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Adaptive decomposition by weighted inner functions
- The Journal of Fourier Analysis and Applications
"... Abstract. In recent study adaptive decomposition of functions into basic functions of analytic instantaneous frequencies has been sought. Fourier series is a particular case of such decomposition. Adaptivity addresses certain optimal property of the decomposition. The present paper presents a fast d ..."
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Abstract. In recent study adaptive decomposition of functions into basic functions of analytic instantaneous frequencies has been sought. Fourier series is a particular case of such decomposition. Adaptivity addresses certain optimal property of the decomposition. The present paper presents a fast decomposition of functions in the L2(∂D) spaces into a series of inner and weighted inner functions of increasing frequencies.
Optimal Approximation by Blaschke Forms and Rational Functions ∗
, 2011
"... AbstractWe study best approximation to functions in Hardy H2(D) by two classes of functions of which one is n-partial fractions with poles outside the closed unit disc and the other is n-Blaschke forms. Through the equal relationship between the two classes we obtain the existence of the minimizers ..."
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Cited by 1 (1 self)
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AbstractWe study best approximation to functions in Hardy H2(D) by two classes of functions of which one is n-partial fractions with poles outside the closed unit disc and the other is n-Blaschke forms. Through the equal relationship between the two classes we obtain the existence of the minimizers in both classes. The algorithm for the minimizers for small orders are practical.
Expansions of Functions Based on Rational Orthogonal Basis with Nonnegative Instantaneous Frequencies
"... We consider in this paper expansions of functions based on the rational orthogonal basis for the space of square integrable functions. The basis functions have nonnegative instantaneous frequencies so that the expansions make physical sense. We discuss the almost everywhere convergence of the expan ..."
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We consider in this paper expansions of functions based on the rational orthogonal basis for the space of square integrable functions. The basis functions have nonnegative instantaneous frequencies so that the expansions make physical sense. We discuss the almost everywhere convergence of the expansions and develop a fast algorithm for computing the coefficients arising in the expansions by combining the characterization of the coefficients with the fast Fourier transform.
Received (Day Month Year)
, 2013
"... Communicated by (xxxxxxxxxx) A sequence of special functions in Hardy space H2(Ts) are constructed from Cauchy kernel on unit disk D. Applying projection operator of the sequence of functions leads to an analytic sampling approximation to f, any given function in H2(Ts). That is, f can be approximat ..."
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Communicated by (xxxxxxxxxx) A sequence of special functions in Hardy space H2(Ts) are constructed from Cauchy kernel on unit disk D. Applying projection operator of the sequence of functions leads to an analytic sampling approximation to f, any given function in H2(Ts). That is, f can be approximated by its analytic samples in Ds. Under a mild condition, f is approxi-mated exponentially by its analytic samples. By the analytic sampling approximation, a signal in H2(T) can be approximately decomposed into components of positive instanta-neous frequency. Using circular Hilbert transform, we apply the approximation scheme in Hs(Ts) to Ls(T2) such that a signal in Ls(T2) can be approximated by its analytic samples on Cs. A numerical experiment is carried out to illustrate our results.
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"... Mathematical theory of signal analysis vs. complex analysis method of harmonic analysis ..."
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Mathematical theory of signal analysis vs. complex analysis method of harmonic analysis
