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David G's avatar

Hi David - In your wavelength spectrogram, how do you balance the "sigma" element of the Gaussian function? How do you balance the trade-off between frequency precision vs time localisation?

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David F's avatar

Hey David, very good question, thank you. It's something I spent a lot of time on when developing the software as it is a crucial parameter. Firstly the widths of the Gaussian element of the morlet wavelet change as frequency increases. Secondly I have a parameter to adjust the overall width in order to optimally balance between time and frequency precision. As for the setting in that context it is entirely subjective!

Since we can never remove the general uncertainty principle I strike a balance between the two. I will add that over the last few years or so using and refining the app on financial markets I have settled upon an optimal balance. This both allows temporal changes (freq/amp mod) to be discerned while retaining a tight *enough* bandwidth of power for trading decisions that are more often that not, right. TSLA a nice example of that here!

https://www.sigma-l.net/p/time-frequency-analysis-financial-markets

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David G's avatar

Thanks for the explanation David!

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670583's avatar

Looking like you nailed it once again 😌 amazing

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David F's avatar

Beautiful signal from Elon

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