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Furthermore, let N 0 denote the additive noise in the range cells, then the total received echo is given as {mathbf{s}}_{mathrm{echo}}left widehat{t},{t}_mright)={mathbf{s}}_Tleft widehat{t},{t}_mright)+{mathbf{s}}_Jleft widehat{t},{t}_mright)+{mathbf{N}}_0.
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Yet at the end, after Echo was given her treatment and the imprint was removed, Dr Saunders asked Echo if she could see OK. "Yes," said Echo, staring at Mr Dominic and replying in a crap-soap-opera-acting tone, "I see... perfectly".
The results for the smoothed decision echoes are given in Tables 3 and 4. The Results for the noise sensitivity test are given in Tables 5 and 6 and the performance for the principle component analysis resampled data were still high above change level in most cases (last row in Tables 5 and 6).
According to the pass-loss model, the power of received echo signal is given by P r ∝ P t Gδ d 2 α (2).
An experimental verification of the efficacy of the novel ESA-HM in comparison to other approaches in terms of echo reduction performance is given in Section 5.2.
For instance, an a priori autocorrelation Φ h profile adapted to single frequency network is characterized by a 0-dB echo channel and is given in Figure 11d.
The estimated magnitude spectrum of echo |Ê i,k)| is given by | E ^ ( i, k ) | = H ( i, k ) | X d ( i, k ) | (9).
Due to the cascaded nature of the acoustic echo path between x(k) and y(k) (first nonlinear playback equipment, then linear transmission through air), a very simple, yet effective nonlinear echo path model is given by the cascade of a memoryless nonlinearity (memoryless preprocessor) with a subsequent linear system [12 22].
The first item of the right-hand side of (47) represents the target echo component, whose energy is given by P t = | wa T | 2 · | α t ∑ p = 0 P − 1 e j 2 π f d − f d ′ pT | 2 · s ( t n − τ ) × s H ( t n − τ ′ ) 2. (48).
The expression of echo signal from target P is given by: begin{aligned} Sleft {tau,X} right) &= {varepsilon_{p}} cdot text{rect}left({frac{{tau - Delta t}}{{{T_{p}}}}} right) cdot text{rect}left({frac{{X - {x_{0}} - x}}{L}} right) &quadtimesexp left[ {j2pi left({ - {f_{c}}Delta t + frac{{alpha {{left {tau - Delta t} right)}^{2}}}}{2}} right)} right] end{aligned} (2).
Assuming negligible acceleration of the reflector, the echo model from a point reflector is given as the delayed and scaled replica of the transmitted pulse.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com