Sentence examples for by transforming the convolution from inspiring English sources

In [9], it was demonstrated that equalization and decoding can be performed jointly by transforming the convolution decoder trellis into a super-trellis, and then using this super-trellis to perform equalization while decoding.

By wavelet decomposition and transform at certain resolutions, the proposed method transforms the convolution relation between responses and loads in time domain into the linear multiplicative relation between system responses and wavelet responses in the wavelet domain.

Regarding one of key results connected to the Laplace transform, the convolution theorem, we first have to introduce a convolution on time scales.

Fourier transforming the output elucidates the convolution, giving (7).

By selecting the optimal fractional Fourier transform order, the chirp CP can remove the ISI as well as transform the linear convolution of the signal and the time-varying channel into fractional circular convolution.

The frequency domain representation was then found by taking the Fourier transform of the convolution kernel, h k), with respect to k.

By using the fuzzy Mellin transform and the convolution rule, we have U t)=mathcal{M}^{-1}bigl[tilde{varphi}(s)odottilde{psi } 1-s) bigr](t)= int_{0} 1-sfty}varphi(ttau)odot f(tau), mathrm{d} tau, where (tilde{varphi}(s)=1/tilde{mathcal{kappa}}(1-s)).

The Fourier transform of the convolution equals the product of the spectra (Fourier transforms) of the convolved functions.

The Sumudu transform of the convolution product of f and u is given by S ( f ⋆ u ) ( y ) = y f s ( y ) u s ( y ), where f s and u s are the Sumudu transforms of f and u, respectively.

The Fourier transform of the convolution product φ 1 ∗ φ 2 is defined by [4] F ( φ 1 ∗ φ 2 ) = F φ 1 F φ 2.

Convolution transforms the impulse response of a system to a response of the system that reflects time-varying input (Małoszewski and Zuber 1982).