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Discrete Frequency Warped Wavelets: Theory and Applications
 IEEE Trans. Signal Processing
, 1998
"... 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 discretetime by alternating the Laguerre transform with perfect reconstruction filterbanks. This scheme provides the unique implementation of ..."
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Cited by 17 (9 self)
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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 discretetime 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 discretetime warped wavelets lead to welldefined continuoustime wavelet bases, satisfying a warped form of the twoscale 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 cutoff frequencies of the wavelets may be arbitrarily assigned while preserving a dyadic structure. The new transform provides an arbitrary tiling of the timefrequency 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 pitchsynchronous wavelets based on warped wavelets, the analysis of transients and denoising of inharmonic pseudoperiodic signals is greatly enhanced.
Dispersive and PitchSynchronous Processing of Sounds
"... The aim of this paper is to present results on digital processing of sounds by means of both dispersive delay lines and pitchsynchronous transforms in a unified framework. The background on frequency warping is detailed and applications of this technique are pointed out with reference to the exi ..."
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Cited by 4 (3 self)
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The aim of this paper is to present results on digital processing of sounds by means of both dispersive delay lines and pitchsynchronous transforms in a unified framework. The background on frequency warping is detailed and applications of this technique are pointed out with reference to the existing literature. These include transient extraction, pitch shifting, harmonic detuning and auditory modeling.
Audio Effects Based on Biorthogonal TimeVarying Frequency Warping
 EURASIP JOURNAL ON APPLIED SIGNAL PROCESSING 2001:1, 27–35 © 2001 HINDAWI PUBLISHING CORPORATION
, 2001
"... 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 allpass filters. In a homogeneou ..."
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Cited by 4 (4 self)
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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 allpass filters. In a homogeneous line with firstorder allpass 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 timevarying 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 timevarying pitch and/or brightness modification that are very useful for sound processing. The basis for timevarying frequency warping is a timevarying 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, timevarying warping results in a spacevarying, inhomogeneous, propagation structure. We show that timevarying frequency warping is associated to an expansion over biorthogonal sets generalizing the discrete Laguerre basis. Slow timevarying characteristics lead to slowly varying parameter sequences. The corresponding sound transformation does not suffer from discontinuities typical of delay lines based on unit delays.
Arbitrary Bandwidth Wavelet Sets
 PROC. ICASSP'98
, 1998
"... In this paper we consider an extension of the wavelet transform leading to the construction of wavelets with arbitrary bandwidth. The new wavelets are complete, orthonormal and dyadic; nevertheless their bandwidth is not constrained to be one octave, rather it may be designed by selecting a set of ..."
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Cited by 3 (3 self)
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In this paper we consider an extension of the wavelet transform leading to the construction of wavelets with arbitrary bandwidth. The new wavelets are complete, orthonormal and dyadic; nevertheless their bandwidth is not constrained to be one octave, rather it may be designed by selecting a set of parameters. The construction of the new bases starts in the discretetime domain, exploiting properties of the Laguerre transform. Furthermore, we provide a procedure to define continuoustime warped wavelets. Flexibility of the bandwidth allocation allows for more and improved applications of the wavelet transform, such as signal coding, the design of auditory model based filterbanks and transient detection in pseudoperiodic signals, pointed out in the paper.
TimeVarying Frequency Warping: Results and Experiments
"... Dispersive tapped delay lines are attractive structures for altering the frequency content of a signal. In previous papers we showed that in the case of a homogeneous line with first order allpass sections the signal formed by the output samples of the chain of delays at a given time is equivalent ..."
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Cited by 2 (1 self)
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Dispersive tapped delay lines are attractive structures for altering the frequency content of a signal. In previous papers we showed that in the case of a homogeneous line with first order allpass sections the signal formed by the output samples of the chain of delays at a given time is equivalent to compute the Laguerre transform of the input signal. However, most musical signals require a timevarying 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. Simulations of these effects require techniques for timevarying pitch and/or brightness modification that are very useful for sound processing. In our experiments the basis for timevarying frequency warping is a timevarying version of the Laguerre transformation. The corresponding implementation structure is obtained as a dispersive tapped delay line, where each of the frequency dependent delay elem...
2D fourchannel perfect reconstruction filter bank realized with the 2D lattice filter structure
 EURASIP Journal on Applied Signal Processing
, 2006
"... In this paper, a novel orthogonal 2D lattice structure is incorporated into the design of a nonseparable 2D fourchannel perfect reconstruction filter bank. The proposed filter bank is obtained by using the polyphase decomposition technique which requires the design of an orthogonal 2D lattice fil ..."
