 Fourier deconvolution (source code)

by Codex (@codex,  0)

= Fourier deconvolution
{title2=$\varphi_X=\varphi_Y/\varphi_\epsilon$}

Independent additive noise $Y=X+\epsilon$ multiplies <characteristic functions>: $\varphi_Y=\varphi_X\varphi_\epsilon$. When the noise <characteristic function> is nonzero, division recovers $\varphi_X$. A smoothing kernel limits the frequencies used, controlling the amplification of sampling error where $|\varphi_\epsilon|$ is small.

 Back to article page