Question about Hilbert transform

1. What is the purpose of Hilbert transform?
2. Which of the following about Hilbert transform is not true?
3. What are the properties of Hilbert transform?
4. Why is Hilbert transform non causal?

What is the purpose of Hilbert transform?

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.

Which of the following about Hilbert transform is not true?

Hilbert transform does not change the magnitude spectrum of the signal.

What are the properties of Hilbert transform?

Properties of the Hilbert Transform

The same amplitude spectrum. The same autocorrelation function. The energy spectral density is same for both x(t) and ˆx(t). x(t) and ˆx(t) are orthogonal.

Why is Hilbert transform non causal?

Thus, the Hilbert transform is a non-causal linear time-invariant filter. degree phase shift at all positive frequencies, as indicated in (4.16). The use of the Hilbert transform to create an analytic signal from a real signal is one of its main applications.