Inconsistent scaled magnitude and scaled magnitude squared in FFT
Sun, 09/11/2022 - 11:47 pm
For FFT of a real-valued input, the output modes of 4 (Scaled magnitude) and of 7 (Scaled magnitude square) seem to have an inconsistent result at the Nyquist frequency.
Specifically, the value of /OUT=3 (magnitude) and /OUT=6 (Scaled magnitude) differ by sqrt(2) at the Nyguist frequency. By contrast, the value of /OUT=4 (magnitude square) and /OUT=7 (scaled magnitude square) are the same at the Nyguist frequency. From the manual:
The scaled quantities apply to transforms of real valued inputs where the output is normally folded in the first dimension (because of symmetry). The scaling applies a factor of 2 to the squared magnitude of all components except the DC. The scaled transforms should be used whenever Parseval's relation is expected to hold.
Is there potentially a bug for /OUT=3 at the Nyguist frequency? And for the manual description, should it be "except the DC and Nyguist frequency"?