In this paper, we extend the definition of dyadic wavelets to include frequency warped wavelets. The new wavelets are generated and the transform computed in discrete-time by alternating the Laguerre transform with perfect reconstruction filterbanks. This scheme provides the unique implementation of orthogonal or biorthogonal warped wavelets by means of rational transfer functions. We show that the discrete-time warped wavelets lead to well-defined continuous-time wavelet bases, satisfying a warped form of the two-scale equation. The shape of the wavelets is not invariant by translation. Rather, the "wavelet translates" are obtained from one another by allpass filtering. We show that the phase of the delay element is asymptotically a fractal. A feature of the warped wavelet transform is that the cut-off frequencies of the wavelets may be arbitrarily assigned while preserving a dyadic structure. The new transform provides an arbitrary tiling of the time--frequency plane, which can be designed by selecting as little as a single parameter. This feature is particularly desirable in cochlear and perceptual models of speech and music, where accurate bandwidth selection is an issue. As our examples show, by defining pitch-synchronous wavelets based on warped wavelets, the analysis of transients and denoising of inharmonic pseudo-periodic signals is greatly enhanced.

Logarithmic frequency representation plays an important role in many audio and acoustic signal processing applications. This article presents a methodology for frequency-warped signal processing where the frequency representation is logarithmic above a certain limit frequency. It is demonstrated how this approach can be used with FFT or linear prediction to perform non-parametric, or parametric constant-Q spectrum analysis, respectively. The benefits of the use of logarithmic frequency representation are demonstrated with harmonic signals. It is also discussed how linear filters can be designed and implemented directly on a logarithmic frequency scale. 1.

In this paper, we introduce a new generation of perfect-reconstruction filter banks that can be obtained from classical critically sampled filter banks by means of frequency transformations.

The goal of the schemes we present in this paper is to obtain an ultra low delay audio coder with a good performance even at low bit rates (around 64 kb/s). The problem to be solved is to gain sufficient frequency resolution at low frequencies for precise low frequency psycho-acoustics and quantization noise shaping, because the ear has a higher frequency resolution at lower frequencies. Our approach is to use a warped linear noise shaping pre- and postfilter, and a short DFT for the psycho-acoustic model (length 256), but with frequency warping. We compare four different psychoacoustic versions: DFT with no warping, DFT without warping using warped pre- and post-filters, warping with the so-called NDFT (WDFT), and a DFT with an all-pass delay chain pre-processing. Listening tests show that the best performance is obtained using the WDFT. 1.

In this paper, the problem of sampling continuous-time spectrally correlated (SC) processes is addressed. SC processes have Loève bifrequency spectrum with spectral masses concentrated on a countable set of support curves. This class of nonstationary processes extends that of the almostcyclostationary processes and occurs in wide-band mobile communications. The class of the discrete-time SC processes is introduced and characterized. It is shown that such processes can be obtained by uniformly sampling the continuous-time SC processes. Sampling theorems are presented and a sufficient condition to avoid aliasing in the whole bifrequency domain is provided. 1.

The linear frequency (constant-bandwidth) scale of the FFT has long been recognised as a disadvantage for audio processing. Long analysis windows are required for adequate low-frequency resolution, while small windows offer lower latency, better handling of transients, and reduced computation cost. A constant-Q form of analysis offers the possibility of increased low-frequency resolution for a given window size, this resolution being essential for many fundamental processing tasks such as pitch shifting. We consider the application of the Sliding Discrete Fourier Transform to a Constant-Q analysis. The increased flexibility of sliding allows for a variety of data alignments, and we produce the mathematical formulation of these. Windowing in the frequency domain introduces further complications. Finally we consider the implementation of the analysis on both serial and parallel computers. 1.