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16
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 ..."
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Cited by 121 (22 self)
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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.
Physical Wave Propagation Modeling for RealTime Synthesis of Natural Sounds
, 2002
"... This thesis proposes banded waveguide synthesis as an approach to realtime sound synthesis based on the underlying physics. So far three main approaches have been widely used: digital waveguide synthesis, modal synthesis and finite element methods. Digital waveguide synthesis is efficient and reali ..."
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Cited by 12 (3 self)
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This thesis proposes banded waveguide synthesis as an approach to realtime sound synthesis based on the underlying physics. So far three main approaches have been widely used: digital waveguide synthesis, modal synthesis and finite element methods. Digital waveguide synthesis is efficient and realistic and captures the complete dynamics of the underlying physics but is restricted to instruments that are welldescribed by the onedimensional string equation. Modal synthesis is efficient and realistic yet abandons complete dynamical description and hence cannot used for certain types of performance interactions like bowing. Finite element methods are realistic and capture the behavior of the constituent physical equations but on current commodity hardware does not perform in realtime. Banded waveguides offer efficient simulations for cases for which modal synthesis is appropriate but traditional digital waveguide synthesis is not applicable. The key realization is that the dynamic behavior of traveling waves, which is being used in waveguide synthesis, can be applied to individual modes and that the efficient computational
Frequencydomain design of overcomplete rationaldilation wavelet transforms
 IEEE Trans. on Signal Processing
, 2009
"... The dyadic wavelet transform is an effective tool for processing piecewise smooth signals; however, its poor frequency resolution (its low Qfactor) limits its effectiveness for processing oscillatory signals like speech, EEG, and vibration measurements, etc. This paper develops a more flexible fami ..."
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Cited by 10 (5 self)
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The dyadic wavelet transform is an effective tool for processing piecewise smooth signals; however, its poor frequency resolution (its low Qfactor) limits its effectiveness for processing oscillatory signals like speech, EEG, and vibration measurements, etc. This paper develops a more flexible family of wavelet transforms for which the frequency resolution can be varied. The new wavelet transform can attain higher Qfactors (desirable for processing oscillatory signals) or the same low Qfactor of the dyadic wavelet transform. The new wavelet transform is modestly overcomplete and based on rational dilations. Like the dyadic wavelet transform, it is an easily invertible ‘constantQ’ discrete transform implemented using iterated filter banks and can likewise be associated with a wavelet frame for L2(R). The wavelet can be made to resemble a Gabor function and can hence have good concentration in the timefrequency plane. The construction of the new wavelet transform depends on the judicious use of both the transform’s redundancy and the flexibility allowed by frequencydomain filter design. I.
An Overcomplete WDFT Sinusoidal Basis for Perceptually Motivated Speech Enhancement
 Proc. of 13th European Signal Processing Conference (EUSIPCO’2005
, 2005
"... ABSTRACT *) This paper considers an application of the warped discrete Fourier transform (WDFT) in the perceptually motivated speech enhancement. Namely, the problem of signal distortions generated by WDFT synthesis block is of interest. Spectral features of the reconstructed signal are analyzed and ..."
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Cited by 1 (0 self)
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ABSTRACT *) This paper considers an application of the warped discrete Fourier transform (WDFT) in the perceptually motivated speech enhancement. Namely, the problem of signal distortions generated by WDFT synthesis block is of interest. Spectral features of the reconstructed signal are analyzed and discussed in context of the perceptual processing. Our proposition is to construct an overcomplete WDFT sinusoidal basis in order to minimize reconstruction error. The new approach is validated in practical speech enhancement system. The results show that the proposed algorithm outperforms both conventional DFT and pure WDFT solutions. 1.
An Overcomplete WDFTbased Perceptually Constrained Variable Bit Rate Wideband Speech Coder with Embedded Noise Reduction System
 The Proc. of XI International Conference ”SPEECH AND COMPUTER
"... The paper considers an application of speech enhancement system in perceptually constrained variable bit rate wideband speech coder based on multiband CELPalgorithm with perceptually monitored structure of codebook (PCVBR). Both parts of the proposed speech coding system use the same overcomplete w ..."
