Speech signal reconstruction based on the symmetric tight wavelet frame decomposition

In this paper, we propose a nonlinear prediction model of speech signal series with an explicit structure. In order to overcome some intrinsic shortcomings, such as traps at the local minimum, improper selection of parameters, and slow convergence rate, which are always caused by improper parameters generated by, typically, the low performance of least mean square (LMS) in updating kernel coefficients of the Volterra model, a uniform searching particle swarm optimization (UPSO) algorithm to optimize the kernel coefficients of the Volterra model is proposed. The second-order Volterra filter (SOVF) speech prediction model based on UPSO is established by using English phonemes, words, and phrases. In order to reduce the complexity of the model, given a user-designed tolerance of errors, we extract the reduced parameter of SOVF (RPSOVF) for acceleration. The experimental results show that in the tasks of single-frame and multiframe speech signals, both UPSO-SOVF and UPSO-RPSOVF are better than LMS-SOVF and PSO-SOVF in terms of root mean square error (RMSE) and mean absolute deviation (MAD). UPSO-SOVF and UPSO-RPSOVF can better reflect trends and regularity of speech signals, which can fully meet the requirements of speech signal prediction. The proposed model presents a nonlinear analysis and valuable model structure for speech signal series, and can be further employed in speech signal reconstruction or compression coding.

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Speech signal reconstruction based on higher order spectra

10.1109/icassp.1988.196683 ◽

2003 ◽

Cited By ~ 5

Author(s):

S. Seetharaman ◽

M.E. Jernigan

Keyword(s):

Speech Signal ◽

Signal Reconstruction ◽

Higher Order ◽

Higher Order Spectra

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Tight wavelet frames in Lebesgue and Sobolev spaces

Journal of Function Spaces and Applications ◽

10.1155/2004/792493 ◽

2004 ◽

Vol 2 (3) ◽

pp. 227-252 ◽

Cited By ~ 15

Author(s):

L. Borup ◽

R. Gribonval ◽

M. Nielsen

Keyword(s):

Sobolev Space ◽

Jackson Inequality ◽

Wavelet Frame ◽

Approximation Rate ◽

Wavelet Frames ◽

Atomic Decompositions ◽

Approximation Spaces ◽

Tight Wavelet Frame ◽

Frame Systems ◽

Term Approximation

We study tight wavelet frame systems inLp(ℝd)and prove that such systems (under mild hypotheses) give atomic decompositions ofLp(ℝd)for1≺p≺∞. We also characterizeLp(ℝd)and Sobolev space norms by the analysis coefficients for the frame. We consider Jackson inequalities for bestm-term approximation with the systems inLp(ℝd)and prove that such inequalities exist. Moreover, it is proved that the approximation rate given by the Jackson inequality can be realized by thresholding the frame coefficients. Finally, we show that in certain restricted cases, the approximation spaces, for bestm-term approximation, associated with tight wavelet frames can be characterized in terms of (essentially) Besov spaces.

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Tight Wavelet Frame Decomposition and Its Application in Image Processing

ITB journal of Sciences ◽

10.5614/itbj.sci.2008.40.2.5 ◽

2008 ◽

Vol 40 (2) ◽

pp. 151-165

Author(s):

Mahmud Yunus ◽

Hendra Gunawan

Keyword(s):

Image Processing ◽

Wavelet Frame ◽

Tight Wavelet Frame

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Frame multiresolution analysis of continuous piecewise linear functions

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691321500326 ◽

2021 ◽

pp. 2150032

Author(s):

S. Pitchai Murugan ◽

G. P. Youvaraj

Keyword(s):

Multiresolution Analysis ◽

Piecewise Linear ◽

Linear Functions ◽

Perfect Reconstruction ◽

Wavelet Frame ◽

Perfect Reconstruction Filter Banks ◽

Reconstruction Filter ◽

Dilation Factor ◽

Tight Wavelet Frame ◽

Frame Multiresolution Analysis

The Franklin wavelet is constructed using the multiresolution analysis (MRA) generated from a scaling function [Formula: see text] that is continuous on [Formula: see text], linear on [Formula: see text] and [Formula: see text] for every [Formula: see text]. For [Formula: see text] and [Formula: see text], it is shown that if a function [Formula: see text] is continuous on [Formula: see text], linear on [Formula: see text] and [Formula: see text], for [Formula: see text], and generates MRA with dilation factor [Formula: see text], then [Formula: see text]. Conversely, for [Formula: see text], it is shown that there exists a [Formula: see text], as satisfying the above conditions, that generates MRA with dilation factor [Formula: see text]. The frame MRA (FMRA) is useful in signal processing, since the perfect reconstruction filter banks associated with FMRA can be narrow-band. So it is natural to ask, whether the above results can be extended for the case of FMRA. In this paper, for [Formula: see text], we prove that if [Formula: see text] generates FMRA with dilation factor [Formula: see text], then [Formula: see text]. For [Formula: see text], we prove similar results when [Formula: see text]. In addition, for [Formula: see text] we prove that there exists a function [Formula: see text] as satisfying the above conditions, that generates FMRA. Also, we construct tight wavelet frame and wavelet frame for such scaling functions.

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