Hilbert transform with strange behavior

1. What does the Hilbert transform do to a signal?
2. How complex signal is generated using Hilbert transform?
3. Is Hilbert transform and Fourier transform are similar in characteristics?
4. What is the application of Hilbert transform?

What does the Hilbert transform do to a signal?

The Hilbert transform facilitates the formation of the analytic signal. The analytic signal is useful in the area of communications, particularly in bandpass signal processing.

How complex signal is generated using Hilbert transform?

When a real signal x(t) and its Hilbert transform y(t)=Htx are used to form a new complex signal z(t)=x(t)+jy(t) , the signal z(t) is the (complex) analytic signal corresponding to the real signal x(t) .

Is Hilbert transform and Fourier transform are similar in characteristics?

The Fourier transform is a way to analyze the frequency or wavenumber content of a signal. The amplitude tells you how pronounced (loud) a certain frequency is. The Hilbert transform is best viewed in terms of what it does in frequency space. In frequency space, it is the same as multiplying by −isgn(ω).

What is the application of Hilbert transform?

In addition to the MathML phase shift that it introduces between the real and imaginary parts, the Hilbert transform can be used in the theory of modulation to determine the amplitude modulation, phase modulation and frequency modulation of a time-dependent signal MathML.