Hi all,

Just a simple question. I've read in the book "Principles of digital audio" a sentence referring to "in-band quantization noise" but I haven't been able to find a simple-minded definition of it. I don't really need any mathematical formula, just want to know what it is. My supposition is that in-band noise (in general, not only quantization), refers to a somehow obtained global noise inside a given frequency band.

Could someone please correct me if I'm wrong? Or corroborate my supposition if I'm right And if someone could refer me to some place with info about it, that would be perfect.

Thank you.

NOTE - I'm not a DSP expert, and I could be completely wrong!...


Yeah... I think it's the noise that happens to fall within the "band of interest", as-if it were filtered. In other words, when we're working with a limited bandwidth we can ignore any out-of-band noise because it could be filtered-out. ....Or, if we're working with audio, there's no reason to worry about 100kHz noise components.

If I understand it correctly, quantization noise is essentially impulse noise, which has an infinite bandwidth. (Or at least a bandwidth up to the Nyquist limit.)

In what context?

If its DACs, then it probably refers to noise falling in the output frequency range of the DAC (vs. ultrasonic noise that is attenuated by the reconstruction filter in an oversampling DAC). So in a 48kHz sampling rate DAC its noise >> 24kHz thats attenuated strongly.

It is simply the error introduced by the graininess of whatever resolution the signal happens to have. It will have finite BW as determined by the sample rate chosen during digitization.

Think of it as an analog signal that you can subtract from the reconstruction of the digital data to essentially recreate the original signal that was sampled.

First off, quantization noise is not really a noise. It is a nonlinear distortion. If you tell me the sample rate, the waveform of the signal being quantized, and what the quantization step size is, I can accurately tell you what the waveform of the so-called quantization noise is. If the quantization is dithered, then also tell me what the dither wave is, and I can still predict the so-called quantization noise is. That's not a noise, it is a nonlinear distortion.

Quantization nonlinear distortion is simply the difference between the quantized data and the data being quantized.

When people refer to in-band quantization noise they are referring to the fact that quantization can be done using oversampling, which naturally puts much of the quantization distortion outside the effective bandpass of the quantizer.

The non-linear distortion of quantization reduces to white noise for the normal case where frequency content of the program material is not correlated with the sampling frequency.

I know of no such general rule.

One of the things that often happens is that the program material has notes that change frequency slowly enough that quantization distortion in the form of a quickly rising short whistle is heard. Simple signals can simply sound gritty.

Even if the quantization distortion takes on the form of a kind of noise, the noise is often modulated.

Poorly dithered requantizations are often rendered trouble-free by the fact that the program material has enough residual noise to dither the result, despite the sloppiness.

I believe that quantization distortion was often heard as a noise in the early days simply because the program material used for testing had so much noise of its own.

I found a reference for you. I said uncorrelated, the reference says wide band, reasonable level. I hope I get partial credit. I hope you've not been listing to 8-bit audio.

Broken link.

Try this: books.google.com

They appear to be my friends! ;-)

The paragraph heading is "Quantization Distortion" and *not* "Qunatization Noise". Furthermore, they say that for low level signals, the error is predictable. The discussion of high level, complex signals is carefully-written, saying that the quantization error is perceived to be noise, rather than saying that it is in fact noise.

In fact qunatization error is completely predictable at all levels given the signal and the details of any predictable quantization scheme. This is true even though the predicted (and actual) error may seem to be noise-like.

Well, actually, if we use a noise diode for dither, then predictability will not exist.

But that is a bit rare.

These days, using noise diodes in audio applications seems to be pretty rare. Pseudo-random noise sources are just a little hardware on the chip that Does Everything Else. However, some of us old-timers remember back in the days when a digital pseudo-random noise source would use up a good chunk of all of the digital hardware in the known universe! ;-)

I thought of that. I thought that using a noise diode or something like it would fall outside of the realm of a "predictable quantization scheme".

Sure, given the two signals (signal and sampling frequency) you can mathematically predict the distortion. Under reasonable operating assumptions, statistically speaking, it has all the characteristics of white noise. So what's the practical difference between noise and noise-like?

I believe we can look to cryptography for an answer. To someone without the keys, well-encrypted data is white noise. With the keys, it's still white noise but predictable through decryption. Unencrypted, it sounds the same whether or not you know the keys.

The formal definition of a signal visualizes a signal as being a sequence in time of states such as voltages. For noise, the probable value of the next state in the sequence cannot be known given full knowlege of even all previoius states. For a signal, the probable value of the next state is in some sense knowable.



That's a reasonable example.

Whoa, no no no no no.

SOME of the probable vaue of the next state is knowable, this is called "prediction", as in treating the system as a markov process, etc.

If the VALUE is completely knowable, no information is conveyed, and the predictor can reproduce the entire bit with one sample.

The part of the signal that is predictable, i.e. knowable, is called 'redundancy'. The rest is called "information".

The easiest way to measure this is called "spectral flatness measure", and for a transform, it is the ratio of the geometric mean to the arithmetic mean. This is a number between 0 and 1, and tells you what amount of the signal is NOT predictable, i.e. is actual information as Shannon would define information.