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/sub w/ in the Walsh domain that performs the sample filtering operation as the prototype complex diagonal Fourier filter matrix G/sub f/ in the Fourier domain. The present authors provide additional information on the structure of G/sub 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/sub 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. >
[1]
Nasir Ahmed,et al.
On Notation and Definition of Terms Related to a Class of Complete Orthogonal Functions
,
1973
.
[2]
A.E. Kahveci,et al.
Sequency Domain Design of Frequency Filters
,
1974,
IEEE Transactions on Computers.
[3]
Christopher J. Zarowski,et al.
Spectral filtering using the fast Walsh transform
,
1985,
IEEE Trans. Acoust. Speech Signal Process..
[4]
H. E. Chrestenson.
A class of generalized Walsh functions
,
1955
.
[5]
J. Tukey,et al.
An algorithm for the machine calculation of complex Fourier series
,
1965
.
[6]
Thompson.
Fourier Transforms in VLSI
,
1983,
IEEE Transactions on Computers.
[7]
H. T. Kung.
Why systolic architectures?
,
1982,
Computer.
[8]
T. Natarajan,et al.
Cooley-Tukey-type algorithm for the Haar transform
,
1973
.