Hilbert Transform FIR Filter

A Hilbert Transform FIR filter produces approximately a 90 degree shift of frequencies in the input signal over a certain range of frequencies..

To design an Hilbert Transform FIR filter, Typically, a low-pass filter is designed, although the gain at zero frequency must be zero, so three-bands might be used for the low-pass filter, with the first band having a relatively small transition region.

The resulting filter is antisymmetric, and thus has linear phase response with frequency.

For a filter with length N:

h(k) = -h(N-k)

k = 0, 1, 2, ... N - 1

For an odd-length filter, the center coefficient is zero.