Arterial blood pressure analysis based on scattering transform II
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Citations
Signal Analysis by Expansion Over the Squared Eigenfunctions of an Associated Schr\"odinger Operator
Signal Analysis by Expansion Over the Squared Eigenfunctions of an Associated Schrödinger Operator
References
Perturbation theory for linear operators
Quantum mechanics: Non-relativistic theory,
Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
Related Papers (5)
Frequently Asked Questions (7)
Q2. What is the spectrum of the Schrödinger operator?
The spectrum of this operator has two components : a continuous spectrum including positive eigenvalues and a discrete spectrum with negative eigenvalues [1], [4], [5], [6], [12].
Q3. what is the main idea of the SBSA technique?
The main idea is then to find the parameter χ such that the signal y is well approximated by the reflectionless part of the potential which can be written then using equation (7) :ŷ = 4χ−1 N∑ n=1 κnψ2n + ymin, (9)where −κ2n and ψn, n = 1, · · · ,N are respectively the N negative eigenvalues and the corresponding L2-normalized eigenfunctions for the potential V , determined by the DST.
Q4. What is the spectral function of the Schrödinger operator?
Denoting the positive eigenvalues by λ = k2, the continuous spectrum is characterized by the following asymptotic boundary conditions where T (k) and R(k) are respectively the transmission and the reflection coefficients associated to V :ψ(x,k)→ T (k)exp(−ikx), x→−∞, (2) ψ(x,k)→ exp(−ikx)+R(k)exp(ikx), x→+∞. (3)Conservation of energy leads to |T (k)|2 + |R(k)|2 = 1.
Q5. What is the main idea of the SBSA technique?
Determining the parameter χ determines the number N(χ) of negative eigenvalues and hence the number of solitons components required for a satisfying approximation of the signal y. Fig. 1 summarizes the SBSA method.
Q6. What is the DST of the potential V?
In this study the authors suppose that the function V belongs to the Schwartz space S (R) of regular and rapidly decreasing functions on R.The DST of the potential V is the solution of the spectral problem for L(V ).
Q7. What is the method used to analyze the ABP?
This approach is based on the scattering transform and deals with the solution of the spectral problem of a perturbed Schrödinger operator for a given potential.