[Bug?] getMeanFreq gives non-monotonous values for some wavelets

[LRBaalmann]

Hi, I've noticed some unexpected behaviour of the function getMeanFreq, which returns non-monotonous values for some wavelets. I stumbled upon this issue when playing around with the example code of the readme; for some wavelets, the heatmap would not be plotted because it requires increasing y-values, which are given by getMeanFreq in the example code. Disclaimer: I have very little knowledge of wavelets and how they function. Perhaps this behaviour is expected or even intended; it does strike me as quite odd, though. I have not done a thorough test but tried only a few cases. My observations are as such:

• no issues for Morlet, no matter what parameters I gave it
• Battle-Lemarie 4 is problematic for β=1 and large signals but fine for short-ish ones (<10000)
• Haar is problematic even for comparable short signals (~1000)

MWE:

using ContinuousWavelets, Plots
x = 100000 # cBatt4 is fine for x<10000 but cHaar has issues even for ~1000
c1 = wavelet(Morlet(), β=1)
f1 = getMeanFreq(computeWavelets(x, c1)[1])
c2 = wavelet(cBatt4, β=1) # no problem for β=2, but β=1 causes issues for large x
f2 = getMeanFreq(computeWavelets(x, c2)[1])
c3 = wavelet(cHaar)
f3 = getMeanFreq(computeWavelets(x, c3)[1])
plot(f1, yscale=:log10, label="Morlet()", xlabel="i", ylabel="νᵢ", key=:bottomright)
plot!(f2, label="cBatt4")
plot!(f3, label="cHaar")

The resulting plot:

Should this behaviour be intended, please feel free to discard this report. Many thanks for providing this package!

[dsweber2]

Thanks for the detailed experimentation and writeup!

Those should be straight lines for β=1; the way the ContOrtho orthogonal wavelets are calculated is quite different from the inherently continuous ones like Morlet or Dog2. Looks like there's a bug in the way I generate those wavelets.

[dsweber2]

Finally got around to this, turns out I was using a pretty nonstandard 1-norm based mean frequency rather than the power (2-norm), as used in DSP. Using that, the finite cut-off really messes with the mean frequency, which becomes glaringly apparent for discontinuous wavelets like Haar (it's a step function, so the frequency decay is particularly abysmal). Haar still looks a bit weird, but it is actually monotonic