The core function of this package making use of the fCWT library. It processes an input signal in form of a real valued numeric vector interpreted as an evenly spaced time series and returns the absolute values of a spectogram, i.e. a graph with a time and a frequency dimension.
fcwt(
signal,
sample_freq,
n_freqs,
freq_begin = 2 * sample_freq/length(signal),
freq_end = sample_freq/2,
sigma = 1,
remove_coi = TRUE,
n_threads = 2L
)The spectogram, a numeric real-valued matrix with dimensions
dim = c(length(signal), n_freqs).
This matrix is wrapped into a S3-class fcwtr_scalogram so that plotting and
coercion functions can be used conveniently.
Real-valued time series. The time steps are assumed to be evenly spaced.
Sampling rate of input time series. This number primarily establishes a connection to physical units which is used in other frequency definitions as well as the units of the output data.
Number of frequency bins generated by the CWT. The frequencies are linearly distributed. Computation time increases when raising the number of frequency bins.
Optionally specifies the frequency range [freq_end, freq_begin]. If not
specified the maximal meaningful frequency range, depending on the input signal,
is taken.
The range and sample_freq need to be specified in the same units.
Sets a dimensionless parameter modifying the wavelet spread which in the time-domain is roughly given by \(\Sigma_t \sim \sqrt{2} \frac{\sigma}{f}\). Changing this parameter adjusts the time/frequency uncertainty balance. Defaults to 1. Larger (lower) value of sigma corresponds to a better (worse) frequency resolution and a worse (better) time resolution.
Boundary effects can result in nonphysical artifacts. If remove_coi = TRUE,
those are effectively removed by setting corresponding values to NA.
We define the essential support of the
(Gaussian) wavelet to be four times its standard deviation,
\(4 \Sigma_t = 2 * \sqrt{2} \frac{\sigma}{f}\), and so a wavelet touches
the boundary if the distance of the center of the wavelet to the boundary
is less then \(4 \Sigma_t\). Values that fall into that range are removed
if remove_coi = TRUE.
Number of threads used by the computation, if supported by your platform. Defaults to 2 threads (to accomodate CRAN requirements).
The wavelet used in this calculation is the so called Morlet wavelet,
a sinusoidal wave modulated by a Gaussian whose spread is controlled by
the argument sigma.
See the original paper Arts, L.P.A., van den Broek, E.L. The fast continuous wavelet transformation (fCWT) for real-time, high-quality, noise-resistant time–frequency analysis. Nat Comput Sci 2, 47–58 (2022). tools:::Rd_expr_doi("10.1038/s43588-021-00183-z")
ts_sin_440 <- sin((1:5000) * 2 * pi * 440 / 44100)
res <-
fcwt(
ts_sin_440,
sample_freq = 44100,
freq_begin = 50,
freq_end = 1000,
n_freqs = 10,
sigma = 5
)
Run the code above in your browser using DataLab