Window effects

Window effects#

This page shows how the window parameters change:

  • the window itself (phi and phitilde), and

  • the resulting time–frequency representation (and reconstruction quality).

If you’re new to the terminology, start with Window function.

Original signal#

All comparisons below use the same simple chirp-like input.

Original signal and spectrogram used for window comparisons

Packetization animation#

Each time bin corresponds to a windowed slice of the spectrum that is inverse-FFT’d and then packed into a column of the wavelet grid.

Time to wavelet packetization animation

Frequency → wavelet intuition#

If you start from a frequency-domain series (from_freq_to_wavelet), you can think of it as sliding a frequency-domain window (phitilde), inverse-FFT’ing that packet, and then packing it into the wavelet grid.

Frequency to wavelet packetization animation

What nx changes (shape of the taper)#

phi(t) for different nx phitilde(omega) for different nx

What mult changes (overlap/support)#

mult increases the window support length K = 2 * mult * Nf. Larger values usually reduce leakage and improve reconstruction, at the cost of runtime.

Residual time series for different nx/mult Wavelet magnitude and residuals for different nx/mult
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