Results 1  10
of
10
Nonuniform Fast Fourier Transforms Using MinMax Interpolation
 IEEE Trans. Signal Process
, 2003
"... The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformlyspaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e.,a nonuniform FT . Several pap ..."
Abstract

Cited by 83 (13 self)
 Add to MetaCart
The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformlyspaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e.,a nonuniform FT . Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents an interpolation method for the nonuniform FT that is optimal in the minmax sense of minimizing the worstcase approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the minmax approach provides substantially lower approximation errors than conventional interpolation methods. The minmax criterion is also useful for optimizing the parameters of interpolation kernels such as the KaiserBessel function.
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 ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
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.
Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors
 In Proc. Fifth SPIE Conference on Wavelet Applications in Industrial Processing
, 2007
"... Most wavelet transforms used in practice are based on integer sampling factors. Wavelet transforms based on rational sampling factors offer in principle the potential for timescale signal representations having a finer frequency resolution. Previous work on rational wavelet transforms and filter ba ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Most wavelet transforms used in practice are based on integer sampling factors. Wavelet transforms based on rational sampling factors offer in principle the potential for timescale signal representations having a finer frequency resolution. Previous work on rational wavelet transforms and filter banks includes filter design methods and frequency domain implementations. We present several specific examples of Daubechiestype filters for a discrete orthonormal rational wavelet transform (FIR filters having a maximum number of vanishing moments) obtained using Gröbner bases. We also present the design of overcomplete rational wavelet transforms (tight frames) with FIR filters obtained using polynomial matrix spectral factorization.
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 ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
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...
Digital Audio Effects In The Wavelet Domain
 In Proceedings of COSTG6 Conference on Digital Audio Effects, DAFX2002
, 2002
"... Audio signals are often stored or transmitted in a compressed representation, which can pose a problem if there is a requirement to perform signal processing; it is likely it will be necessary to convert the signal back to a time domain representation, process, and then retransform. This is timecon ..."
Abstract
 Add to MetaCart
Audio signals are often stored or transmitted in a compressed representation, which can pose a problem if there is a requirement to perform signal processing; it is likely it will be necessary to convert the signal back to a time domain representation, process, and then retransform. This is timeconsuming and computationally intensive; it is potentially more efficient to apply signal processing while the signal remains in the transform domain. We have implemented a scheme whereby linear processing of the traditional type often instinctively understood by those working in the audio field may be applied to signals stored in a wavelet domain representation. Results are presented which demonstrate that the method produces the same output  to within the limits of machine precision  as timedomain processing, for less computational effort than would be required for the full explicit process through the time domain and back again. The potential benefits for linear effects processing (for example, EQ and samplelevel delays and echoes) and also for nonlinear processing such as dynamics processing, will be introduced and discussed.
ResonanceBased Signal Decomposition: A New SparsityEnabled Signal Analysis Method
"... Numerous signals arising from physiological and physical processes, in addition to being nonstationary, are moreover a mixture of sustained oscillations and nonoscillatory transients that are difficult to disentangle by linear methods. Examples of such signals include speech, biomedical, and geoph ..."
Abstract
 Add to MetaCart
Numerous signals arising from physiological and physical processes, in addition to being nonstationary, are moreover a mixture of sustained oscillations and nonoscillatory transients that are difficult to disentangle by linear methods. Examples of such signals include speech, biomedical, and geophysical signals. Therefore, this paper describes a new nonlinear signal analysis method based on signal resonance, rather than on frequency or scale, as provided by the Fourier and wavelet transforms. This method expresses a signal as the sum of a ‘highresonance ’ and a ‘lowresonance ’ component — a highresonance component being a signal consisting of multiple simultaneous sustained oscillations; a lowresonance component being a signal consisting of nonoscillatory transients of unspecified shape and duration. The resonancebased signal decomposition algorithm presented in this paper utilizes sparse signal representations, morphological component analysis, and constantQ (wavelet) transforms with adjustable Qfactor. Keywords: sparse signal representation, constantQ transform, wavelet transform, morphological component analysis 1.
