Spectral Band Replication (SBR) compression technology: Survey of the unified efficient low-cost implementations of complex exponential- and cosine-modulated QMF banks

Spectral Band Replication (SBR) is an enhancement compression technology, a bandwidth extension method which significantly improves the compression efficiency of perceptual audio and speech coding schemes. There are two versions of the SBR technology: Standard SBR and low delay SBR (LD-SBR). Central to the operation of standard and LD-SBR are dedicated complex exponential-modulated and real-valued cosine-modulated quadrature mirror filter (QMF) banks as the basic mathematical tools to analyze and synthesize audio signals. This tutorial paper presents the complete unified efficient implementations of complex exponential-modulated and real-valued cosine-modulated QMF banks used both in the standard SBR and LD-SBR encoder and decoder. In general, for each QMF bank is presented: Definition of its equivalent block transform with a common parameter M representing the number of sub-bands, its general symmetry property in the frequency or time domain, and the derivation of a fast algorithm for its efficient implementation. All fast algorithms are analyzed in detail in terms of the arithmetic complexity, regularity and structural simplicity for a potential real-time low-cost implementation in hardware or software.