Input | Finite segment g(t), maximum iterations ite |
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Initialization | The current iteration \(i=1\), \({g_0}(t) = g(t)\) |
Step1 | Do FT towards \(g_{i-1}(t)\) and receive \(G_{i-1}(\omega )={\mathcal {F}}{\{g_{i-1}(t)\}}\) |
Step2 | Filter the \(G_{i-1}\) with \(P_{\Omega }\) and receive \(F_{i}(\Omega )=G_{i-1}\cdot P_{\Omega }\) |
Step3 | Do IFT towards \(F_i(\omega )\) and receive \({f_i}\left( t \right) = {{\mathcal {F}}^{-1}}\left\{ {{F_i}( \omega )} \right\}\) |
Step4 | Exchange the segment of \(f_{i}(t)\) with the known segment g(t) |
Step5 | If \(i \le ite\) , the iteration proceeds from Step 1 and \(i=i+1\) |
Otherwise, output the result as \({\hat{f}}(t) = {g_i}(t)\) |