ANALOG - DIGITAL

There is a fairly large group of people that say digital audio has a digital sound and an equally large group that say nonsense, digital sound is pure. Now considering that it's not just a few who think digital sound sounds digital, there must be something going on. Here are a few thoughts comparing digital and analog recordings.

Analog and digital recordings will both by nature add unnatural color (distortion) to the audio signal. In both cases, the higher the quality of the recorded file the less distortion is added. Some types of distortion are less objectional than others. For instance, if 2nd harmonic distortion is dominant there may actually be an added warmth to the sound. If the dominant distortion is 3rd harmonic or higher odd harmonics, then the sound will have an unnatural edge to it. The type of distortion resulting from digital audio using compression or low sampling rates is of the unnatural nature and can vary from slight to severe depending on how much data is dropped.
Analog recordings are recorded complete in real time. Digital is recorded as sampled coded numerical bits. The resolution, or accuracy of analog is dependent on amplifying devices and form of storage. The resolution, or accuracy of digital is dependent on how many numerical samples of the original are taken and form of storage.
Since analog does not work on a sampling system, there is no sampling error distortion with analog. Digital uses a sampling system and sampling error distortion is a factor.

Pictured above is a sine wave, or single tone. In the analog process, the entire waveform is recorded and played back in its original form.
With digital, a single sine wave is sampled and stored as numerical bits. Sample points along the waveform can be few or many; this depends on the sampling rate. The higher the sampling rate the higher the resolution or accuracy of the numerical sample. Then using mathematical algorithms, the numerical samples are used to reproduce the original waveform. As you can see, a single sine wave would not require a large amount of sampling to get an accurate reproduction. The algorithm would easily fill in the missing information between samples.
Most people who've look at digital audio before know about the Nyquist theorem, sample an analog signal at a rate of at least twice its highest frequency component, you can convert it back to analog, passing through a low-pass filter, and get back the same thing you put in. This theorem then led to establish the standard 44.1KHZ sampling rate, aprox twice that of 20KHZ audio.
In the real world, the highest audio frequency is much higher than you think if you include all the harmonic and image frequencies that result from adding and subtracting the mix of frequencies in complex music waveforms. And even fundamental frequencies of complex waveforms suffer from lost data distortion at 44.1KHZ.

A complex waveform requires much more sampling. An algorithm cannot accurately reproduce missing information between sampling points. The algorithm makes a mathematical approximation (guess) to fill in the gaps between sampling points. Although algorithm filters do more than just "connect-the-dots", some information is lost. The results of these approximations are distortion sometimes referred to as artifacts, an unnatural sound added to the recording. The amount of distortion depends on sampling rates and how complex the audio is, the resulting distortion can be high at times with lower sampling rates.
Besides sampling errors, another factor adding distortion in digital audio is various methods used to save storage space by condensing the numerical information sometimes referred to as digital compression.
In the analog process, the entire complex waveform is recorded and played back in its original form without any missing information.
Compressed file formats like MP3 or WMA. most software supports various compressed formats. Compressed audio is great for distribution over the Internet or to load on your favorite music player, but it's not up to the standard of high fidelity audio. Compressed audio formats all use something called perceptual coding. In order to achieve their dramatic size reduction, perceptual coders analyze the audio and decide which portions of the audio can be thrown out, based on the idea that the human ear is not capable of hearing very high and very low frequencies. Compare an original CD track to a compressed version and you'll hear reduced highs, flat lows and general mush in the middle. Another secret of compressed audio is the division of bit rate. A stereo track needs about twice the bit rate of a mono track. So, your 128kbps MP3s are actually two 64kbps channels. While this may sound fine on the subway or in your car, played on a high quality system will quickly reveal the compression artifacts in the sound.
A term sometimes used for wav files is Linear because there is no data compression used on a pure wav file. There is no such thing as a linear digital file, digital is non-linear by nature. The only linear audio source is analog.

The level of distortion in a digital recording is going to depend on how dense the audio is. The more dense the audio the more information will be lost in the sampling process. Distortion in digital audio cannot be measured by single tone harmonic distortion methods. This is because digital algorithms easily filter out data missing in the sampling process of a simple sine wave. It's when several frequencies are mixed together, as in the case of music and other complex audio waveforms, that distortion is generated. Single tone harmonic distortion specs mean little in digital audio reproduction fidelity. Dense Audio Distortion can only be measured using multiple simultaneous test frequencies over the entire audio spectrum. And in the case of stereo or multiple channel audio, the frequencies need to be staggered so different channels do not use the same frequencies.

Analog audio has its own set of problems. Careful attention must be made in amplifying stages to keep noise and distortion low. Analog recordings are subject to developing noise with use. Making copies of analog recordings requires skill and knowledge of dubbing process to keep quality high. However, the resolution of analog audio is very high and distortion very low if the equipment is properly operating.

Low distortion, low noise digital recordings are possible if very high sampling rates are used and no digital compression is used. However, in the real world it is difficult to find digital audio sources that are of such high quality because of the large bandwidth or file size required. In general, some compromise is used to squeeze the digital audio into a smaller size resulting in some form of distortion level. The Internet is a good example of audio sources with high distortion. In an effort to keep file sizes down, lower sampling rates and heavy digital compression is usually the rule for anything downloaded. Distortion artifacts include highs that sound like shattering glass and audio that has a duller sound due to loss of natural harmonic content.

Digital audio is very easy to overload or distort. Back in the days of analog tape, you could go a little "past zero" on the meters and the audio would remain unaffected. In the digital world, once all bits are set to "1," there is nowhere else to go. Any volume beyond that point is drastically distorted. Digital distortion isn't the soft distortion you get with analog equipment; it's a harsh, nasty sound.