Piano World Home Page Forums Our Most Popular Forums Digital Pianos - Electronic Pianos - Synths & Keyboards Any Kawai piano with USB audio interface?

That is for analog signal conversion.

We are discussing in the domain of Digital Signal Processing (not continuous signal processing).

Only the addition operation itself is deterministic. The data that's being added is not. It was created through analog to digital conversion with the resulting quantization error. Summing signals with small quantization errors creates bigger errors (you are correct that it will create the same bigger errors each time you sum the same numbers). That leads you to do much more sophisticated DSP than simple addition (i.e. noise shaping) in order to improve the perceived signal-to-noise ratio.

Quantization noise happens in the world of ADC. When you convert an analog signal to a digital it happens.

We don't have quantization errors in digital signal processing in the sense you are saying.


If you are changing a signal's bit-depth from 16 to 24 or 24,000,000bit all you do is to pad zeros in each bit you read. You can retrieve your original 16bit signal as long as you are not manipulating it.

Let's say I do a transformation like amplification: how does it work? amplification is done in a discrete world. As long as you know the operations and those operations meet certain mathematical properties (invertible functions etc let's say) you can retrieve the original data uniquely.

So let's say you do 22.0005^2 = 484.02200024999996

If you find the sqr root you will get:

484.02200024999996^.5 = 22.0005

Every single time.

Don't mix discrete and continuous worlds with each other. Digital doesn't work the same way you think.

My friend, what are you talking about?

We are talking about a digital signal that is coming from a USB cable. It is digital it is not analog. Where did you get the analog stuff from?

We're talking about digital signals that came from analog sources and will be converted back to analog after they've been processed.

Even if you were only working with digitally synthesized data (say a modeled piano versus a sampled one), the data still represents an analog waveform. Analog waveforms can have infinitely many amplitudes, so when you have to represent smooth analog waveforms using only 16-bit samples you will have quantization error in the data that you're working with.

As far as I remember: we were talking about external vs internal audio interfaces and if the internal interfaces are better at mixing digital signals.

The answer to this is no. Even if it is modeled and synthesized, it is 100% digital. It means it is discrete. So it is the responsibility of the DAC to transform that signal into a continuous analog signal.

It is really hard (or even impossible!) to find pure analog synths these days. The most famous (and my fav) is Dave Smith Instrument (DSI) which manufactures hybrid synths as far as I can tell and they are not pure analog.


True, but nothing is analog in terms of the synths/keyboards we have.

The only time we have an analog signal is when we use the line in/aux-in of a mixer/keyboard.

better at mixing digital signals that were converted from analog and will be converted back to analog.



We are exclusively dealing with analog music here that's just temporarily being represented digitally between the time it was captured (or synthesized) and when it's played back through speakers or headphones. We're not talking about a spreadsheet for balancing your checkbook here.

I have no idea what you are talking about, but:

There is no synth in the market that generates an analog signal (except those pure analog ones that you pay a fortune for them). All of the VSTs have ever been manufactured as of today, are digital. None of them generates continuous signals.

The signal is always discrete, it will be sent to the audio interface's Digital to Analog Converter (DAC) module.

When you mix two discrete signals, you will not have those artifacts (like quantization issues) if you are working in the same bit depth or your destination has a higher bit depth.

If you are down-sampling, you will experience some loss but this is what is being practiced in the industry. The original works are always done in 24bits, 96kHz+ and then it gets downgraded for mass use.

Most digital pianos are sampled and not synthesized, plus the music you're mixing in also came from analog sources. But that's not even relevant. In all cases the digital data is *representing* a continuous analog waveform even if it didn't originate from one. The digital representation is just an approximation with some inherent quantization error.

Since the US just had an election I'll use another analogy. Political polls are just a bunch of numbers, but each one has inherent error (e.g sampling error). You can't simply sum the data from multiple political polls and get meaningful results without understanding the nature of the errors in the underlying data.

Nope, it was a cancellation error that can result from subtracting two numbers very close to one, which is a very well known issue in the field of numerical analysis. The error may be small, but can be multiplied by subsequent multiplications or exponentiations.


It is the DSP tier of a DP where floating point errors will accumulate, not additions.

This is a funny joke.

So if I do

2.01+1.94 on my computer I might get 4.332 and you might get 5.81?

Numerical analysis is a very mature branch of applied math. It is the study of numerical algorithms that find approximations to solutions of problems for which there is no precise mathematical solution method available.

Error analysis is an area of numerical analysis that deals with computational errors in the implementations of numerical algorithms. These are not shallow subjects.

Here is an article about the evolution of HP calculators with respect to engineering work to make the calculations more accurate from a numerical computation error perspective. You can see that even computing 2^3 accurately took some numerical engineering work.

https://www.scribd.com/document/240534272/The-New-Accuracy-Making-2-Cubed-Equal-8-Harms-HPJ-1976-11

The posting I replied to was also discussing A:D conversion, which is needed when a digital mixer receives an analog signal.

You are wrong Sweelinck.

This is something totally irrelevant to our topic.

Go add two numbers on your computer and get back to me. If you got 2.0+2.0=2.00001 on your computer, then get back to me.

I don't want to turn the 1ms BS detection mode on.

I did not claim that about addition. You need other operations to implement DSP transformations.

What you are arguing is implementation specif. The addition of two signals is just about summing them together and making sure it will not go beyond 0dB.

The addition and division are the only operations needed to add two signals. You add two signals and you get an amplitude that can go up to twice as loud as the original signal. For this purpose, you can do your arithmetics in 32bits (16bitx2) and then normalize it back. To convert two signals to 32bits you only pad them with zeros. It doesn't do a harm to your signal.

This is just my guess and in reality, it might be different but the addition is the only way to add two signals.

Now different implementations of mixing can exist. It has nothing to do with the hardware you are using.

The numerical analysis you mentioned is not for discrete and finite operations that we are considering here.


I can imagine different implementations of mixing two audio signals have subtle differences but that's just part of the implementation, or the algorithm. For example, the concept of headroom is implementation specific. limiting signals, trimming, compressing... there are many ways to make sure the final signal does not gets distorted.

That said, when we are performing live, you always adjust the gain no matter if it is digital or analog. You also leave some headroom. It is probably 2-4dB or something like that. I'm not a pro at mixing and mastering. But this is what you must always do!

If you have a link please share it but you are talking about floating point again.

Fixed point is what is being used.

And didn’t you say additions produce noise because of round off error?


There is science behind sampling and how many levels you need and sample rates.

Your basically saying digital signal processing doesn’t work

And analog doesn’t have any issues?

No, was not distinguishing between fixed point and floating point arithmetic. And nothing I said would imply that "DSP doesn't work" leading to a contradiction. But it is not noise free.

My point is just that both digital and analog audio have sources of noise. Digital audio is not noise free, but has less noise if implemented well.

This will be my last post to the thread. One of the top audio engineers in the world, Bob Katz, has a book on mastering audio, that is recommended reading for anyone wanting to learn about audio engineering in the digital realm.

PS Here is a discussion of cancellation errors during a subtraction.

Note that a subtraction of two numbers is just the addition of the additive inverse of one number to the other. When the numbers have opposite sign, adding them is subject to the same kind of cancellation error that subtracting two numbers of the same sign is susceptible to.

PPS Some more info:

https://scilogs.spektrum.de/hlf/built-in-errors-william-kahan-and-floating-point-arithmetic/

Who is William Kahan referred to in the previous link?

https://en.m.wikipedia.org/wiki/William_Kahan