Audio Signal Processing - Optimal Noise Shaping Quantiser Virtual Laboratory

Summary

In many applications continuous valued signals have to be converted into digitised ones whose amplitude belongs to a finite set. This procedure is called quantisation and forms an essential part of analog to digital converters.

A quintessential example occurs in the mastering process of compact-discs. Quantisation unavoidably introduces loss of information. In the case of audio signals, the challenge is to preserve the perceived sound quality as much as possible.

In view of the importance of the perceived sound quality, significant research effort has been concentrated into the development of psychoacoustically optimal quantisers. The most popular scheme in this context is the optimal noise shaping quantiser which will be the subject of this virtual laboratory.

Figure 15.1: Screenshot of Program
Figure 15.1: Screenshot of Program

The Physical Apparatus

In many applications continuous valued signals have to be converted into digitised ones whose amplitude belongs to a finite set. This procedure is called quantisation and forms an essential part of analog to digital converters.

The related issue of requantisation corresponds to lowering the resolution of a finely quantised signal in order to provide a coarser quantised signal and can often be dealt with as if it were a quantisation problem.

This problem arises in many situations. A quintessential example occurs in the mastering process of compact discs (see Figure 15.2). In this application, each sample is typically quantised to 16 bits, based upon master recordings of higher resolution (e.g. 24 bit) or of an analog nature.

Quantisation unavoidably introduces loss of information. In the case of audio signals, the challenge is to preserve the perceived sound quality as much as possible. The final aim corresponds to making the difference between the original and the quantised signal, as far as possible, inaudible to the listener.

In view of the importance of the perceived sound quality, significant research effort has been concentrated into the development of psychoacoustically optimal quantisers. The most popular scheme in this context is the optimal noise shaping quantiser which will be the subject of this virtual laboratory.

The music used in this and the next laboratory is an original piece composed by Andrew Goodwin and played by him on guitar and electronic synthesiser.

Prerequisites

This virtual laboratory straddles two areas, namely, audio signal processing and simple feedback control. Readers need have no prior knowledge of audio signal processing since the necessary ideas are developed as the laboratory evolves. The laboratory uses only relatively simple ideas in feedback control. Thus, this laboratory would be entirely suitable for a first course in control.

Figure 15.2: Compact Disc Audio Mastering Equipment
Figure 15.2: Compact Disc Audio Mastering Equipment

Indeed, it is the authors experience that this laboratory is extremely interesting to students. It shows that control ideas play a central role in modern high technology equipment, e.g., CD Mastering. The laboratory dramatically illustrates the “Power of Feedback” in a simple and easily understood example. Also, since the users of this laboratory will actually “hear” the difference that feedback makes then one can say, “if a picture is worth a thousand words, then hearing is also beyond the written word”.

Learning Objectives

This laboratory studies 2 related areas:

  • The psychoacoustic properties of human hearing
  • The effect of quantisation error feedback on the performance of a quantiser

A key aspect of this laboratory is to demonstrate that feedback control ideas play an important role in many high technology problems including audio signal processing as demonstrated in this laboratory.