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2.2 Nyquist theorem and antialiasing low-pass filter relaxation The Nyquist theorem states that to reconstruct the analog input signal, the signal must be sampled at a rate Fs (sampling frequency) that is greater than twice the maximum frequency compone...
Now, using the Assumptions 2 and 6, we conclude that \(\sum _{k=k_1}^{\infty } {\mathbb {E}}_{B}(\Vert \nabla f(x_k)\Vert ^2)<\infty \) and continuing as in the proof of Theorem 1, we conclude $$\begin{aligned} {\mathbb {P}}(\lim _{k\rightarrow \infty } \Vert...
For baseband signal, the sampling is straight forward. By Nyquist Shannon sampling theorem, for faithful reproduction of a continuous signal in discrete domain, one has to sample the signal at a ratefsfshigher than at-least twice the maximum frequencyfmfmcontained in the signal (actually, it is...
We give the error bounds of matrix reconstruction using the standard Nyström method with uniform sampling (with or without replacement) as follows. Theorem 4 Error Bounds for the Standard Nyström Method with Uniform Sampling [37] Let K be an n×n SPSD matrix and μ denote the coherence...
3.5.1.1 Sampling theorem An analog signal is defined at every point t of the signal x(t). Discrete signals, on the other hand, are defined only at the sampling points x(nTs), where n is the sampling number. Here, the signal x(t) is sampled every Ts seconds, where Ts is called th...
they still experience slow convergence speed and low convergence accuracy when addressing complex high-dimensional problems. There is still a lot of room for improvement in the exploitation capability and algorithm adaptability of the WOA. And because of the theorem that there is no free lunch and ...
And because of the theorem that there is no free lunch and Ref.36, no optimization algorithm can solve all optimization problems in all domains, it is necessary to further improve the WOA when it is applied to image segment-rays of X-rays of the lungs of patients with novel coronary ...
Earlier, this seemed to immediately get us in trouble (recall our interpretation of Theorem 5.1), but now we will do further encoding. The quantized values give us a lossless distributed compression problem with side information (V,Φ) available at the decoder. Using Slepian–Wolf coding, we ...