra sophisticated songs in 12bit samplers aren't professional, or the number of ultra successful beat makers using FL studio and fab filters...
That's a pretty assholish argument...

Anyway, the funny things is that in the war, "CPU consumption" vs "64bits sound" defenders, both parties arguments are exactly transposable.

"SN of 150db does matter" vs "worry about noise when you actually hear it" and
"CPU consumption does matter" vs "worry about CPU consumption when you actually have issue with it".

To be fair, it wasn't the noise per se that I had an issue with. It was the fact that I didn't know what exactly was causing it. In my head, I was thinking: “if this plug-in is causing noise that it's not supposed to cause, what else is going on that I'm not aware of?”. Because in my mind when I entered -6.0205999dB on the first Gain plug-in and +6.0205999dB on the second, my assumption was that the plug-ins were using those exact numbers without any rounding error being involved. So in my mind, they were supposed to null, but they didn't and there was a noise floor at around -150dBFS. Even if the noise floor was around -600dBFS, I still would've wanted to find out why. Not that I could ever hear the noise floor obviously.

But as soon as TJ mentioned rounding error in the numbers, it immediately clicked. So I think TJ's answer that positive and negative numbers have *different* rounding errors is a very compelling case as to why I wasn't able to null them. It's at least the best possible answer so far.

Having said that, I'm still waiting for the folks at Kilohearts to reply to my email. I'm sure they have useful information to share. And if they're okay with it I'll definitely share it here.

By the way, you may not believe it, but I like the aesthetics of 12-Bit recordings.

Well... From an engineering standpoint, this is a pretty interesting topic hehe.

Now if you want to open a topic about the Nyquist-Shannon theorem, high resolution audio and MQA, I am all in. I am on the side of MQA over high-resolution (and may be the only one on this side)...

[csscp]

Anyway, be aware that no matter, where it comes from it has no practical impact since:

1.) Much higher noise is already in any physical recorded signals

No doubt.

3.) Think of all the emulating plugins, which add intentional noise to mimic analog sound. Much higher noise signal then

Of course, but that's not what you expect when you're using a “transparent” plug-in.

4.) What about guys, using analog gear in their signal path? What do you think, how much noise is there introduced and amplified in the signal path?

A lot and it probably sounds good to them. And good for them. But then again, this discussion was/is about plug-ins that are supposed to be as transparent as possible.

5.) And last but not least you talk about noise in zero signal, which is barely there in music. As soon as you have a wanted signal, a noise, even beeing just -20 - -30 db under this signal, you are not able to hear it, since your ear is masking it. So even if you would reach a noise level around of -50dbFS, it wouldnt be perceived, assumed that your gain staged loudness during production is somewhere around -20 LUFS

I never claimed I could hear the noise by the way. This discussion is not about that (at least you won't hear that argument from me).

6.) Don't forget, there are really people out there, who are convinced, that vinyl is the much more audiophile medium. What is the s/n ratio there? 50-60db or so?

And good for them. More power to them.

... And I can only agree with your answers. I mean, I don't think this SN ratio thing is important but I am sure there is a ton of things I find important and don't matter for you. So if you find it important and want to lobby about it, good for you...

I am a bit less comfortable on some people going on your side by arguing it is a professional vs amateur things... Like The prodigy doing ultra sophisticated songs in 12bit samplers aren't professional, or the number of ultra successful beat makers using FL studio and fab filters...
That's a pretty assholish argument...

Anyway, the funny things is that in the war, "CPU consumption" vs "64bits sound" defenders, both parties arguments are exactly transposable.

"SN of 150db does matter" vs "worry about noise when you actually hear it" and
"CPU consumption does matter" vs "worry about CPU consumption when you actually have issue with it".

To be fair, it wasn't the noise per se that I had an issue with. It was the fact that I didn't know what exactly was causing it. In my head, I was thinking: “if this plug-in is causing noise that it's not supposed to cause, what else is going on that I'm not aware of?”. Because in my mind when I entered -6.0205999dB on the first Gain plug-in and +6.0205999dB on the second, my assumption was that the plug-ins were using those exact numbers without any rounding error being involved. So in my mind, they were supposed to null, but they didn't and there was a noise floor at around -150dBFS. Even if the noise floor was around -600dBFS, I still would've wanted to find out why. Not that I could ever hear the noise floor obviously.

But as soon as TJ mentioned rounding error in the numbers, it immediately clicked. So I think TJ's answer that positive and negative numbers have *different* rounding errors is a very compelling case as to why I wasn't able to null them. It's at least the best possible answer so far.

Having said that, I'm still waiting for the folks at Kilohearts to reply to my email. I'm sure they have useful information to share. And if they're okay with it I'll definitely share it here.

By the way, you may not believe it, but I like the aesthetics of 12-Bit recordings.

Floating point precision is a huge deal in certain areas of DSP. The link below is written for Python but it touches on the nature of these problems and offers a deeper glimpse into the (terrible) world of floating point arithmetic.

https://docs.python.org/3/tutorial/floatingpoint.html

[rafa1981]

You aren't measuring noise floor. To measure the noise floor you need to input silence and hear noise.

If you input zeroes to the EQ/gain it will output zeroes and will null.

You are measuring a kind-of distortion. A distortion added to a signal. That distortion will never be audible because it will masked with the signal itself which is orders of magnitude bigger.

Also that distortion is almost value independent as long as the floating point exponents are normalised (in the floating point sense) after the gain.

Basically a sample at 0dBfs will be displaced to linear(0dBfs) +- linear(-150dBfs).

Floating point is a power, so at any range between an exponent and the next it has 24 bits.

That means that if you do the same operation to a -60dbfs signal your noise will appear at -60 + -150dBfs. (If the resulting fp range allows/is normalized).