A 2-D digital filter design technique using separate approximation of phase and magnitude responses by denominator and numerator (original) (raw)
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Electronics and Communications in Japan (Part III: Fundamental Electronic Science), 1990
F a c u l t y of Engineering, Tohoku U n i v e r s i t y , Sendai, J a p a n 980 SUMMARY T h i s paper p r o p o s e s a new t e c h n i q u e f o r d e s i g n of separable-denominator two-dimens i o n a l d i g i t a l f i l t e r s (2DDF's) i n t h e f r equency domain. The t e c h n i q u e i s based on decomposing b o t h t h e t r a n s f e r f u n c t i o n of a separable-denominator 2DDF and t h e g i v e n 2DDF frequency domain s p e c i f i c a t i o n i n t o a product of two one-dimensional ones. By t h e s e decompositions, t h e d e s i g n problem of a separable-denominator 2DDF can b e reduced t o t h e d e s i g n of two I D D F -s .
Electronics and Communications in Japan (Part III: Fundamental Electronic Science), 1990
posed t o decompose 3-D a r r a y s i n image c o d i n g . I n t h e proposed m e t h o d , t h e g i v e n s p e c i f i c at i o n f o r t h e 3-D f i l t e r i s decomposed i n t o t h e s p e c i f i c a t i o n s f o r 1-D f i l t e r s u s i n g 3-D o u t e r p r o d u c t e x p a n s i o n and r e d u c i n g t h e des i g n of t h e 3-D f i l t e r t o t h a t of the 1-D f i l t e r s . When t h e g i v e n impulse r e s p o n s e spec i f i c a t i o n i s s y m m e t r i c a l , t h e computation r e q u i r e d f o r t h e d e s i g n i n t h e proposed method can b e r e d u c e d . 1. I n t r o d u c t i o n R e s e a r c h e r s i n the f i e l d s of dynamic e v e r , w i t h t h e r e c e n t development of t h e d i g it a l computer t e c h n o l o g y , one c a n e x p e c t t h a t 3-D s i g n a l p r o c e s s i n g c a n b e e x e c u t e d i n t h e n e a r f u t u r e w i t h a p r a c t i c a l p r o c e s s i n g speed. With t h e f o r e g o i n g a s t h e background, s t u d i e s h a v e been made on t h e d e s i g n of 3-D d i g i t a l f i l t e r s [ 2 % 81. The s t a b i l i t y c r it e r i o n f o r 3-D f i l t e r i s complex. A l a r g e amount of computation i s r e q u i r e d i n t h e des i g n . A s a r e s u l t of t i o n h a s a symmetry i n t h e proposed method, t h e computation i n t h e d e s i g n can b e reduced. The d i g i t a l f i l t e r d e s i g n e d by t h e proposed method b e l o n g s t o t h e s e p a r a b l e denominator t y p e * I n t h e f o l l o w i n g , components/elements of a v e c t o r a , m a t r i x A and 3-D a r r a y B are w r i tt e n a s a( z ) ,
IEEE Transactions on Signal Processing, 1991
It is shown that the singular-value decomposition (SVD) of the sampled amplitude response of a two-dimensional (2-D) digital filter possesses a special structure: every singular vector is either mirror-image symmetric or antisymmetric with respect to its midpoint. Consequently, the SVD can be applied along with 1-D finite-impulse response (FIR) techniques for the design of linear-phase 2-D filters with arbitrary prescribed amplitude responses which are symmetrical with respect to the origin of the (a1, a*) plane. In the second half of the paper, the well-known balanced approximation method is applied to linear-phase 2-D FIR filters of the type that may be obtained by using the SVD method. The method leads to economical and computationally efficient filters, usually infinite-impulse response filters, which have prescribed amplitude responses and whose phase responses are approximately linear.
Optimal parallel 2-D FIR digital filter with separable terms
IEEE Transactions on Signal Processing, 1997
. RMSE of the estimates of d 5 = 808 rad/s versus the peak SNR. The range of is [0.5 1 1.5 2 2.5]. f 4 = 353 Hz, d 4 = 117 rad/s are known a priori. N = 128: M = 20; 85; 64 is used, respectively, for the LCTLS-FLP method, the LCTLS-BLP method, and the HTLS(-PK) method (see ).
A Projection Technique for The Design of Fir Digital Filters.(Dept.E)
MEJ. Mansoura Engineering Journal, 2021
A method for synthesis of Chebyshev PIR digital filters is presented. The beat approximation in the chebyshev (Loo \ sense is obtained making use of the method of successive ?rojectione, waich redu.ces the problem to one of findine; a poir_t in the intersection of tJ. system of convex flets.. rhe rnetr.or. i~ fast converging and does not require solving a set of nonlinear equations as in otner minimax tecnniques. An e~emple is presented to illustrate the procedure aI.!.<! toe result;;, aJ.~e compared with a recently publ1sned minimax tecnnique. I. IRTRODUCTIOll: oeveral techniques have been developed for tne design of FIR digital iiI ters with ]!rescribed frequency response. iilllOfl,f, these techniques are: Windowing, frequency sampling and minimax appr oximation (11 , (2]. Each of these 'echniques has i oc own s"trenclth and weakness. J:o'or example; tne windowi!1g tecrtnique is tedious unless a closed forrr. expression for the l,.,1.::ldOw coefficients is found. The frequency sacnpliD.t:; tecnnqiue i;:; amenable only for f11ters having frequenoy responses tnat s;,re reasonably smooth. PreB~nt minircax techniques [lJ, [21 suer. as tne rtemez algorithm and its modifications require the 201uion of a aet of nonlinear equations to derive tile filtE:::" iI'€':-Gue~cy response. In addition, tne band edges il'! ~ne0e tecrm~ ques are not speci:fied by the a€:eigner. t.:..us leavir16 t;,"(~~. tr~r .. ~ ition bands unconstrained. This leaas to relatively :SJ.~;::B transition oands and .sometimes ul!desirable spikBS in ~;i.eSe ~)ands.
Optimal frequency domain design of two-dimensional digital IIR filters
IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP-95, Detroit, MI, 1995
A least-squares technique is presented for designing quarter-plane separable denominator 2-D IIR filters to best approximate prescribed frequency domain (FD) specification. It is shown that the FD error vector is linearly related to the 2-D numerator coefficients whereas the relationship with the 2-D denominators is quasi-linear. Furthermore, the numerator and denominator estimation problems are theoretically decoupleld. The quasi-linear relationship is used to formulate an algorithm for iterative estimation of the denominator. The numerator is found in one step using the estimated denominator. Computer simulations show the effectiveness of the proposed method and its superior performance compared to several existing methods.
1984_Signal Processing_Block 2D, vol. 7, pp. 135-149.pdf
A new structure for the block realization of IIR, 2-D digital filters is proposed. This approach is based on a matrix representation of 2-D convolutions and results in a 2-D state variable description with block feedback. The block recursive equation in a matrix form is first extracted for the quarter-plane filters and in the sequel it is extended in the most general and powerful case of half-plane filters. Finally the computational cost of the proposed method is studied in terms of the multiplication efficiencies. It is shown that the proposed block realization method can become more efficient for filters with orders exceeding approximately (5, 6), while the corresponding filters' order in the I-D case is 25. Therefore, the advantages of the 2-D block realization parallel the known advantages of block realization in the 1-D case and they are much more remarkable.