From: An improved denoising method for eye blink detection using automotive millimeter wave radar
Input: the extracted signal \(x\left( t \right)\) | |
Decompose: | |
1. Add the white noise \({n^g}\left( t \right)\) with a standard normal distribution to x(t): \({x^g}\left( t \right) = x\left( t \right) + {n^g}\left( t \right)\), | |
\(g = 1,2, \ldots ,{\mathrm{G}}\). Then, apply the EMD on \({x^g}\left( t \right)\) to obtain the \({{\mathrm{IMF}}}_1^g\left( t \right)\). | |
Thus, \({{\mathrm{IMF}}_1}\left( t \right) = \frac{{\mathrm{1}}}{{\mathrm{G}}}\sum \nolimits _{g = 1}^{{\mathrm{G}}} {{\mathrm{IMF}}}_1^g\left( t \right)\), and \({r_1}\left( t \right) = x\left( t \right) - {{\mathrm{IMF}}_1}\left( t \right)\). | |
2. Add \({n^g}\left( t \right)\) with a standard normal distribution to \({r_1}\left( t \right)\): \(r_1^g\left( t \right) = {r_1}\left( t \right) + {n^g}\left( t \right)\),\(g = 1,2, \ldots ,{\mathrm{G}}\). | |
Then, obtain the \({{\mathrm{IMF}}}_2^g\left( t \right)\) like step 1. Thus, \({{\mathrm{IMF}}_2}\left( t \right) = \frac{{\mathrm{1}}}{{\mathrm{G}}}\sum \nolimits _{g = 1}^{{\mathrm{G}}} {{\mathrm{IMF}}}_2^g\left( t \right)\), | |
and \({r_2}\left( t \right) = {r_1}\left( t \right) - {{\mathrm{IMF}}_2}\left( t \right)\). | |
3. Repeat the above decomposition process, until \({r_J}\left( t \right)\) is a monotonic function. | |
end | |
Output: \(x\left( t \right) = \sum \nolimits _{j = 1}^J {{\mathrm{IM}}{{\mathrm{F}}_j}\left( t \right) } + {r_J}\left( t \right)\). |