eegkit (version 1.0-5)

eegresample: Change Sampling Rate of EEG Data

Description

Turn a signal of length N into a signal of length n via linear interpolation.

Usage

eegresample(x, n)

Value

Resampled version of input data with n time points.

Arguments

x

Vector or matrix (time by channel) of EEG data with N time points.

n

Number of time points for the resampled data.

Author

Nathaniel E. Helwig <[e-mail]>

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.

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. tools:::Rd_expr_doi("10.1016/j.jbiomech.2010.09.015")

Examples

##########   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)