The first statement is not true, it is true for convolution1, since the hilbert transform itself is a convolution $H(x) = h(t) * x(t)$ from the convolution properties $H(x*y) = x*H(y) = y*H(x)$
The second is correct 2, (the imaginary case is follows by the fact that the product of an analytic function and a constant is analytic)
The meaning of the third is ...
It looks like artifacts due to the derivative. I used this code in Octave:
c=chirp(t, 20, 2, 100);
and this is what comes out:
I also tested the equivalent of this in LTspice and, without any form of unwrapping, this is the ...
I computed and compared the minimum phase HRIR and the original one.
This is my final code:
:param HRIR: the desired HRIR impulse response to convert into minimum phase
:return: the minimum phase version of the original HRIR
HRIR_fft = fft(HRIR,44100)
#computing magnitude, tested with sinusoid,...