it is defined for one-variable signals. However, the monogenic signal can be extended to arbitrary number of variables in a straightforward manner, producing an -dimensional vector-valued function for the case of n-variable signals. See also Practical considerations for computing Hilbert transforms Negative frequency Applications Single-sideband modulation Quadrature filter Causal filter Notes References Further reading Leon Cohen, Time-frequency analysis, Prentice Hall, Upper Saddle River, 1995. Frederick W. King, Hilbert Transforms, vol. II, Cambridge University Press, Cambridge, 2009. B. Boashash, Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, Elsevier Science, Oxford, 2003. External links Analytic Signals and Hilbert Transform Filters Signal processing Time–frequency analysis Fourier analysis