About digital effects
Most compressors and gates are based on analog circuits. Most of the effects that apply time change in any form are based on digital electronics: delay, reverbs, pitch shifters, multi-effects processors, etc. Before considering the operation of any particular processor, you need to have an idea of how the digital system works (this will help to understand a lot of what is written in the technical documentation of such devices).
The digital processor receives an analog signal (for example, music). First, this signal must be converted to digital.
An analog signal is a change in voltage in proportion to changes in the state of the signal source and changes in the environment. In the case of sound, an analog signal is a change in voltage proportional to a change in sound pressure. For example, string vibrations cause rapid, frequent changes in sound pressure, and an alternating voltage appears at the microphone output.
The digital system works with binary numbers – ones and zeros; in a circuit, this is the presence or absence of a rated DC voltage. Converting an analog signal to digital is measuring the voltage of an analog signal at regular intervals and obtaining a binary code.
Each second of sounding of a signal can be expressed in the form of several tens of thousands of numbers, each of which corresponds to a specific moment in time. As a film strip: each next frame is slightly different from the previous one. When the tape passes quickly through the projector, you get the impression of movement. The same with sound: if there is a sufficient number of instantaneous measurements per second, then you can restore the original sound.
The process of measuring and digitalizing the individual parts of the input signal is called sampling. A lot of signal slices are made; the height of these sections is measured. Slices (samples) have a flat top, that is, they do not exactly correspond to the waveform. It follows that the thinner the slices, the more accurately (or less distorted) they describe the signal.
The theory of sampling is too complex to be considered here. But the basic concepts are as follows: for the proper reconstruction of the signal at the output, the sampling frequency should be at least twice the frequency of the highest harmonic of the signal. However, in practice, the sampling frequency exceeds the highest harmonic by two and a half to three times. Thus, in order to sample a signal containing harmonics up to 10 kHz, the sampling frequency should be 30 kHz.
To create a time delay of 1 second, you will need a memory in which these 30,000 samples are written. They are written to RAM (random access memory). A 30 kilobyte memory contains 1 second of instrument sound with a 10 kHz top harmonic frequency. By constantly updating the contents of the memory and outputting it outside (reading), you can create a delay of 1 second.
If you need to do this for a signal with an upper limit of 20 kHz, then you need a memory capacity of 60 kilobytes.
You need not only to choose the right sampling rate. Resolution is also important. The digital numbers corresponding to the samples are grouped in steps. The number of possible steps depends on how many bits an ADC (analog-to-digital converter) can pass. 8 bits – 2 to the 8th degree of groups (steps) = 256. This means that a loud signal can consist of 256 steps, and a quiet one – from a smaller number. This is considered a poor resolution. These are distortions of quantization.
Quantization distortion sounds like noise, but, unlike analog noise, it disappears with the signal. Using 12- and 16-bit devices improves resolution. Most modern digital devices use a 16-bit system (such as a CD). Each bit is 6 dB of dynamic range; therefore, an 8-bit system can only reproduce 48 dB (just like a tape recorder without Dolby). The 16-bit system allows you to skip the dynamic range of 96 dB, which is an excellent indicator for audio targets. A 12-bit system is 72 dB, which allows it to be used for many effects.
So, the higher the sampling frequency, the greater the frequency range the system covers (the better the frequency response). But the higher the frequency, the more samples can be obtained, and the more memory is required to store data. Therefore, such a device is either expensive, or its delay time is not too long (for digital delays and samplers).
Early DDLs (Digital Delay Line, Digital Delay Lines, Digital Delay Devices) were not distinguished by either a high sampling frequency or a long delay time. Modern low-cost devices have a bandwidth of 15 kHz and at least 1 s delay. If the device allows you to create a long delay, then you can always make a shorter one.