# Digital Audio Basics

The future of audio is digital and the quality produced by digital audio is of great importance to broadcasters, producers, live venues and the listening audience. Digital audio can be prone to mysteriously disappearing or producing annoying pops or clicks. With the increasing amount and complexity of digital audio equipment, video multiplexing/de-multiplexing, complex routing paths and cable defects/influences, problems can develop with the digital audio signal. Having a test and measurement tool to diagnose these problems becomes essential in producing high quality digital audio.

## Digital sampling to binary bits

The analog audio signal is converted to digital using a sampling process involving a digital-to-analog converter (D/A). To convert an analog audio signal from continuous changes vs. time to discrete digital values vs. time, the level of the signal is measured at certain intervals in time. This process is known as digital sampling. Sampling is like taking snapshots of the signal level as it increases and decreases over time. The sampled voltage levels are converted to digital binary values. The captured sequential digital binary value samples represent the audio levels as the audio varies in time.

Fig. 1. Sampling an analog waveform at a specific rate.
Click image to enlarge

Sampling happens at equally separated intervals. The number of intervals in which the values of the signal level are captured (snapshots) in one second is the sampling rate (see Fig. 1). The sampling rate frequency is the reciprocal of a sampling interval (time). The measurement unit of the sampling rate is the hertz (Hz) or number of samples per second.

The conversion process samples voltage levels of the changing audio at a much faster rate than the audio changes frequency. The Nyquist Theorem states the sampling rate must be equal or greater than two times the highest audio frequency component. Therefore, to recreate audio at 20kHz, the minimum sampling rate must be higher than 40kHz.

## Quantization

Fixing a digital value to the audio level at each sample interval is called quantization. The amplitude range of the audio waveform is divided into level steps. For example, there are 16 discrete binary values to specify the amplitude or level using a 4-bit binary system. The 16 values are divided in half (almost), with seven binary values to indicate positive voltage levels and eight values to indicate negative voltage levels.

Fig. 2. Assigning amplitude values to a sampled waveform.
Click image to enlarge

The 4-bit quantization provides an example of how audio levels can be converted to digital 4-bit words representing the audio signal. However, the binary range is not symmetrical for positive and negative values and it has insufficient values for adequate low audio level reproduction. It should be noted that with digital quantization, the audio level must not exceed the quantization range or largest digital code word (1111), or digital clipping occurs. Fig. 2 shows the quantization levels on a sampled waveform.

A quantized binary value may be encoded in a form adapted to the sampled signal and system requirements to provide overall system improvements. The most-used and adopted coding system is the Pulse Code Modulation (PCM) encoding. PCM linearly quantifies all quantizing intervals by means of a fixed scale over the signal amplitude range. PCM makes use of a two's complement system to distinguish positive and negative binary coded values (see Fig. 3). The analog-to-digital (A/D) conversion resolution accuracy is determined by the number of quantizing levels possible. The bit word length determines the number of quantizing level steps or amplitudes (resolution) that can be achieved. For example, an 18-bit digital code word provides 262,144 increments for coding analog signal amplitudes.

Fig. 3. The two’s complement numbering system is used to differentiate positive and negative binary encoded values.
Click image to enlarge

The number of bits used to form the PCM digital words (bytes) used to represent each of the sampled audio levels can vary, but typically range from 8 to 24 bits. The more bits used to represent the amplitude, the greater the dynamic range that can be represented. Each bit provides approximately 6dB of range. An 8-bit digital audio signal has a 48dB dynamic range (quiet to loud audio range) while 16-bit digital audio provides 96dB of dynamic range. A 24-bit digital audio word length provides 144dB of dynamic range.

PCM digital audio is often sampled at 44.1kHz or 48kHz, although other rates are possible. Sampling rates up to 192kHz can easily be found in some equipment.

In a digital audio system, the maximum audio level corresponds to 0dBFS (dB full scale) which is assigned the largest digital code word. Manufacturers have adopted the familiar 0VU level equal to +8dBm as a standard operating level (SOL). This level corresponds to -20dBFS, in which the digital values are well below the largest digital code word value. This provides 20dB of range for audio peaks to go above +8dBm before digital clipping occurs

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