WRITING AND COMPILING DSP ALGORITHMS IN AN ASYNCHRONOUS. APPLlCATIVE LANGUAGE. Frcericks, M.; Kno ll, A. A TOPOLOGICAL METHOD FOR ...
PROCEEDINGS OF INTER NATIO NAL CO NFERE NCE O N
SIGNAL PROCESSING Oct. 26 -30, 1993, Beljlng, C hina V 01.
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Edited by Yuan Baozong
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INTERNATIONAL ACADEMIC PUBLISHERS
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Published and Distributed by International Academic Publishers
137 Chaonei Dajie, Beijng 100010 the People's Republic or China
Copyright
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1993 by International Academic Publishers Technical Program Committee ofICSP'93
The book has been photographically reproduced from the best available copy . The papers were not refereed but were reviewed for their technical contents. Editing was restricted to matters of format. general organization and retyp ing . The editors assume no responsibility for the accuracy. completeness or usefuln ess of the information disclosed in this volume. Unauthorized use might infringe on privately owned patents of publication right. For permission to reprint or otherw ise use information from the papers . please contact Prof. Yuan Baozong. Northern Jiaotong University . editor of the book .
First edition 1993 Edited by Yuan Baozong
Proceedings oflnternational Conference on Signal Processing (ICSP'93)
ISBN 7-80003-281-7/TN • 23 Printed by the Printing House of China Building Industry Press
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INTERNATIONAL CONFERENCE ON SIGNAL PROCESSING SPONSORED BY
Chinese Institute of Electronics (CIE)
. CO-SPONSORED BY
The Institution of Electrical Engioneers (lEE) Union Radioscientifique Internationale (URSn IEEE Signal Processing Society IEEE Beijing Section National Natural Science Foundation of China CIE Committee for URSI IEEE Computer Society Beijing Chapter IEEE SP Society Beijing Chapter
ORGANIZED BY
CIE Signal Processing Society
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ICSP'93 Conference . Committee
Conference Chairman:
Zhang Yanzhong, China
Co-Chairmen:
T.S. Huang, D.S.A. Hiroya Fujisaki, Japan Ke Youan, China Yuan Baozong, China
Advisors:
Lou Peilin, China Cheng Mingde, China Chen Fangyun, China Technical rro~ram Committee Chairman: Yuan Baozong, China Co-chairman: K.T. Park Korea
Local Organizlng Committee
Sha Zong, CIE China Zhou Mengqi, CIE, China Wei Futong, China
Financial Committee
Secretaries
Mr. Ruan Qiuqi, China Ms. Tang Xiaofang, China Mr. Qiu Zhengding, China Ms. Fang Min, China
Cheng Qiansheng, China Publication Committee Han Yuxian, China
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The Technical Program Committee of ICSP'93 CHAIRMAN: Yuan Baozong, China CO -CHAIRMAN: K . T . Part, Korea
He Zhenya, China MEMBERS:
H.T.Kung T.S.Huang M.R. Sehroeder K.R .Rao P.M.Grant A.G . Constantinides J.S.D. Mason Ernst Luder K.M . Won g Y. Neuvo Hiroya Fujisaki R.M . Ha ralick C1audo M oraga Claude GUEGUEN Yuri V Gu lyaev M.Kaveh ph. W. Bcsslich Wan -ChiSIU Y.T. Chen A.N .Venetsanopou!os Petros Maragos Chrysostomos L. Nik ias Kyu Tae Park M.H.Er K.F. Lee T.S. Durrani D. Bttcr M. Hunt S. Furui M.N .S. Swamy Larry Dooley AloisKnoll HongYan J. ~ittler R.J. Jannarone
Cheng Qiansheng Zhang Xianda Mao Shiyi Li Changli ZhuWeiming Zeng Yifang Lin Maoyong KeYouan Mo Fuyuan CaiDefu Run Qiuqi Yuan Baozong WuJingtang Wang Kaix i Wang Qingbao Zhang Yanzhong Mao Erke WuGuowei He Zhenya Han Yux ian Li Qihu Hou Chaohuan Zhao Rongehun Han Yuxian
U.S.A. U.S.A. Germany U.SA. U.K . U.K. U.K. Germ any Canada Finland Japan U .S.A. Germ ary France Russia
U.S.A . Germany Hongkong Canada Canada U.S.A. U.S.A. Korea Singapore U.SA. U.K. U.S.A. U.K . Japan Canada U.K . Germany Australia U.K . U.S.A. - vi -
China China China China China China China China China China China China China China China China China China China China China China China China
Contents Vol.!
