Discrete Hilbert Transform. Numeric Algorithms

The Hilbert and Fourier transforms are tools used for signal analysis in the time/frequency domains. The Hilbert transform is applied to casual continuous signals. The majority of the practical signals are discrete signals and they are limited in time. It appeared therefore the need to create numeric algorithms for the Hilbert transform. Such an algorithm is a numeric operator, named the Discrete Hilbert Transform. This paper makes a brief presentation of known algorithms and proposes an algorithm derived from the properties of the analytic complex signal. The methods for time and frequency calculus are also presented.