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A new type of discrete-time orthogonal and biorthogonal filter bank structures based on multirate Laguerre sequence expansions is introduced. This new generation of perfect-reconstruction filter banks is derived from critically sampled filter banks through frequency transformations. The novel filters are constructed by introducing generalized downsampling and upsampling operations based on lossless dispersive delay lines. Varying a single parameter enables the design of wavelets with desired bandwidth at a given scale.

The integration of the filter bank structure and Laguerre transform has yielded the extensions of the wavelet transform scheme which allows the implementation of orthogonal or biorthogonal warped wavelets. The warped wavelet bases are generated from the discrete-time warped wavelets and by extending the theory, pitch-synchronous warped wavelets can be analyzed. The properties of the wavelets are useful in understanding signal processing problems such as signal identification, denoising and feature detection.

The performance of coders based on multiplexed wavelet transforms (MWT) is better compared to conventional coders. A broadband pseudo-periodicity of the input signal, as in the case of LPC excitation signals, is a necessary condition for good performance. The long coding delay of MWT coder is not a critical factor. The performance of pitch adaptation of the MWT transform is efficient.

Novel wavelet bases are use to synthesize and analyze pseudo-periodic digital signals to enable signal representation in terms of a periodic trend and aperiodic fluctuations at many scales. The frequency domain has periodic trends as harmonic-centered bands while the fluctuations are spread over many side bands.

A wavelet representation with pitch-synchronous vector representation adapts to oscillating signal characteristics. Pitch-synchronous wavelet transforms (PSWT) permit arbitrary reduction of oscillator bandwidth by increasing the number of stages of filter bank implementation. The transform converts to the normal wavelet transform over nonfluctuating signal portions. PSWT is ideal for speech signal synthesis and can function as a preprocessing block in automatic speech identification systems.

We illustrate the mathematical background and musical use of a class of audio effects based on frequency warping. These effects alter the frequency content of a signal via spectral mapping. They can be implemented in dispersive tapped delay lines based on a chain of all-pass filters. In a homogeneous line with first-order all-pass sections, the signal formed by the output samples at a given time is related to the input via the Laguerre transform. However, most musical signals require a time-varying frequency modification in order to be properly processed. Vibrato in musical instruments or voice intonation in the case of vocal sounds may be modeled as small and slow pitch variations. Simulation of these effects requires techniques for time-varying pitch and/or brightness modification that are very useful for sound processing. The basis for time-varying frequency warping is a time-varying version of the Laguerre transformation. The corresponding implementation structure is obtained as a dispersive tapped delay line, where each of the frequency dependent delay element has its own phase response. Thus, time-varying warping results in a space-varying, inhomogeneous, propagation structure. We show that time-varying frequency warping is associated to an expansion over biorthogonal sets generalizing the discrete Laguerre basis. Slow time-varying characteristics lead to slowly varying parameter sequences. The corresponding sound transformation does not suffer from discontinuities typical of delay lines based on unit delays.

The Phase Vocoder plays a central role in sound analysis and synthesis, allowing us to represent a sound signal in both time and frequency, similar to a music score - but possibly at much finer time and frequency scales - describing the evolution of sound events. According to the uncertainty principle, time and frequency are not independent variables so that any time-frequency representation is the result of a compromise between time and frequency resolutions, the product of which cannot be smaller than a given constant. Therefore, finer frequency resolution can only be achieved with coarser time resolution and, similarly, finer time resolution results in coarser frequency resolution. While most of the conventional methods for time-frequency representations are based on uniform time and uniform frequency resolutions, perception and physical characteristics of sound signals suggest the need for nonuniform analysis and synthesis. As the results of psycho-acoustic research show, human hearing is naturally organized in nonuniform frequency bands. On the physical side, the sounds of percussive instruments as well as piano in the low register, show partials whose frequencies are not uniformly spaced, as opposed to the uniformly spaced partial frequencies found in harmonic sounds. Moreover, the different characteristics of sound signals at the onset transients with respect to stationary segments suggest the need for nonuniform time resolution. In the effort to exploit the time-frequency resolution compromise at its best, a tight time-frequency suit should be tailored to snuggly fit the sound body. In this paper we overview flexible design methods for phase vocoders with nonuniform resolutions. The methods are based on remapping the time or the frequency axis, or both, by employing suitable functions acting as warping maps, which locally change the characteristics of the time-frequency plane. As a result, the sliding windows may have time dependent duration and/or frequency dependent bandwidth. As an example, in a constant Q frequency band allocation, the ratios of center band frequencies over bandwidth remains constant, so that the frequency bands become wider and wider as center frequency increases, similarly to the frequency distance of 12-tone scale notes or of octaves. While time-frequency allocation can be performed in an arbitrary way, the ability to reconstruct the original signal from Vocoder analysis data is essential in sound processing and transformation applications. Moreover, even the analysis or the production of spectrograms benefits from the perfect reconstruction property if one needs to be confident that no important information is hidden, which serves to completely describe the signal. [ABSTRACT FROM AUTHOR]

