ADC Acronym for analog to digital conversion, a device that converts a continuous quantity to a discrete time digital representation
DAC Acronym for digital to analog conversion, device that converts a digital (usually binary) code to an analog signal (current, voltage, or electrical charge)
Quantization error - A truncation error that occurs during the analog to digital conversion stage. It is the difference between the actual analog value and quantized digital value
In my opinion, the most misunderstood part of the entire digital recording process is converters. People often disregard them completely when making a new interface purchase, but they are entirely the most critical part in faithfully recreating what's captured in the digital world. To make matters simple, its like the difference between a film and real life. A film take slices of time, as where real life is continuous. Digital audio is a slice of time and analog is just like life, continuous.
When an analog signal enters the converter, it encodes it to a digital signal. It's always an approximation and a degree of the original. DAC converters, on the other hand, decode the digital signal and convert it back to an analog signal.
Converters are like many kinds of equipment in that they have their own sound, character, and personality. When you run a signal through converters it will impart something to your signal, for better or worse.
Let's start by talking about why conversion is necessary in the first place. Computers operate using binary, which is a system of numerical notation that has 2 rather than 10 as a base. Conversion is the process of the computer taking the analog information it is receiving and digitizing it. It is then translated into binary numerical information that can be manipulated by the computer. An analog signal, in order to be processed in the binary world, must be converted into 0s and 1s in order to be understood by the computer. This is conversion. There will always be a gap in what analog sources you capture to digital. No matter how small the gap, something is lost. Digital is ON/OFF (discontinuous) where analog is always "ON" (continuous).
When sound gets converted from an analog waveform to digital 0's and 1's, then back from digital to the analog sound that we hear, some of the information that is in the original analog signal is lost in the process of truncating everything to 0's and 1's. This truncation is certainly perceivable to some people and I am not sure digital will ever be able to do exactly what analog does because of this fundamental difference that cannot be overcome.
It is hard for digital to render a 100% replication of analog for the mere fact that in digital we are taking an interpretation of an analog waveform versus analog were taking all of the audio wave form. Digital is leaving certain pieces of audio information out and filtering and adding stuff to fill in the gaps so it sounds natural to us.
analog tape has less frequency response and far less dynamic range than even a minimal consumer recording session running at 16-bit/44.1kHz PCM.
When you make a digital recording, an analog waveform (represented by an electrical signal with a continuously varying voltage) is sampled at regular intervals and converted to a set of numbers. Each number, or sample , corresponds to the voltage of the electrical signal at a specific point in time. These numbers are stored in binary form with a specific word size (typically 16-24 bits). The minimum and maximum numbers that can be stored depends on the word size, and corresponds to the voltage range of the electrical signal. For example, the maximum digital sample in a 16-bit recording is 32,767 and this is also referred to as 0dBFS (0dB "full scale").
When a recording that has been converted from analog to digital is played back, a digital to analog converter alters these binary values back to a set of voltages, and a reconstruction filter is applied to convert these voltages back into a continuous signal.
It is possible for the reconstructed analog waveform to have voltages that are higher than the highest digital sample recorded. So, if the highest digital sample captured happens to correspond exactly to 0dBFS, the recording when played back may result in an analog waveform exceeding 0dBFS. In short, the DAC in this example has generated an invalid signal. The subsequent analog stage of the playback chain may not be capable of handling a signal greater than 0dBFS (also known as "0DBFS+"), resulting in clipping distortion.
Under specific conditions the DAC can produce an analog signal that momentarily exceeds the level of the digital signal from which it was converted. This is known as an inter-sample peak, and while it may at first seem just a curious side effect of the conversion process, these peaks have implications for anyone working with digital audio.
How these peaks affect your workflow really depends on a few factors, including the quality of the DAC, and the fidelity of the signal chain after the converter. In the worst case, you could have a recording that has audible clipping when the system tries to generate the illegal voltage. But even if no clipping occurs, the analog side of the DAC will only handle the signal cleanly if the DAC's analog circuitry has sufficient headroom. If the DAC's designers assumed that 0dBFS is the loudest signal the converter will emit (technically, a valid assumption,) then an analog peak above this level will cause distortion. Not a warm, Marshall stack kind of distortion. Abrasive, painful, digital distortion.
If you hear any pops or clicks, it's a good sign that your setup doesn't allow for inter-sample clipping. Most likely, though, the track sounds just fine to you. Many systems, especially those equipped for mixing audio, allow some head room between the maximum digital signal level and the onset of analog distortion.
If you mix hot, especially if your meters peak within 1dB of full scale, your mixes probably contain these peaks. And though your DAC protects you, there's no guarantee that your listeners have quality converters. In other words, you may be sharing clipped or distorted audio without realizing it, because it isn't apparent upon playback.
Inter-sample peaks are not something to be overly concerned with, though, and there are some simple steps you can take to ensure they are not inhibiting your production workflow. Always being mindful of headroom, dealing with the peaks in the mastering stage via a plugin, or using a meter designed to point out these flaws are all excellent ways to avoid these nasty overs. Either way, as long as you keep your levels sane, these will never be an issue for even a decently modest D/A converter.
This type of conversion is definitely worth mentioning. Dedicated outboard converters are usually reserved for the large studios, as they are very expensive. They are usually also found in only one format, whether it be ADC or DAC.
It seems most of the deficiencies of converter chips are due to requiring a wide range of sample rates and not knowing how another manufacturer might configure the conversion chips in their products. Cheap brickwall filters, multiple oversampling switches, on top of taking extremely wide ranges of clocks all seem to be points of compromise in the manufacture of conversion chips.