NearPerfect Reconstruction Oversampled Nonuniform CosineModulated Filter Banks Based on Frequency Warping and Subband Merging
"... Abstract—A novel method for designing nearperfect reconstruction oversampled nonuniform cosinemodulated filter banks is proposed, which combines frequency warping and subband merging, and thus offers more flexibility than known techniques. On the one hand, desirable frequency partitionings can be ..."
Abstract
 Add to MetaCart
Abstract—A novel method for designing nearperfect reconstruction oversampled nonuniform cosinemodulated filter banks is proposed, which combines frequency warping and subband merging, and thus offers more flexibility than known techniques. On the one hand, desirable frequency partitionings can be better approximated. On the other hand, at the price of only a small loss in partitioning accuracy, both warping strength and number of channels before merging can be adjusted so as to minimize the computational complexity of a system. In particular, the coefficient of the function behind warping can be constrained to be a negative integer power of two, so that multiplications related to allpass filtering can be replaced with more efficient binary shifts. The main idea is accompanied by some contributions to the theory of warped filter banks. Namely, group delay equalization is thoroughly investigated, and it is shown how to avoid significant aliasing by channel oversampling. Our research revolves around filter banks for perceptual processing of sound, which are required to approximate the psychoacoustic scales well and need not guarantee perfect reconstruction. Keywords—warped nearperfect reconstruction oversampled nonuniform cosinemodulated filter bank, allpass filter/transformation, subband/channel merging, frequency warping, critical bands, Bark scale. I.
REALTIME AND EFFICIENT ALGORITHMS FOR FREQUENCY WARPING BASED ON LOCAL APPROXIMATIONS OF WARPING OPERATORS
"... Frequency warping is a modifier that acts on sound signals by remapping the frequency axis. Thus, the spectral content of the original sound is displaced to other frequencies. At the same time, the phase relationship among the signal components is altered, nonlinearly with respect to frequency. Whil ..."
Abstract
 Add to MetaCart
Frequency warping is a modifier that acts on sound signals by remapping the frequency axis. Thus, the spectral content of the original sound is displaced to other frequencies. At the same time, the phase relationship among the signal components is altered, nonlinearly with respect to frequency. While this effect is interesting and has several applications, including in the synthesis by physical models, its use has been so far limited by the lack of an accurate and flexible realtime algorithm. In this paper we present methods for frequency warping that are based on local approximations of the warping operators and allow for realtime implementation. Filter bank structures are derived that allow for efficient realization of the approximate technique. An analysis of the error is also presented, which shows that both numerical and perceptual errors are within acceptable limits. Furthermore, the approximate implementation allows for a larger variety of warping maps than that achieved by the classical (noncausal) firstorder allpass cascade implementation. 1.
EURASIP Journal on Applied Signal Processing 2004:7, 964–977 c ○ 2004 Hindawi Publishing Corporation Physically Inspired Models for the Synthesis of Stiff Strings with Dispersive Waveguides
, 2003
"... 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 fourthorder equations of stiff systems in order to reduce it to t ..."
Abstract
 Add to MetaCart
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 fourthorder equations of stiff systems in order to reduce it to two secondorder equations. By introducing scattering boundary matrices, the eigenfrequencies are determined and their n 2 dependency is discussed for the clamped, hinged, and intermediate cases. On the basis of the frequencydomain physical model, the numerical discretization is carried out, showing how the insertion of an allpass delay line generalizes the KarplusStrong 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 allpass 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.
Wavelet Signal Generation for Nonlinear Device Testing Applications
"... Abstract Testing using standard function generators for frequency response, pulse response is common. Oftentimes, certain nonlinear systems such as testing of saturable reactors, semiconductors of the pnpn type as well as testing of avalanche conditions in power transistors need sharp rise and s ..."
Abstract
 Add to MetaCart
Abstract Testing using standard function generators for frequency response, pulse response is common. Oftentimes, certain nonlinear systems such as testing of saturable reactors, semiconductors of the pnpn type as well as testing of avalanche conditions in power transistors need sharp rise and slow fall signals To this end, a PC based function generator where any kind of signal pattern such as the above, including wavelets could be realized with a very simple circuit, combined with a power OPAMP. Circuits of the above type could be tested using this setup. The software is developed in Visual Basic.