For the FIR Hilbert transformer we will use an odd length filter which is
computationally more efficient than an even length filter. Albeit even
length filters enjoy smaller passband errors. The savings in odd length
filters is a result that these filters have several of the coefficients that
are zero. Also, using an odd length filter will require a shift by an
integer time delay, as opposed to a fractional time delay that is required
by an even length filter. For an odd length filter, the magnitude response
of a Hilbert Transformer is zero for w=0 and w=π. For even length filers the
magnitude response doesn't have to be 0 at π, therefore they have increased
bandwidths. So for odd length filters the useful bandwidth is limited to
0 < w < π.
- https://en.wikipedia.org/wiki/Analytic_signal --> Smith, J.O. "Analytic Signals and Hilbert Transform Filters", in Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications, Second Edition