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Cited by 2 (0 self)
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In this paper, a novel orthogonal 2D lattice structure is incorporated into the design of a nonseparable 2D fourchannel perfect reconstruction filter bank. The proposed filter bank is obtained by using the polyphase decomposition technique which requires the design of an orthogonal 2D lattice filter. Due to constraint of perfect reconstruction, each stage of this lattice filter bank is simply parameterized by two coefficients. The perfect reconstruction property is satisfied regardless of the actual values of these parameters and of the number of the lattice stages. It is also shown that a separable 2D fourchannel perfect reconstruction lattice filter bank can be constructed from the 1D lattice filter and that this is a special case of the proposed 2D lattice filter bank under certain conditions. The perfect reconstruction property of the proposed 2D lattice filter approach is verified by computer simulations
Fractal modulation effects
 in Proc. of the Int. Conf. on Digital Audio Effects (DAFx06
"... Fractal modulation is obtained by forming a power weighted superposition of scaled and modulated versions of the signal. The resulting signal is selfsimilar with fractal characteristics. In this paper we explore fractal modulation as a powerful method to generate rich signals, useful both for the s ..."
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Fractal modulation is obtained by forming a power weighted superposition of scaled and modulated versions of the signal. The resulting signal is selfsimilar with fractal characteristics. In this paper we explore fractal modulation as a powerful method to generate rich signals, useful both for the synthesis of complex sounds, like the sounds from natural events or ecological sounds, or as control functions of audio effects. The wavelet transform can be used as an efficient tool in order to generate a subset of fractal modulated signals that are power homogeneous. Any signal used as a seed for fractal modulation is transformed into a multiscale sound by means of a treestructured multirate filter bank. Moreover, by superimposing a structured modulation scheme one can generate pseudoperiodic sounds whose partials have fractal behavior. 1.
RealTime TimeVarying Frequency Warping via ShortTime Laguerre Transform
 In Proceedings of COST G6 Conference on Digital Audio Effects (DAFX00
, 2000
"... In this paper we address the problem of the realtime implementation of timevarying frequency warping. Frequency warping based on a oneparameter family of onetoone warping maps can be realized by means of the Laguerre transform and implemented in a noncausal structure. This structure is not dir ..."
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Cited by 1 (0 self)
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In this paper we address the problem of the realtime implementation of timevarying frequency warping. Frequency warping based on a oneparameter family of onetoone warping maps can be realized by means of the Laguerre transform and implemented in a noncausal structure. This structure is not directly suited for realtime implementation since each output sample is formed by combining all of the input samples. Similarly, the recently proposed timevarying Laguerre transform has the same drawback. Furthermore, long frequency dependent delays destroy the time organization or macrostructure of the sound event. Recently, the author has introduced the ShortTime Laguerre Transform for the approximate realtime implementation of frequency warping. In this transform the shorttime spectrum rather than the overall frequency spectrum is frequency warped. The input is subdivided into frames that are tapered by a suitably selected window. By careful design, the output frames correspond to warped versions of the input frames modulated by a stretched version of the window. It is then possible to overlapadd these frames without introducing audible distortion. The overlapadd technique can be generalized to timevarying warping. However, several issues concerning the design of the window and the selection of the overlap parameters need to be addressed. In this paper we discuss solutions for the overlap of the frames when the Laguerre parameter is kept constant but distinct in each frame and solutions for the computation of full timevarying frequency warping when the Laguerre parameter is changing within each frame. 1.
Supported by the Austrian Federal Ministry of Education, Science and Culture
"... ABSTRACT. Conventional TimeFrequency and TimeScale Representations are often too rigid to capture fine details of sound or musical signals. Adaptation of ideal timefrequency tilings is often desirable in order to represent the signal in terms of components that are meaningful from a physical or p ..."
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ABSTRACT. Conventional TimeFrequency and TimeScale Representations are often too rigid to capture fine details of sound or musical signals. Adaptation of ideal timefrequency tilings is often desirable in order to represent the signal in terms of components that are meaningful from a physical or perceptual point of view. Remapping of the time and frequency axes by means of time and frequency warping can help achieve the desired flexibility of the representation. However, in the general case, the conjugate variable is affected as well, so that the resulting representation plane is distorted. In this paper we show methods to redress the conjugate distortion introduced by warping, both in the unsampled case of the integral ShortTime Fourier Transform and in the sampled case of generalized Gabor frames.
EURASIP Journal on Applied Signal Processing 2001:1, 27–35 © 2001 Hindawi Publishing Corporation Audio Effects Based on Biorthogonal TimeVarying Frequency Warping
, 2001
"... 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 allpass filters. In a homogeneou ..."
Abstract
 Add to MetaCart
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 allpass filters. In a homogeneous line with firstorder allpass 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 timevarying 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 timevarying pitch and/or brightness modification that are very useful for sound processing. The basis for timevarying frequency warping is a timevarying 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, timevarying warping results in a spacevarying, inhomogeneous, propagation structure. We show that timevarying frequency warping is associated to an expansion over biorthogonal sets generalizing the discrete Laguerre basis. Slow timevarying characteristics lead to slowly varying parameter sequences. The corresponding sound transformation does not suffer from discontinuities typical of delay lines based on unit delays.