DFT spectrum filtering

A.E. Kahveci and E.L. Hall (see IEEE Trans. Comput., vol.C-23, no.9, p.976-81, Sept. 1974) introduced the concept of filtering discrete Fourier transform (DFT) spectra in the Walsh sequency domain. This is accomplished by finding a real and block-diagonal Walsh filter matrix G_w in the Walsh domain that performs the sample filtering operation as the prototype complex diagonal Fourier filter matrix G_f in the Fourier domain. The present authors provide additional information on the structure of G_w and generalize some results by C.J. Zarowski and M. Yunik (see ibid., vol.ASSP-33, p.1246-52, Oct. 1985). They consider a more general class of transforms, the T transforms, and the structure of the resulting T transform filter matrices G _t. Examples of T besides T=W are considered, such as the Harr transform and fourth-order Chrestenson transform. The implementation of the presented DFT spectrum filtering techniques using linear systolic arrays is briefly considered