In the frequency domain, the Hilbert transform changes the sign of the
frequency content on the negative side of the spectrum. The
simplest example is sine/cosine. The Hilbert transform of a sine
wave is a cosine wave and vice versa. These signals together are
considered a Hilbert pair. Just like in the simple sine/cosine
case, where cos^2 + sin^2 = 1, the same is true for any Hilbert pair.
Since any signal can be represented as a sum of sines and cosines, then
the Hilbert transform will generate a signal where each sine is matches
with a cosine function and every cosine function is matches with a sine
function. So if you take your original signal and make it the
real part of a complex signal and take the Hilbert transformed signal
and make it the imaginary part of a complex signal (the form is called
an 'analytic signal'), then the resulting magnitude signal should be
easier to deal with when trying to do peak detection, which is the
whole point of the process.
Randall Pursley