Hacker News Reader

Comment by IshKebab | Hacker News Reader

You don't need to know the entire signal in advance - you can just window the wavelets at some reasonable size.

Yes, but then you are back at time-windows, a window-function, overlap and artifacts, which is defeating the purpose.

I'm more familiar with Fourier transforms and have limited experience with wavelets. But if each wavelet intrinsically falls off at a Gaussian curve, cutting it off (possibly with a window) at 3-4 sigmas won't change the wavelet substantially. Maybe for some use cases, the wavelet will be narrower at high frequencies (short delay), and wider at low frequencies (high delay). I don't know how you'd perform incremental updates of a plot drawn with non-uniform delays though...

The signal will continue over the seam between two windows, meaning you will cut the wave in the signal "in half". Mathematically, waves are always infinite and to cut them you would actually introduce overtones (higher frequencies) to model the sharp end / start of the base wave. These then result in artifacts regardless of what method is used for the transformation (Fourier or Wavelet).

> The signal will continue over the seam between two windows, meaning you will cut the wave in the signal "in half".

You can window the wavelet, then slide the finite-duration wavelet by a few samples at a time, even if the wavelet is hundreds to thousands of samples long. This is possible in STFT as well (each part of the original signal shows up in many separate FFTs).

Again, I don't know the implementation details of wavelet transforms. Maybe I'll look into your repo when I have time. What's your asymptotic and practical runtime?

O(n log n) for the x axis (time samples) and O(n) for the y axis (frequencies).

But you can downsample the signal in frequency domain, meaning you will pay mostly for the output resolution.

You often want a wavelet with compact support anyway so you don't even need to choose the window size: it's built-in.

Reply on news.ycombinator.com