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A continuous function can be constructed from a set of values sampled at a closely spaced discrete points, if the function is band-limited, i.e. its Fourier transform is nil outside a finite …

To begin, we concern ourselves exclusively with band-limited signals. The reasons are both mathematical and physical, as we discuss later. A signal is said to be band-limited if the …

The combination of this infinite set of scaled and shifted sinc functions, each bandlimited to (−ωc, ωc), is what creates the expression in Eq. (11), which we refer to as the ideal bandlimited …

A plot indicating how sinc functions sum together to reconstruct bandlimited signals is shown in Fig.2. The figure shows a superposition of five sinc functions, each at unit amplitude, and …

Oct 28, 2022 · A family of sampling theorems for the reconstruction of bandlimited functions from their uniform or non-uniform samples is presented. The bandlimited functions may be square …

The definition of band-limited functions (and random processes) is extended to include functions and processes which do not possess a Fourier integral representation. This definition allows a …

A function cannot be simultaneously limited in frequency and limited in time. One must choose either a band-limited function, which extends infinitely in time, or a time-limited function, …

Nov 1, 2006 · Many signals encountered in science and engineering are approximated well by bandlimited functions. We provide suitable error bounds for the approximation of bandlimited …

Jan 1, 2013 · We shall call a function (analogue signal) \ (f\left (t\right )\) bandlimited if its Fourier transform \ (F\left (\omega \right )\) vanishes outside a finite frequency interval, i.e., $$\left \vert …

Bandlimited interpolation of discrete-time signals is a basic tool having extensive application in digital signal processing. In general, the problem is to correctly compute signal values at …

Apr 9, 2015 · A Band-limited signal is defined as a signal whose Fourier Transform is zero above a specified frequency. Shannon Sampling Theorem is also stated for a strictly band-limited …

A plot indicating how sinc functions sum together to reconstruct bandlimited signals is shown in Fig.4.22. The figure shows a superposition of five sinc functions, each at unit amplitude, and …

Bandlimited interpolation: f ˇ2B2 ˇ exists and is given by f ˇ(t) = X1 k=-1 f(k) sin(ˇ(t-k)) ˇ(t-k), t 2R. For B2 2ˇ downsampling and bandlimited interpolation are well-behaved. Equivalence between …

In this paper we demonstrate how to use bases for bandlimited functions in algorithms of wave propagation. Using bandlimited functions allows us to achieve a low sampling rate while …

Let f : R ! C be a bandlimited function, and let K 2 N be its bandlimit. Then, for J 2 N and j such that 0 j < J , if we dene ~xj such that 0 ~xj < 2 ,x k = 2 k=K , and fk = f (x k), we can use the …

Nov 5, 2019 · In this article, we discuss the Lagrange interpolation of the entire functions on the real line, which is motivated by the sampling theory. We first define the uniform distribution of …

Let f : R ! C be a bandlimited function, and let K 2 N be its bandlimit. Then, for J 2 N and j such that 0 j < J, if we define ~x j such that 0 ~x j < 2ˇ, x k = 2ˇk=K, and f k = f(x k), we can use the …

Let f be a real or complex function of R. The idea of f being band-limited is that it is composed of components eikx spanning a finite range of wave numbers k. To be concrete, let us take the …