Question

A Hilbert transformer is a
(A) non-linear system (B) non-causal system
(C) time-varying system (D) low-pass system

Answer 1

the Hilbert transform is a specific linear operator that takes a function, u(t) of a real variable and produces another function of a real variable

Answer 2

Answer:

A Hilbert transformer is a a time varying system

Explanation:

Hilbert transform of a signal u(t) is defined as the transform which has the phase angle of all components of the signal shifted by ±90 degrees.

It takes a linear function u(t) of real variable and produces another function of real variable.

Properties of the Hilbert Transform

A signal u(t) and its Hilbert transform u^(t) have

• The same amplitude spectrum.

• The same auto correlation function.
• The energy spectral density is same for both u(t) and u^(t).
• u(t) and u^(t) are both orthogonal.
• The Hilbert transform of u^(t) is -u(t)
• If Fourier transform exist for a signal then Hilbert transform will also exists for energy and power signals.