DOI link for Hilbert Transforms
Hilbert Transforms book
The Hilbert transformations are of widespread interest because they are applied in the theoretical description of many devices and systems and directly implemented in the form of Hilbert analog or digital ﬁlters (transformers). Let us quote some important applications of Hilbert transformations:
1. The complex notation of harmonic signals in the form of Euler’s equation exp( jvt)¼ cos(vt)þ j sin(vt) has been used in electrical engineering since the 1890s and nowadays is commonly applied in the theoretical description of various, not only electrical systems. This complex notation had been introduced before Hilbert derived his transformations. However, sin(vt) is the Hilbert transform of cos(vt), and the complex signal exp( jvt) is a precursor of a wide class of complex signals called analytic signals.