'Morlet' wavelet transform (Discrete)

Transform analog voltage signals with 'Morlet' wavelets: complex wavelet kernels with \(\pi/2\) phase differences.

Usage

wavelet_kernels(freqs, srate, wave_num)

morlet_wavelet(
  data,
  freqs,
  srate,
  wave_num,
  precision = c("float", "double"),
  trend = c("constant", "linear", "none"),
  signature = NULL,
  ...
)

wavelet_cycles_suggest(
  freqs,
  frequency_range = c(2, 200),
  cycle_range = c(3, 20)
)

Arguments

freqs: frequency in which data will be projected on
srate: sample rate, number of time points per second
wave_num: desired number of cycles in wavelet kernels to balance the precision in time and amplitude (control the smoothness); positive integers are strongly suggested
data: numerical vector such as analog voltage signals
precision: the precision of computation; choices are 'float' (default) and 'double'.
trend: choices are 'constant': center the signal at zero; 'linear': remove the linear trend; 'none' do nothing
signature: signature to calculate kernel path to save, internally used
...: further passed to detrend;
frequency_range: frequency range to calculate, default is 2 to 200
cycle_range: number of cycles corresponding to frequency_range. For default frequency range (2 - 200), the default cycle_range is 3 to 20. That is, 3 wavelet kernel cycles at 2 Hertz, and 20 cycles at 200 Hertz.

Value

wavelet_kernels returns wavelet kernels to be used for wavelet function; morlet_wavelet returns a file-based array if precision is 'float', or a list of real and imaginary arrays if precision is 'double'

Examples


if(interactive()){

# generate sine waves
time <- seq(0, 3, by = 0.01)
x <- sin(time * 20*pi) + exp(-time^2) * cos(time * 10*pi)

plot(time, x, type = 'l')

# freq from 1 - 15 Hz; wavelet using float precision
freq <- seq(1, 15, 0.2)
coef <- morlet_wavelet(x, freq, 100, c(2,3))

# to get coefficients in complex number from 1-10 time points
coef[1:10, ]

# power
power <- Mod(coef[])^2

# Power peaks at 5Hz and 10Hz at early stages
# After 1.0 second, 5Hz component fade away
image(power, x = time, y = freq, ylab = "frequency")

# wavelet using double precision
coef2 <- morlet_wavelet(x, freq, 100, c(2,3), precision = "double")
power2 <- (coef2$real[])^2 + (coef2$imag[])^2

image(power2, x = time, y = freq, ylab = "frequency")

# The maximum relative change of power with different precisions
max(abs(power/power2 - 1))

# display kernels
freq <- seq(1, 15, 1)
kern <- wavelet_kernels(freq, 100, c(2,3))
print(kern)

plot(kern)

}