# Bivariate EMD decomposition Function `bemd` implements the Bivariate EMD (Scheme 2 in the cited article). ```r bemd(input, directions = 64L, num_imfs = 0L, num_siftings = 50L) ``` ## Arguments - `input`: Complex vector of length N. The input signal to decompose. - `directions`: Vector of directional angles (in radians) to use for the decomposition, or an integer defining the number of equally spaced angles to use. - `num_imfs`: Number of Intrinsic Mode Functions (IMFs) to compute. If num_imfs is set to zero, a value of num_imfs = emd_num_imfs(N) will be used, which corresponds to a maximal number of IMFs. Note that the final residual is also counted as an IMF in this respect, so you most likely want at least num_imfs=2. - `num_siftings`: Use a maximum number of siftings as a stopping criterion. If `num_siftings` is zero, this stopping criterion is ignored. Default is 50. ## Returns Time series object of class `"mts"` where series corresponds to IMFs of the input signal, with the last series being the final residual. @references 1. G. Rilling, P. Flandrin, P. Goncalves and J. M. Lilly, "Bivariate Empirical Mode Decomposition", IEEE Signal Processing Letters, Vol. 14 (2007) 936--939 ## Examples ```r N <- 512 t <- 2 * pi * (0:(N-1))/N input <- cos(0.3 * t) * exp(2i * t) + 0.3 * abs(sin(2.3 * t)) * exp(17i * t) # Use evenly spaced angles as directions num_directions <- 64 directions <- 2 * pi * 1:num_directions / num_directions imfs <- bemd(input, directions, num_imfs = 4, num_siftings = 10) # plot the data plot(Re(input), Im(input), xlim = c(-1, 2)) # plot signal and the imfs for(i in 1:4) points(Re(imfs[,i]), Im(imfs[,i]), col = 1 + i) legend("bottomright", col = 1:5, legend = c("signal", paste0("IMF ",1:4)), pch = 1) data("float") plot(float, type = "l") signal <- float[, 1] + float[, 2] * 1i imfs <- bemd(signal, num_siftings = 10, num_imfs = 4) # plot the data and the imfs oldpar <- par() par(mfrow = c(5, 1), mar = c(0.5, 4.5, 0.5, 0.5), oma = c(4, 0, 2, 0)) ts.plot(float, col = 1:2, lty = 1:2, ylab = "signal", gpars = list(xaxt = "n")) for(i in 1:4) { ts.plot(Re(imfs[, i]), Im(imfs[, i]), col = 1:2, lty = 1:2, ylab = if(i < 4) paste("IMF", i) else "residual", gpars = list(xaxt = "n")) } axis(1) title(xlab = "Time (days)", main = "Bivariate EMD decomposition", outer = TRUE) par(oldpar) ```

bemd function