MathUtils.FftUtils

MathUtils/FftUtils.py

compute_standard_wCD(N)

class FftInvPdf(cf)

Bases: object

Numerically invert a characteristic function (CF) to obtain a PDF via FFT.

The FFT operates on a fixed integer grid [0, N] (default N=1024). The input time array passed to __call__ must therefore be pre-scaled so that the peak of the PDF falls within roughly [10, 100] on that grid.

Typical usage in a model wrapper:

_impl = FftInvPdf(my_cf)

def my_pdf(x, ..., timescale=None):
    # Rule of thumb: map the peak position t_peak to ~80 on the grid.
    if timescale is None:
        timescale = 80.0 / t_peak
    ts = timescale
    return ts * _impl(ts * x, ...)   # inverse-scale the amplitude

The caller is responsible for both the forward scaling (ts * x) and the inverse-amplitude scaling (ts * result) so that the returned values form a proper PDF integrating to 1 over the original (unscaled) time axis.