# Tag Info

3

Let's follow the math from incubation to delivery. It begins with psi, a rescaled morlet2 (as shown previously) at a scale $a=64$, and $\sigma=5$: $$\psi = \psi_{\sigma}(t/a) = e^{j\sigma (t/a)} e^{-(t/a)^2/2} \tag{2}$$ gets integrated and L1-normalized: -- (see caveat2 below)  \psi = \psi_{\text{int}}(t) = \frac{1}{a} \int \psi_{\sigma}(t/a)\ dt \tag{3} ...

2

Short version: DFT's bin indices are input length-dependent; "center frequency" is measured relative to the function generating the wavelet. Generated length can vary, so must be accounted for to yield 'correct' $f_c$. This requries injecting information from knowledge of the function, as DFT is blind to "absolute duration"; PyWavelets ...

1

Transform to time domain Center Plot real & imag separately, or use complex colormap, or take modulus Results below. Python code -- more examples -- other examples Minimal code import numpy as np from numpy.fft import ifft, ifftshift import matplotlib.pyplot as plt N = 2048 w = np.linspace(0, 1, N, 0) psi_x = ifftshift(ifft(np.exp(-(w - .0125 )**2 * 2*...

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