Quantization - the process of converting continuous values into a series of distinct values. In digital audio, the values are voltages .
Remember, the two characteristics of digital audio are sampling (time) and quantization (level).
While sampling represents the time of capturing a signal, quantization is the amplitude component of sampling. In other words, while sampling measures the time (for instance 44,100 samples per second), quantization is the technique where by an analog event is measured and given a numerical value.
An example is a clock. Time is a continuous event, yet the second or minute hand jumps from number to number, value to value.
To do this, the amplitude of the audio signal is broken down into a series of discrete steps. Each step is then given a binary word that digitally encodes the level of the signal. length of the digital word determines the quality of the representation. Once again , the larger the word, the better the quality (16 bit word compared to an 8 bit word). Also, the larger the bit word, the greater the headroom of the audio system (6 dB for every bit).
| DISCRETE VOLTAGE STEPS |
| 8 bit word = 256 steps |
| 16 bit word = 65,536 steps |
| etc. |
The word 'step' is used in reference to the stepped appearance of the quantized wave form.
You are probably familiar with flip card animation where you create a cartoon by drawing say a man running with each successive card showing a small movement of the mans legs. If you have only 4 cards to use, the result would be jerky . If you had 100 cards, each card showing a small amount of movement, the result would be more life-like and smooth.
Quantized is a similar function. the more steps with which to describe the signal the smoother the result will be.
QUANTIZATION ERROR
Quintile error is the difference between actual analog value and the assigned quantization value.
| 1111 | bit 4 | 24 dB | |
| 1110 | | | ||
| 1101 | | | ||
| 1100 | | | ||
| 1011 | | | ||
| 1010 | | | ||
| 1001 | | | ||
| 1000 | bit 4 | ||
| 0111 | bit 3 | 18 dB | |
| 0110 | | | ||
| 0101 | | | ||
| 0100 | bit 3 | ||
| 0011 | bit 2 | 12 dB | |
| 0010 | | | ||
| 0001 | bit | TDB | |
| 0000 | off | TDB |
The waveforms is sampled at the frequency of the sample rate. Each section is held - its voltage analyzed - and then assigned the binary word that is closest to it.
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We will discuss this more in the chapter on incoming components.
No matter which bit resolution is used, there will always be an error. The problem with having only 0s and 1s to work with is, that there is not a half way measurement. The audio level of a sample can be rounded up or down in relation to whether it is above or below the half-way mark. But if the level falls right on the one half mark, which way does it go? This error is usually contained in the last bit of the digital word and is considered to be the least significant bit (LSB). To measure the rise and fall of an amplitude level would require an infinite number of samples, so rounding off is a necessary evil of quantized.
Quintile errors may appear as white noise (usually found at high signal levels), 'birdying' sounds (caused by quintile error aliening frequencies close to a multiple of the sample rate) , or distortion (usually found at lower signal levels).
If the voltage is exactly at the halfway mark, proper rounding off becomes impossible. The half value is kicked back to the Least Significant Bit instead of allowing it to corrupt the value of a more important bit that contains more information.
The digital recorder assigns a numeric value to each level of each bit. In our example, we had 4 bits, each with twice the capacity of its right neighbor. Each level is a voltage description.
| Ex: voltage of 1.2v = 00100110 |
| &n bsp; 1.3 v= 00100111 |
| &n bsp; 1.4v = 00101000 |
| etc. |
The greater the number of bits we have, the greater number of levels we have for finer measurements. 16 bits has up to 65,536 levels (steps) with which to measure. Which means that the rounding off process is much finer than our 8 bit example. The recorder can assign more detailed numerical values to the sample level.
1. Watch the VU meters while you record. If you go past zero into the red the recorder runs out of 0s and 1s and you get digital garbage.
2. Play a kick drum into an 8 bit reverb
and listen to the reverb tail as it fades. You will hear the reverb turn
to sizzle as the last bit is reached. Even with 24 bit reveres, when all
of the signal that is left resides in the Least Significant Bit, you get
sizzle. Of course with a 24 bit reverb there is a long time before the
LSB is reached and you'll have to turn the volume up loud to hear
it.
So the moral of point 1&2 is...keep the level as close to 0
as possible to fill up the bits, but do not cross the line into the
red
!
Now, like looking at an atom, lets pull back and look at the bigger picture. If we are sampling at 44.1 kHz, the whole process of attaining a numerical value takes place once 44,100 times a second ! And just as we cannot see individual atoms with our eyes, but can see the accumulation of the atoms, we cannot differentiate 1 sample in a 44.1 kHz recording but can hear a second or more (44,100 samples). Amazing !
We know about quantizing error. How can it be fixed? through a process called dithering. Dithering is the process of actually adding noise to the signal to correct quantize error.
Error is caused when a measurement falls on the half way point. Since binary is comprised of only 1s and 2s , on or off, yes and no, etc., there is no halfway measurement. The error (cannot round up or down) is sent to the least significant bit where it is still a problem since it cannot be rounded. A little noise is added to nudge it above the half-way point so that it can then be rounded up.
The dither noise is added just before sampling and is quantized with the audio signal. Random noise numbers are calculated so that a different digital number (noise) is added to every sample. In a stereo sampler the random numbers are different for the right and left sides so that phase problems wont occur. This is known as non subtractive dither because the dither noise becomes a permanent part of the signal. The dither noise is below the amplitude of the LSB. When a signal begins to flow in, the dither noise is pushed above the LSB floor. The noise can be heard if only the LSB has signal. But fortunately , as more bits kick in with increased amplitude the dither becomes lost in the mix.
By pushing up the information in the LSB, dither also accomplishes more clarity. The information pushed up is important to the audio signal. It may be the decay of a reverb or room ambiance. It is part of the sample and if it is pushed to a higher bit, its definition contributes more to the overall sample.
Also , by adding noise, the information of the LSB has a better chance of being heard down to about -115 dB, compared to -96 dB undithered. The dynamic range is therefore expanded (music can be heard below the noise floor).
The down side of dithering is that noise (white noise) is being added to the signal which could add a slight veil to the sound. But until technology supplies us with higher an higher bits, it is a good trade off.
It is possible to hear dithering by
turning
a system up at extreme volumes with dithering turned on. We will listen
to dither created by WAVES software. We will look closely at dithering
next chapter.