Physically inspired sound synthesis techniques have been devised for several instruments including guitar. Less well studied are methods to model the interactions of the player with strings and of the strings with other mechanical parts of the instrument. In this paper, we present methods based on simple scattering junctions to be inserted at various points along a digital waveguide simulating transversal wave propagation along a string. These junctions, which are derived using a balanced perturbation method for displacement wave variables, connect the waveguide with the external stimuli provided by the player or with objects that are part of the instrument. A model for plucking is revisited and improved. New nonlinear structures for the accurate model of collisions are developed. The proposed junctions achieve realistic synthesis of the interaction of the plucking finger or pick with the string, of the interaction of the fingers on the neck-side hand with strings, such as in the production of harmonics, and of the strings themselves with frets or fingerboard in a fretless instrument. [ABSTRACT FROM AUTHOR]

In this paper, we propose a binaural source localization method based on interaural time differences (ITDs) and interaural level differences (ILDs). The two cues, computed from a two-channel time-frequency representation, are combined in order to estimate the azimuth of sources in binaural recording. We introduce an individual parametric model for the ITD and ILD, and an average parametric model that sets us free from measurements of the subjects' HRIRs for sound localization. We conduct several experiments to validate the proposed approach and show that it compares favorably with available techniques. [ABSTRACT FROM AUTHOR]

In a situation where multiple sound sources are concurrently active, the signals of the individual sources often overlap in time and in frequency. This is particularly likely for voiced instruments where the frequencies of some of the partials of one single note coincide with the frequencies of some of the partials of another instrument playing a harmonically related note. A source separation algorithm suitable for musical applications must address the problem of overlapping partials. A method is proposed for the separation of overlapping narrowband partials in multichannel mixtures. The method is based on the observation that, for many instruments, all the partials of a single note have similar temporal envelopes. For narrow band partials these similarities can be exploited in order to estimate demixing matrices in the frequency domain. Effectively, one can recover estimates of the original partials from a multichannel mixture where they overlap. The method is computationally efficient in that it works on highly downsampled narrow frequency bands. It performs well for closely spaced and colliding partials, and (to some extent) also for frequency modulations such as vibrato effects. [ABSTRACT FROM AUTHOR]

Musical signals require sophisticated time-frequency techniques for theirrepresentation. In the ideal case, each element of the representation is ableto capture a distinct feature of the signal and can be attached either a perceptualor an objective meaning. Wavelet transforms constitute a remarkable advancein this field and have several advantages over Gabor expansions or short-timeFourier methods. However, application of conventional wavelet bases on musicalsignals produces disappointing results for at least two reasons: (1) the frequencyresolution of dyadic wavelets is one-octave, too poor for any meaningful acousticdecomposition and (2) pseudoperiodicity or pitch information of voiced soundsis not exploited. Fortunately, the definition of wavelet transform can beextended in several directions, allowing for the design of bases with arbitraryfrequency resolution and for adaptation to time-varying pitch characteristicin signals with harmonic or even inharmonic structure of the frequency spectrum.In this paper we discuss refined wavelet methods that are applicable to musicalsignal analysis and synthesis. Flexible wavelet transforms are obtained bymeans of frequency warping techniques. [ABSTRACT FROM AUTHOR]

Voiced musical sounds have nonzero energy in sidebands of the frequency partials. Our work is based on the assumption, often experimentally verified, that the energy distribution of the sidebands is shaped as powers of the inverse of the distance from the closest partial. The power spectrum of these pseudo-periodic processes is modeled by means of a superposition of modulated 1/f components, that is, by a pseudo-periodic 1/f -like process. Due to the fundamental self-similar character of the wavelet transform, 1/f processes can be fruitfully analyzed and synthesized by means of wavelets. We obtain a set of very loosely correlated coefficients at each scale level that can be well approximated by white noise in the synthesis process. Our computational scheme is based on an orthogonal P-band filter bank and a dyadic wavelet transform per channel. The P channels are tuned to the left and right sidebands of the harmonics so that sidebands are mutually independent. The structure computes the expansion coefficients of a new orthogonal and complete set of harmonic-band wavelets. The main point of our scheme is that we need only two parameters per harmonic in order to model the stochastic fluctuations of sounds from a pure periodic behavior. [ABSTRACT FROM AUTHOR]

We illustrate the mathematical background and musical use of a class of audio effects based on frequency warping. These effects alter the frequency content of a signal via spectral mapping. They can be implemented in dispersive tapped delay lines based on a chain of all-pass filters. In a homogeneous line with first-order all-pass sections, the signal formed by the output samples at a given time is related to the input via the Laguerre transform. However, most musical signals require a time-varying frequency modification in order to be properly processed. Vibrato in musical instruments or voice intonation in the case of vocal sounds may be modeled as small and slow pitch variations. Simulation of these effects requires techniques for time-varying pitch and/or brightness modification that are very useful for sound processing. The basis for time-varying frequency warping is a time-varying version of the Laguerre transformation. The corresponding implementation structure is obtained as a dispersive tapped delay line, where each of the frequency dependent delay element has its own phase response. Thus, time-varying warping results in a space-varying, in homogeneous, propagation structure. We show that time-varying frequency warping is associated to an expansion over biorthogonal sets generalizing the discrete Laguerre basis. Slow time-varying characteristics lead to slowly varying parameter sequences. The corresponding sound transformation does not suffer from discontinuities typical of delay lines based on unit delays. [ABSTRACT FROM AUTHOR]