A. DIGITAL SIGNAL PROCESSING (DSP) SEVERAL TliviE-VARYING SIGNAL,PROCESSING METHODS AND THEIR.
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APPLICATIONS IN ENGINEERING Geng, Z.M.; Zhang, J.H.; He, D.G.
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A METHOD OF APPLICATION OF FIR FILTER TO HIGH PRECISION DIGITAL DELAY Zhao, I.W.; Ma, V .L.; Zhang, Y.W. A SYSTEM WITH TWO CHANNELS AT DIFFERENT RESOLUTIONS FOR. . . . . . . . . . . . . .
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DETECTING SPIKE BASED ON THE HAAR-W AVELET TRANSFORM Tang, Z.W.; Isbii, N.H. A NOVEL DECONVOLUTION ALGORITHM. . . . . . . . . . . . .
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Wang,X.Z. ON THE CONSIDERATION OF THE GENERALIZED SHORT TIME DFT AND
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ITS APPLICATION TO THE HILBERT TRANSFORMER Kisbi, M .; Y oshida, T.
STUDY ON EIGENSPECTRUM OF SPACE-TIME 2-D CLUTTER COVARIANCE
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... . . . . . . . . .
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. . . . . . . . . . . . ..
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MATRIX Chen, X .C. e,
FADING NOISE REDUCTION EFFECT THROUGH THE SHORT TIME DFT COMPANDER
Kisbi, M.; Yuan, X.H. A NEW SYSTOLIC ARRAY FOR DISCRETE HARTLEY TRANSFORM Zhao, Z .J.; Qian, H .S. USING MARTINGALE REPRESENTATIONS TO ADAPT MODELS FOR
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NON-LINEAR FILTERING Hetzheim, H . MIN-MAX SIGNAL DESIGN FOR DETECTION SUBJECT TO LINEAR
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DISTORTION Rippin, B.; Weinstein, E.
AN EFFICIENT METHOD OF USING HIGH-LEVEL-LANGUAGE ON DIGITAL
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.. .. . . . . . . . .
44
SIGNAL PROCESSORS
Zbao, T .; Cbcn, Y.;Cheng, W.D. LEE MEDIAN FILTER
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and stopband (wJ . -Maximum attenuation in passband (a ,,) and minimum attenuation in stopband (a J . The output data are the zeros, the poles and the scaling factor of the transfer function Htz) . Also, you can change the cutoff frequencies by applying a first-order frequency transformation. If you want a bandpass filter a second-order frequency transformation have to be applied. The realization of the transfer function H(z) is based on the state-space representation of the filter' and. in the following, we present roundoff noise results of some statespace realizations (structures) implemented by digital systems. We have considered the minimum roundoff noise structure (optimal structure). block-optimal structures and the direct structure. The output roundoff noise power for each filter was obtained by the computation of formulas (also tested by computer simulations), and presented in tables or curves (only state-variables nodes are consider in the computation of the output roundoff noise). Now, we comment on the results for low-pass and bandpass filters with the following parameter values: is the output roundoff noise power (noise variance). supposing a white sequence of unitpower at the filter input. -w, is the passband cutoff frequency of a low-pass filter. ~Wo.:I and W ,,2 are the lower and the upper passband cutoff frequencies of a bandpass filter. -a; is the maximum attenuation (ripple) of the passband (a ,=O.5 dB). -n is the filter order (n = 4 , 8, 12). Also. we consider 16-bit fixed-point arithmetic and singleprecision accumulators (rounding after multiplications).
