Digital Audio - By Paul Doornbusch

Digital audio, at its most fundamental level, is representing audio waveforms as a series of numbers. Typically, the numbers represent the amplitude of the waveform at regular times. For CDs, the numbers are 16 bits large and they occur 44,100 times a second. 16 bit numbers can represent 65,535 discrete values, and this equates to an amplitude range or dynamic range (the difference between the quietest and loudest sounds) of about 96dB. Numbers with fewer or more bits can represent fewer or more numbers respectively and this translates into a lower or greater dynamic range. The frequency at which the waveform amplitude is measured is called the sampling rate, and the highest audio frequency that can ideally be encoded and decoded digitally is half of the sampling rate. In practice, it is a little less than that. Audio signals are “analog” and they are converted to and from their digital representation by hardware chips called Digital-to-Analog Converters (DAC) and Analog-to-Digital Converters (ADC).

There are several benefits of digital audio over analog audio. For audio distribution, there are benefits in the simplicity of making very accurate copies of an original. For electronic instruments and music, the benefits lie in the capacity and flexibility for manipulation and synthesis that it offers. For example, digital recording avoids the analog distortions of tape hiss and so on (analog recording may also have advantages over digital too). This also allows non destructive editing of the sound in a digital audio work-station (DAW), a massive improvement over analog editing. Digital audio also opens a world of Digital Signal Processing (DSP), either by standard computers or by dedicated hardware.

DSP technology is nowadays commonplace in such devices as mobile phones, multimedia computers, video recorders, CD players, hard disc drive controllers and modems, and will soon replace analog circuitry in TV sets and telephones. One important application of DSP is in signal compression and decompression. For example, signal compression is used in digital cellular phones to allow a greater number of calls to be handled simultaneously and DSP compression is the technology behind MP3 encoding. DSP technology is also behind all current synthesisers and signal processors.

While the mathematical theory underlying DSP techniques such as Fast Fourier Transforms, Hilbert Transforms, filter design and signal compression algorithms can be quite complex, the numerical operations required to implement these techniques are in fact very simple, being mainly simply adding, subtracting and multiplying. However, for real time applications, millions of these operations must be carried out on perhaps millions of samples each second and this is a non-trivial task. The examples of DSP applications mentioned earlier, such as hard disc drives and mobile phones, demand real-time operation, as does real time digital processing or synthesis for a digital musical instrument.

Digital filters basically come in two types; Infinite Impulse Response (IIR) and Finite Impulse Response (FIR). The main difference is that an FIR filter does not use any feedback and an IIR filter feeds some percentage of its output back to its input. Most musical applications use IIR filters, sometimes to achieve the familiar resonant filter effect.

A Discrete Fourier Transform (DFT) is a way to work out what frequencies, or sine waves, exist in a signal and what amplitude and phase those signals are, this is called the spectrum of the sound. There have been ways developed to do this very quickly and this is called a Fast Fourier Transform (FFT). Once the signal components are known, they can be manipulated in a number of musically useful ways and then reconstructed into a complete signal by a process known as an Inverse Fast Fourier Transform (IFFT). This is called frequency domain processing, as opposed to time domain processing in IIR and FIR filters. For example, if the frequency of all of the signal components was doubled and then recombined through an IFFT, the sound would be an octave higher.

DSP techniques are at the core of sound synthesis and modification processes. Most musicians building digital instruments use some original configuration of DSP synthesis and processing to create a unique sound.