Digital Audio - Quantization noise

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In the quantization operation, every sample is represented by an approximation of its real value. This is where the conversion into digital of an analogue signal introduces a degradation. The voltage-value gets picked up by an appropriate circuit and must then be stored on a digital support system, therefore it needs to be first converted into binary form. To do this we need to add a quantization operation which identifies a binary number as an approximation of the real value introducing an error called: quantization noise. The latter's maximum amplitude is identified with the amplitude of the quantization-interval.

Quantization noise is only generated when the audio signal is present. When there is silence no quantization errors take place. This characteristic, contrary to what one may think, is actually a negative factor, because it creates a noise-oscillation that the ear picks up far easier than a constant background noise (as is the "hiss" noise we get with magnetic tapes). To solve this problem we can increase the number of intervals in order to reduce the quantization error. Otherwise another solution consists in adding background white noise, and this can be carried out in two ways:

Analogue mode: white noise [White noise ] is added to the signal before it is sampled, so that when the audio signal is absent, background noise remains and gets sampled anyway.

Digital mode (dither): the last bit in each sample (sometimes the last 2 or 4 when resolution is high enough, i.e: 24 bit) is randomly modified. This allows the presence of white noise to be simulated. Its technical term is: dither. Many audio software production companies have begun to introduce a series of plug-ins[26 ] to the market, specifically intended for hard-disc recording, and which contain "intelligent" dithering algorithms. Their special characteristic consists in the ability adapt their interventions depending on the characteristics of the signal they have to manipulate.

The greater the number of intervals used, the smaller the error. Theoretically, if we had infinite amounts of quantization intervals, each voltage value would be exactly represented by the quantization interval that identifies it (which would coincide with a point). Not only would this solution be technically unrealistic, but we'd also need to use infinite amounts of bits to represent each interval. In our example we used 3 bits. With Audio CDs a 16 bit quantization takes place, which implies the sub-division of the voltage-axis into 65536 distinct intervals. In professional recording studios manipulation is performed using a 24 bit format (or even more) and reconverting the signal back to 16 bit before storing it on a CD.

The standard quantities used in the production of an audio CD are:

Table 18.7. Audio CD format specifications 

Sampling frequency44.1KHz
Quantization bits16 (65536 intervals)

Sampling a signal at frequency f means extracting f samples per second from the signal. In the case of an audio signal sampled with CD standard, 44100 samples are extracted each second. Every sample is represented by a binary 16 bit number. So, a stereo signal produces the following number of samples per second:

2 (stereo) x 16 (bit) x 44100 (samples) = 1411200 bit/s

if we wanted to express this result in bytes we'd have:

1411200/8 = 176400 bytes = 172.26 KB

So, to sample stereo signal for one second 'costs', in terms of mass memory, 172 KB.

A normal CD can record 74 minutes, therefore it has:

176.26 (KB/s) x 60 (sec)x 74min = 764 MB

available for storing audio data.

The most common blank CDs are sold with a 74 min capacity for audio, or 650 MB for data. We've just seen that in order to store 74 minutes of stereo music we'd need 746 MB, whereas the above-mentioned CD seems to allow for "only" 650 MB to be memorized. How can we explain this discrepancy? The answer lies in the way data is stored. In an audio CD, data is memorized once only, even though it is arranged in a way that reduces reading errors. Instead, in the case of CDROMs, data is copied on different parts of the CD so that it can still be read if part of the optical disc's surface were to get damaged.

[26 ] What is meant with this word is an extension of a computer software which enriches its functions.


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