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Identity fails for odd signals GUM_iDFT(GUMDFT(odd_signal, cov_odd_signal))
#310
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Currently,
GUM_DFT
andGUM_iDFT
are based onnumpy.fft.rfft
andnumpy.fft.irfft
respectivly.Assume two signals of even and odd length:
As mentioned in the numpy documentation,
numpy.fft.irfft
requires the length of the original signal for a proper reconstruction, otherwise an original signal of even length is assumed. Therefore, to achieve identity of the reconstruction for the above signals, it is necessary to call:The
n=...
parameter ofnumpy.fft.irfft
is not reachable when callingGUM_iDFT
. Hence, the reconstruction always assumes an original signal of even length. Also workarounds with zero-padding and removal via theGUM_iDFT(..., Nx=...)
cannot yield the desired result.This might be related to #99 . I would suggest to stick to the numpy behavior, in order to simplify transition from existing routines based on numpy/scipy to the uncertainty-enhanced versions in PyDynamic. However, this would probably require some careful adjustments in the uncertainty evaluation.
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