A new criterion is derived that relates the stability of two-dimensional recursive filters to the properties of its cepstrum. It provides a procedure for the decomposition of unstable recursive filters having nonzero, nonimaginary frequency response into stable recursive filters. The optimal solution of the decomposition problem is discussed, including numerical implementation and nonrecursive solutions. Several numerical examples show the potentialities and limitations of the rules for decomposition and for truncation of the operators.
[1]
G. Tolstov.
Fourier Series
,
1962
.
[2]
W. I. Smirnow, Lehrgang der Höheren Mathematik, Teil III, 2. 3. Aufl. XI + 599 S. m. 85 Abb. Berlin 1961. VEB Deutscher Verlag der Wissenschaften. Preis geb. DM 24,80
,
1962
.
[3]
J. Bednar,et al.
Stability of spatial digital filters
,
1972
.
[4]
Thomas S. Huang,et al.
Stability of two-dimensional recursive filters
,
1972
.
[5]
S. Treitel,et al.
Stability and synthesis of two-dimensional recursive filters
,
1972
.
[6]
Enders A. Robinson,et al.
Statistical Communication and Detection
,
1967
.
[7]
A. Oppenheim,et al.
Nonlinear filtering of multiplied and convolved signals
,
1968
.
[8]
Alan R. Jones,et al.
Fast Fourier Transform
,
1970,
SIGP.
[9]
J. Shanks.
RECURSION FILTERS FOR DIGITAL PROCESSING
,
1967
.