Tools for Signal Compression: Applications to Speech and Audio Coding

Chapter 3

Sub-band Transform Coding

3.1. Introduction

Until very recently, a classic distinction was made between transform coding and sub-band coding. In a transform coder, an N-dimensional vector is first determined from the signal. Next, a generally orthogonal or unitary matrix is applied (for example, a matrix constructed from the discrete Fourier transform or the discrete cosine transform), then the coefficients are encoded in the transformed domain. At the receiver, the reverse transform is applied. In a sub-band encoder, the signal is first filtered by a bank of analysis filters, then each sub-band signal is downsampled and the downsamples are encoded separately. At the receiver, each component is decoded, an upsampling and interpolation by a bank of synthesis filters is carried out, then the separate reconstituted signals are added together. These two encoding techniques are equivalent, as will be shown in section 3.2. For further details, refer to the theory of perfect reconstruction filter banks [MAL 92, VAI 90], multi-resolution systems, and wavelet transforms [RIO 93].

An important issue in a coding system is the allocation of available bits to different sub-sets. Two extremes can be imagined: distributing bits over several heterogeneous parts, for example, over the filter coefficients and the excitation signal in speech coding, or distributing bits between different elements which present a priori the same distribution, for example, successive samples in a signal. ...