Gianpaolo Evangelista

Pitch-synchronous wavelet representations of speech and music signals

A new wavelet representation is explored. The transform is based on a pitch-synchronous vector representation and it adapts to the oscillatory or aperiodic characteristics of signals. Pseudo-periodic signals are represented in terms of an asymptotically periodic trend and aperiodic fluctuations at several scales. The transform reverts to the ordinary wavelet transform over totally aperiodic signal segments. The pitch-synchronous wavelet transform is particularly suitable to the analysis, rate-reduction coding and synthesis of speech signals and it may serve as a preprocessing block in automatic speech recognition systems. Feature extraction such as separation of voice from noise in voiced consonants is easily performed by means of partial wavelet expansions. A stochastic model of aperiodic fluctuations is proposed. >

Comb and multiplexed wavelet transforms and their applications to signal processing

As an extension of wavelet theory, new wavelet bases that are discrete in nature and suitable for the analysis and synthesis of pseudo-periodic digital signals are introduced. By means of these bases, the signal is represented in terms of a periodic trend and aperiodic fluctuations at several scales. In the frequency domain, the periodic trend lies in bands that are centered on the harmonics while the fluctuations are distributed in several sidebands. Properties of comb and multiplexed wavelet transforms are examined and the concepts applied to the analysis of real-life signals. In one dimension, the new transforms have interesting applications to speech and music signal processing. Their extension to two dimensions may be useful for the analysis of pseudo-periodic images. >

Frequency-warped filter banks and wavelet transforms: a discrete-time approach via Laguerre expansion

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 novel filters are Laguerre type IIR filters that can be directly derived and designed from ordinary orthogonal or biorthogonal filter banks. Generalized downsampling and upsampling operators based on dispersive delay lines are the building blocks of our structures. By iterating the filter banks, we construct new orthogonal and complete sets of wavelets whose passbands are not octave spaced and may be designed by selecting a single parameter.

Player–Instrument Interaction Models for Digital Waveguide Synthesis of Guitar: Touch and Collisions

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.

A method for separation of overlapping partials based on similarity of temporal envelopes in multichannel mixtures

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 narrow-band 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.

Separation of harmonic instruments with overlapping partials in multi-channel mixtures

When instruments play together, different partials often overlap in time and frequency. This is particularly likely for harmonic instruments. We present a new method for the separation of overlapping partials in multi-channel mixtures. The method is based on the observation that when a harmonic instrument plays a note, all the partials have similar shapes, i.e. common onset, offset, amplitude and frequency modulation. For narrowband partials, we devise a method to estimate a demixing matrix that can recover the original source partials from the multi-channel mixture where they overlap. The method is computationally efficient in that it works on highly downsampled narrow frequency bands and it performs equally well for closely spaced partials as for crossing partials, e.g., due to frequency modulations such as vibrato effects. It is able to separate partials in mixtures with a high number of overlapping partials, such as two instruments playing notes where the fundamental frequencies are in fifth (3:2) or octave (2:1) relation.

Physically inspired models for the synthesis of stiff strings with dispersive waveguides

We review the derivation and design of digital waveguides from physical models of stiff systems, useful for the synthesis of sounds from strings, rods, and similar objects. A transform method approach is proposed to solve the classic fourth-order equations of stiff systems in order to reduce it to two second-order equations. By introducing scattering boundary matrices, the eigenfrequencies are determined and their dependency is discussed for the clamped, hinged, and intermediate cases. On the basis of the frequency-domain physical model, the numerical discretization is carried out, showing how the insertion of an all-pass delay line generalizes the Karplus-Strong algorithm for the synthesis of ideally flexible vibrating strings. Knowing the physical parameters, the synthesis can proceed using the generalized structure. Another point of view is offered by Laguerre expansions and frequency warping, which are introduced in order to show that a stiff system can be treated as a nonstiff one, provided that the solutions are warped. A method to compute the all-pass chain coefficients and the optimum warping curves from sound samples is discussed. Once the optimum warping characteristic is found, the length of the dispersive delay line to be employed in the simulation is simply determined from the requirement of matching the desired fundamental frequency. The regularization of the dispersion curves by means of optimum unwarping is experimentally evaluated.

Last stage control and mechanical transfer function measurement of the VIRGO suspensions

The automatic control of the suspended mirrors is a major task in operating an interferometric gravitational wave antenna. To reach the extreme sensitivity required for this kind of detector, an accurate alignment and a stable locking of the interferometer on its working point are crucial. The solution of this problem is particularly complex in the case of a multistage pendulum, such as the suspension system for seismic isolation adopted in VIRGO. A precise knowledge of the suspension mechanical transfer functions (TFs) for different forces applied in the control servo-loops represents essential information to reach the goal. In this article, we describe the apparatus we developed to measure the VIRGO suspension TF and we report the results thus obtained on full-scale suspensions at the VIRGO site. Preliminary results for the implemented control system of the last suspension stage are also presented.

Analysis and synthesis of pseudo-periodic1/f-like noise by means of wavelets with applications to digital audio

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 components, that is, by a pseudo-periodic-like process. Due to the fundamental selfsimilar character of the wavelet transform, 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-band filter bank and a dyadic wavelet transform per channel. The 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.

Audio Effects Based on Biorthogonal Time-Varying Frequency Warping

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.