Sentence examples for using the convolution theorem from inspiring English sources

The GPU-based convolution using the convolution theorem is described in [8].

To improve computational time the operation is done in the frequency domain using the convolution theorem of the Fourier-transform : (3).

Proof Applying the Laplace transform on both sides of (5.9), using the convolution theorem as well as Lemma 5.1, we find 1 p λ ∑ k 1, …, k r = 0 ∞ ( γ 1 ) k 1 ⋯ ( γ r ) k r k 1 !

By using the convolution theorem, we obtain hat{F}_{alpha } bigl( vartheta_{n}ast^{alpha } varepsilon_{m} bigr) =hat{F}_{alpha } bigl( theta_{m}ast^{alpha }delta_{n} bigr) quad ( m,nin N ).

For example, having a signal of 1000 × 1000 × 100 voxels and a filter kernel of 100 × 100 × 100 voxels, which is common in optical microscopy, the calculation using the convolution theorem takes tens of seconds, instead of several days, on the most recent CPU architecture.

It is used not only for calculating the Fourier coefficients but, using the convolution theorem, also for computing the convolution of two finite sequences.

end{aligned}The estimate (2.7) is now deduced using the convolution identity (2.5) and Young's inequality (cf. [79, Chapter II, Theorem 1.15]).

DWT has traditionally been implemented using the convolution method.

In [44, 45], by making use of the convolution theorem for the Laplace transform and the logarithmically convex properties of the function q α, β ( x ) on ( 0, ∞ ), an alternative proof of Theorem 2 was supplied.

Fig. 2 Residuals after removing the smoothed DEM based on the convolution theorem using one-dimensional Gaussian filter: (Top) Sigma 0.45 (Middle) Sigma 0.65 (Bottom) Sigma 0.85.

Finally, apply the inverse of (mathcal{N}_{a}) and use the discrete convolution theorem, Proposition 2, or (27) to conclude that (g(t)=( ^{ABR} _{a}nabla^{alpha} f)(t)).