Event

Transforming the transform: introducing complex filter-banks in audio compression

Marios Athineos

Tuesday, August 05, 2008
12:30

Time-frequency analysis, in the form of a transform or a filter bank, is ubiquitous and often constitutes the very first building block in many signal processing applications. In automatic speech recognition (ASR) for example, one computes the short-time Fourier transform (STFT) in order to extract PLP or MFCC features. Being a complex representation and calculated on 25ms analysis frames every 10ms, the magnitude squared of the STFT provides an accurate estimate of the "local" power spectrum. This experimentally-validated choice of parameters (25/10ms) works well in ASR but it generates a highly redundant representation (2.5 times) which is unsuitable for audio compression. On the other hand, virtually every audio compression scheme today is based on a non-redundant (aka critically sampled) time-frequency representation, the modified discrete cosine transform (MDCT). As opposed to the complex STFT though, the MDCT is real thus losing the ability to decouple the "what" (magnitude) from the "when" (phase) of sinusoids and generating poor estimates of the power spectrum. It appears that when it comes to non-redundant magnitude-phase representations we cannot have our pie and eat it too and this indeed is a fundamental theorem of time-frequency analysis theory. In this talk I will show how to use linear algebra to demonstrate the concept of redundancy and how to work our way around it. Using this framework, I will construct a non-redundant complex transform thus circumventing the above mentioned theorem. After interpreting the frequency response of the proposed transform, I will evaluate its performance in audio compression by showing improvement in coding gain over the MDCT. If time permits, I will discuss applications in orthogonal frequency division multiplexing (OFDM) communication scheme and show peak-to-average-ratio (PAPR) reduction over the STFT.