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Cited by 1 (1 self)
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The paper considers an application of speech enhancement system in perceptually constrained variable bit rate wideband speech coder based on multiband CELPalgorithm with perceptually monitored structure of codebook (PCVBR). Both parts of the proposed speech coding system use the same overcomplete warped discreteFourier transform (OWDFT). An overcomplete basis of the WDFT is used to minimize reconstruction error in high frequency range in the synthesis block of noise reduction system and to provide more accurate representation of high band frequency components. A robustness of the coder with embedded noise reduction system in noise presence is discussed. 1.
1FrequencyDomain Design of Overcomplete RationalDilation Wavelet Transforms
"... Abstract—The dyadic wavelet transform is an effective tool for processing piecewise smooth signals; however, its poor frequency resolution (its low Qfactor) limits its effectiveness for processing oscillatory signals like speech, EEG, and vibration measurements, etc. This paper develops a more flex ..."
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Abstract—The dyadic wavelet transform is an effective tool for processing piecewise smooth signals; however, its poor frequency resolution (its low Qfactor) limits its effectiveness for processing oscillatory signals like speech, EEG, and vibration measurements, etc. This paper develops a more flexible family of wavelet transforms for which the frequency resolution can be varied. The new wavelet transform can attain higher Qfactors (desirable for processing oscillatory signals) or the same low Qfactor of the dyadic wavelet transform. The new wavelet transform is modestly overcomplete and based on rational dilations. Like the dyadic wavelet transform, it is an easily invertible ‘constantQ ’ discrete transform implemented using iterated filter banks and can likewise be associated with a wavelet frame for L2(R). The wavelet can be made to resemble a Gabor function and can hence have good concentration in the timefrequency plane. The construction of the new wavelet transform depends on the judicious use of both the transform’s redundancy and the flexibility allowed by frequencydomain filter design. I.
REPUBLIC OF KOREA
"... Abstract: In this paper, we propose a nonuniform DFT based on nonequispaced sampling in the frequency domain. It is useful to detect some specific frequencies such as in DTMF which is composed on two different frequencies, main (fundamental) frequency component among lots of harmonics, and feature ..."
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Abstract: In this paper, we propose a nonuniform DFT based on nonequispaced sampling in the frequency domain. It is useful to detect some specific frequencies such as in DTMF which is composed on two different frequencies, main (fundamental) frequency component among lots of harmonics, and feature detection from noisy signals. Some trials for nonuniform data processing via DFT are discussed and resampling method to obtain nonlinearly spaced samples in the frequency domain.
Biosignal Processing Applications for Speech Processing
"... Speech is a biosignal that is amenable to general biosignal processing methodologies such as frequency domain processing. This is supported today by the availability of inexpensive digital multimedia hardware and by the developments of the theoretical aspects of signal processing. However, sound pro ..."
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Speech is a biosignal that is amenable to general biosignal processing methodologies such as frequency domain processing. This is supported today by the availability of inexpensive digital multimedia hardware and by the developments of the theoretical aspects of signal processing. However, sound processing must be also regarded through the prism of the psychoacoustic reality of the human hearing system. Speech processing applications such as speech synthesis and compression and the analysis of speech data, alongside with the frequency domain analysis and the traditional statistical tools, have started to employ adaptive approaches such as artificial neural networks, in the attempts to improve the overall analysis and processing efficiency.
Estimation of frequency offset using warped discreteFourier transform
, 2005
"... In this paper, the problem of estimating a small frequency offset in a signal with a large carrier frequency is addressed. The warped discreteFourier transform (WDFT) [A. Makur, S.K. Mitra, IEEE Trans. Circuits Systems—I: Fundam. Theory Appl. 6 (9) (September 2001) 1086–1093] is used and the accura ..."
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In this paper, the problem of estimating a small frequency offset in a signal with a large carrier frequency is addressed. The warped discreteFourier transform (WDFT) [A. Makur, S.K. Mitra, IEEE Trans. Circuits Systems—I: Fundam. Theory Appl. 6 (9) (September 2001) 1086–1093] is used and the accuracy of estimation and computational complexity of this technique is compared with the conventional discreteFourier transform (DFT) and the nonuniform discreteFourier transform (NDFT). A numerical example is provided to illustrate the comparison. r 2005 Elsevier B.V. All rights reserved.