Determine Sigma from a relative frequency resolution requirement

Setting the correct value for sigma in fcwt() for a particular use case is important. Sigma controls the wavelet spread used by the FCWT and so determines the time-/frequency resolution (depending on a given reference frequency).

Usage

sigma_from_freq_res_rel(res)

Arguments

res

The required relative frequency resolution, a number between 0 and 1.

Value

A dimensionless number controlling the FCWT wavelet spread, corresponding to the sigma argument in fcwt().

Details

If you set a high frequency resolution, the time resolution of the output signal will suffer, and vice versa. Determining the correct balance for a particular use case can be crucial. This function determines the value of sigma for a particular relative frequency resolution requirement. Note that the relative frequency resolution does not depend on the frequency itself, in contrast to the absolute frequency resolution.

See also

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

Examples

ref_freq <- u(440, "Hz")
sigma <- sigma_from_freq_res_rel(0.2)

sigma_res(sigma, ref_freq)
#> $time
#> 0.02893726 [1/Hz]
#> 
#> $freq
#> 88 [Hz]
#>