# Change Sampling Rate of EEG Data Turn a signal of length `N` into a signal of length `n` via linear interpolation. ```r eegresample(x, n) ``` ## Arguments - `x`: Vector or matrix (time by channel) of EEG data with `N` time points. - `n`: Number of time points for the resampled data. ## Details Data are resampled using the "Linear Length Normalization" approach described in Helwig et al. (2011). Let $\mathbf{x} = (x_1, \ldots, x_N)'$ denote the input vector of length $N$, and define a vector $\mathbf{t} = (t_1, \ldots, t_n)$ with entries $$ t_i = 1 + (i - 1) \delta $$ for $i = 1, \ldots, n$ where $\delta = (N - 1) / (n - 1)$. The resampled vector is calculated as $$ y_i = x_{\lfloor t_i \rfloor} + (x_{\lceil t_i \rceil} - x_{\lfloor t_i \rfloor}) ( t_i - \lfloor t_i \rfloor) $$ for $i = 1, \ldots, n$ where $\lfloor \cdot \rfloor$ and $\lceil \cdot \rceil$ denote the floor and ceiling functions. ## Returns Resampled version of input data with `n` time points. ## References Helwig, N. E., Hong, S., Hsiao-Wecksler E. T., & Polk, J. D. (2011). Methods to temporally align gait cycle data. Journal of Biomechanics, 44(3), 561-566. ## Author(s) Nathaniel E. Helwig ## Note Typical usage is to down-sample (i.e., decrease the sampling rate of) a signal: `n < N`. ## Examples ```r ########## EXAMPLE 1 ########## # create vector with N = 200 time points N <- 200 x <- sin(4 * pi * seq(0, 1, length.out = N)) # down-sample (i.e., decrease sampling rate) to n = 100 y <- eegresample(x, n = 100) mean((y - sin(4 * pi * seq(0, 1, length.out = 100)))^2) # up-sample (i.e., increase sampling rate) to n = 500 z <- eegresample(x, n = 500) mean((z - sin(4 * pi * seq(0, 1, length.out = 500)))^2) # plot results par(mfrow = c(1,3)) plot(x, main = "Original (N = 200)") plot(y, main = "Down-sampled (n = 100)") plot(z, main = "Up-sampled (n = 500)") ########## EXAMPLE 2 ########## # create matrix with N = 500 time points and 2 columns N <- 500 x <- cbind(sin(2 * pi * seq(0, 1, length.out = N)), sin(4 * pi * seq(0, 1, length.out = N))) # down-sample (i.e., decrease sampling rate) to n = 250 y <- eegresample(x, n = 250) ytrue <- cbind(sin(2 * pi * seq(0, 1, length.out = 250)), sin(4 * pi * seq(0, 1, length.out = 250))) mean((y - ytrue)^2) # up-sample (i.e., increase sampling rate) to n = 1000 z <- eegresample(x, n = 1000) ztrue <- cbind(sin(2 * pi * seq(0, 1, length.out = 1000)), sin(4 * pi * seq(0, 1, length.out = 1000))) mean((z - ztrue)^2) # plot results par(mfrow = c(1,3)) plot(x[,1], main = "Original (N = 500)", cex = 0.5) points(x[,2], pch = 2, col = "blue", cex = 0.5) plot(y[,1], main = "Down-sampled (n = 250)", cex = 0.5) points(y[,2], pch = 2, col = "blue", cex = 0.5) plot(z[,1], main = "Up-sampled (n = 1000)", cex = 0.5) points(z[,2], pch = 2, col = "blue", cex = 0.5) ```

eegresample function