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In The Leading Edge tutorial article Phase and the Hilbert transform (Purves 2014), there is the following line:
So we apply a Hilbert transform by multiplying all negative frequencies by i and all positive frequencies by -i, leaving any DC component untouched.
I have two questions following this:
1) What is the DC component?
2) What is the significance of not affecting any DC component?
The 'DC Component' is a standard term used to describe the mean energy of a signal ( https://en.wikipedia.org/wiki/DC_bias ), which in the frequency domain corresponds to the component of 0 frequency. The DC component does not depend on the time -- while the other frequencies 'wiggle' around it. In seismic signals I think we don't generally have a DC components: the signal moves around a point of 0 pressure/displacement.
The authors then make their statement in a bit of an awkward way in my opinion. What they mean, is that the Hilbert transform applied to any 'DC component' is 0: thrown away!
