Calculates Time/Frequency Resolution

For a given sigma and reference frequency freq this function calculates the expected time and frequency resolution respectively.

Usage

sigma_res(sigma, freq)

Arguments

sigma

The dimensionless positive parameter in fcwt() controlling the wavelet spread.

freq

The reference frequency where the frequency and time resolution are calculated. Must be a quantity with frequency units (see u()).

Value

A named list with two elements: "time" and "freq", in time and frequency units. They obey the property \(time \times freq = \frac{8}{\pi}\).

Details

Note that this resolution depends on the reference frequency, since the FCWT scales the wavelet spread depending on the frequency in a natural way. (in contrast to a simple fixed-windowed Fourier Transform).

See also

Other sigma: sigma_freq_res_rel(), sigma_from_freq_res(), sigma_from_freq_res_rel(), sigma_from_time_res()

Examples

sigma_res(1, u(440, "Hz"))
#> $time
#> 0.009090909 [1/Hz]
#> 
#> $freq
#> 280.1127 [Hz]
#>