Matrix formulation of the discrete Hilbert transform
F. Burris · IEEE Transactions on Circuits and Systems · 1975
The discrete Hilbert transform (DHT) of a periodic sequence is interpreted as a matrix product\bar{\phi} = \bar{C}\bar{A}. A new singleequation form of the DHT operation for any number of sample pointsNis shown and is used to establish the unique properties of the coefficient matrix\bar{C}.\bar{C}is shown to be highly symmetric in nature, and the determination of the elements of\bar{C}is shown to require a minimum of computation; i.e., less thanNelements need to be computed for anN \times N\bar{C}matrix. For theNeven case, the relatively sparse nature of\bar{C}is established; i.e., at least half the elements of\bar{C}are zeros.