Behringer DSP1200P User Manual download pdf (Page 28)

Quantization Steps

U (Voltage)

-8 -7 -6 -5 -4 -3 -2

Digital Words

1111

1110

1101

1100

1011

1010

1001

1000

0000

t (Time)

0001

0010

0011

0100

0101

0110

0111

Conversation Rate

1 2 3 4 5 6 7 8

-1

-2

-3

-4

-5

-6

-7

-8

Quantization Errors

(Noise)

Continuous

Analog Signal

Fig. 4.1: Transfer diagram for an ideal linear ADC (2s complement representation)

In a digital signal processor, such as the DSPs in the MODULIZERPRO, the data will be modified in a number

of ways, in other words, various calculations, or processes, will be done in order to achieve the desired effect

on the signal. This gives rise to further errors, as these calculations are approximations, due to their being

rounded off to a defined number of decimal places. This causes further noise. To minimize these rounding off

errors, the calculations must be carried out with a higher resolution than that of the digital audio data being

processed (as a comparison, an electronic calculator may operate internally with a greater number of decimal

places than can be shown on its display). The DSPs in the MODULIZERPRO operate with a 24 bit resolution.

This is accurate enough to reduce quantizing noise to levels which are usually below the audible threshold.

However, when using extreme equalizer settings, some quantizing side effects may be detected.

Digital sampling has one further, very disturbing effect: it is very sensitive to signal overload. Take the following

simple example using a sine wave. If an analog signal starts to overload, it results in the amplitude of the signal

reaching a maximum level, and the peaks of the wave starting to get compressed, or flattened. The greater the

proportion of the wave being flattened, the more harmonics, audible as distortion, will be heard. This is a

gradual process, the level of distortion as a percentage of the total signal rising with the increase of the input

signal level.

Digital distortion is quite different, as illustrated by this simplified example. If we take the situation where a 4 bit

word has the positive maximum value of 0111, and add to it the smallest possible value of 0001 (in other words,

the smallest increase in amplitude possible), the addition of the two results in 1000 - the value of the negative

maximum. The value is turned on its head, going instantly from positive max to negative max, resulting in the

very noticeable onset of extreme signal distortion.

4.2 Reverberation and reflection

In a concert hall the sound the listener hears comprises both the source signals (e.g. acoustical instruments,

P.A. system) and thousands of reflections of these "primary signals", which bounce off floor, ceiling and walls

to reach the ear after a short delay. These reflections represent thousands of echoes of the direct signal, which

are not perceived any longer as single echoes but - due to their sheer number - as reverberation. Basically, the

reflected signal portions reach the ear later than the source signal, and the very fact that they do not arrive from

the same direction as the direct signal (see fig. 4.2), makes it possible to hear spatial information, i.e. to

perceive the direct signal as it is embedded in the room acoustics.

4. TECHNICAL BACKGROUND

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Behringer DSP1200P User Manual Page 28

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