Question

If fl and fu are the cutoff frequencies, then what is the desired real valued frequency response of a Hilbert transform filter in the frequency range 2π fl < ω < 2πfu?

(a) -1

(b) -0.5

(c) 0

(d) 1

This question was addressed to me at a job interview.

My question comes from Design of Hilbert Transformers topic in chapter Digital Filters Design of Digital Signal Processing

Answer 1

Right choice is (d) 1

Best explanation: The bandwidth of Hilbert transformer need only cover the bandwidth of the signal to be phase shifted. Consequently, we specify the desired real valued frequency response of a Hilbert transformer filter is

H(ω)=1; 2π fl < ω < 2πfu

where fl and fu are the cutoff frequencies.