eegfft {eegkit}

Fast Fourier Transform of EEG Data

Description

Finds the strength (amplitude) and phase shift of the input signal(s) at a particular range of frequencies via a Discrete Fast Fourier Transform (FFT). Can input single or multi-channel data.

Usage

eegfft(x, Fs, lower, upper)

Arguments

x

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

Fs

Sampling rate of x in Hz such that n = s * Fs where s is the number of seconds of input data (some positive integer).

lower

Lower band in Hz. Smallest frequency to keep (defaults to 0).

upper

Upper band in Hz. Largest frequency to keep (defaults to Fs/2 - Fs/n).

Details

The fft function (or mvfft function) is used to implement the FFT (or multivatiate FFT). Given the FFT, the strength of the signal is the modulus (Mod), and the phase.shift is the angle (Arg).

Value

If x is a vector, returns a data frame with variables:

frequency

vector of frequencies

strength

strength (amplitude) of signal at each frequency

phase.shift

phase shift of signal at each frequency

If x is a matrix with J channels, returns a list with elements:

frequency

vector of frequencies of length F

strength

F by J matrix: strength (amplitude) of signal at each frequency and channel

phase.shift

F by J matrix: phase shift of signal at each frequency and channel

Note

The strength of the signal has the same unit as the input (typically microvolts), and the phase shift is measured in radians (range -pi to pi).

Author(s)

Nathaniel E. Helwig <[e-mail]>

References

Cooley, James W., and Tukey, John W. (1965) An algorithm for the machine calculation of complex Fourier series, Math. Comput. 19(90), 297-301.

Singleton, R. C. (1979) Mixed Radix Fast Fourier Transforms, in Programs for Digital Signal Processing, IEEE Digital Signal Processing Committee eds. IEEE Press.

Examples

##########   EXAMPLE   ##########

### Data Generation ###

# parameters for signal
Fs <- 1000                             # 1000 Hz signal
s <- 3                                 # 3 seconds of data
t <- seq(0, s - 1/Fs, by = 1/Fs)       # time sequence
n <- length(t)                         # number of data points
freqs <- c(1, 5, 10, 20)               # frequencies
amp <- c(2, 1.5, 3, 1.75)              # strengths (amplitudes)
phs <- c(0, pi/6, pi/4, pi/2)          # phase shifts

# create data generating signals
mu <- rep(0, n)
for(j in 1:length(freqs)){
  mu <- mu + amp[j] * sin(2*pi*t*freqs[j] + phs[j])
}
set.seed(1)                           # set random seed
e <- rnorm(n)                         # Gaussian error
y <- mu + e                           # data = mean + error


### FFT of Noise-Free Data ###

# fft of noise-free data
ef <- eegfft(mu, Fs = Fs, upper = 40)
head(ef)
ef[ef$strength > 0.25,]

# plot frequency strength
par(mfrow = c(1,2))
plot(x = ef$frequency, y = ef$strength, t = "b",
     xlab = "Frequency (Hz)", 
     ylab = expression("Strength (" * mu * "V)"),
     main = "FFT of Noise-Free Data")

# compare to data generating parameters
cbind(amp, ef$strength[ef$strength > 0.25])
cbind(phs - pi/2, ef$phase[ef$strength > 0.25])


### FFT of Noisy Data ###

# fft of noisy data
ef <- eegfft(y, Fs = Fs, upper = 40)
head(ef)
ef[ef$strength > 0.25,]

# plot frequency strength
plot(x = ef$frequency, y = ef$strength, t = "b",
     xlab = "Frequency (Hz)", 
     ylab = expression("Strength (" * mu * "V)"),
     main = "FFT of Noisy Data")

# compare to data generating parameters
cbind(amp, ef$strength[ef$strength > 0.25])
cbind(phs - pi/2, ef$phase[ef$strength > 0.25])