Question

It is impossible to design an all-pass digital Hilbert transformer.

(a) True

(b) False

The question was asked in class test.

The origin of the question is Design of Hilbert Transformers topic in section Digital Filters Design of Digital Signal Processing

Answer 1

Right option is (a) True

The explanation: We know that when h(n) is anti-symmetric, the real valued frequency response characteristic is zero at ω=0 for both M odd and even and at ω=π when M is odd. Clearly, then, it is impossible to design an all-pass digital Hilbert transformer.