-er
1. Optimal state-space structures In Fig.I , the straight lines 01 , 0 2 and 0 3 correspond to optimal structures and DJ. D2 and D3 curves correspond to direct ones (the respective filter orders are n = 4, 8 and
12). For bandpass filters, w,,=0.51l" and w" sweeps from 0 to O.5 1r ~ and the bandwidth is Wc2-W d - As can be seeing from Fig. I , the roundoff noise power of optimal structures is independent of the position of the cutoff frequencies (w, or Wc! and Wc:2) ; on the other hand, the roundoff noise
power of direct structures increases to infinite as the
bandwidth decreases to zero or any cutoff frequency (wc. wc1 or W"2) approaches to 0 or 1r. Empirical formulas can be given for low-pass filters: -For elliptic and Chebyshev filters u.' .; u,' + IOlog( n(n+ 1)/6). n =2,3 •. .. , 16 (u.' in dB) -For Butterworth u.' ~ u,' + 7.610g(n(n+l )/ 6) . n=2. 3, . .. ,16 (u.' in dB) For bandpass filters, obtained from low-pass filters by frequency transformations, the theoretic relation is verified : u,.' = u.'+ I0I0g(2 (2n+ I)/ (n + I», n= 1.2.3•... (u.' in dB) being a..2 the roundoff noise power for the low-pass filter of order n, and 0"2n2 the noise power of the corresponding bandpass filter of order 2n. Consequently, for elliptic and Chebyshev filters, the empirical formula of roundoff noise power of low-pass filters is valid also for bandpass filters.
power of direct structures increases to infinite as the bandwidth decreases to zero or any cutoff frequency approaches to 0 or to il'". If single-precision accumulators are used the blockoptimal structure can be less noisy than the optimal one, and the difference increases with the filter order. For example, for elliptic and Chebyshev filters, the optimal structure has roundoff noise power greater than the block-optimal parallel structu re; but the optimal structure is better than the blockoptimal cascade. On the other hand. for Butterwo rth filter , the block-optimal cascade is better than the optimal structure. Moreover, block structures have less computatinal complexity than optimal state-space one; and block-d irect structures have less computational complexity than blockoptimal ones. Elliptic and chebyshev filters, realized with optimal (and block-optimal) structure. have similar roundoff noise power for the same filter order and passband ripple. Finally. for bandpass filters of narrow passband realized in block-direct structures, the roundoffnoise power is very low, in contrast to the direct structures, whose roundoff noise is very high.
2. Bloc-optimal structures.
REFERENCES.
Roundoff noise power for bandpass filters realized with block structures are presented in Fig.2. The filter orders are: n=4 (or i=l ) and n= 8 (or i= 2). Continuous lines (a., b, and C;, i = I . 2) correspond to block-optimal structures and the discontinuous curves (d;, e, and f;, i=l , 2) correspond to block-direct structures. The structures are parallel and cascade with second-order sections, being the realization of each section both optimal and direct structure. The optimum pole-zero pairing for minimum noise bandpass filters in cascade structure is the minimum distance criterion', as in low-pass filters. On the other hand, criteria for the optimum section ordering in cascade structure are not known; also, there is no relationship with the section ordering of the corresponding low-pass filter' . In Fig.2 , the line b, (i = 1, 2) corresponds to the best orde ring of the cascade. and line c;) i = l , 2) to the worst (the other cases are in between). . For elliptic and Chebyshev filters, parallel structures are better.than cascade ones, for Bunerworth filters cascade structures are bener than parallel ones. Although, empirical formulas of the roundoff noise power can be given for low pass filters' realized in cascade structures, it is not possible presently to give formulas for bandpass filters. If double-precision accumulators were used, the optimal structure would have always lower roundoff noise power than block-optimal structures; butthe latter have less operation s (4.5n multiplications) than the former «n+ 1)' multiplications , where n is the filter order) CONCLUSIONS In this paper, results of roundoff noise power for low-pass and bandpass filters were presented. The roundoff noise power of optimal structures is independent of the locations of the cutoff frequencies; however, the roundoff noise
1. R.A. Roberts and C.T. Mullis, Digital Signal Processing. Reading, MA: Addison-Wesley, 1987. 2. B.O. Rao, "Floating-point ar ithmetic and digital filters". IEEE Trans . Signal Processing, v eil. 40, pp. 85-95. Jan. 1992 . 3. L. Montgomery Smith, B.W. Bomar , R.D. Joseph and C.G.-J . Yang. "Floating-point roundoff noise analysis of second-order state-space digital filter structures". IEEE Trans. Circuits Syst. 11: Analog and Digital Signal Processing. Vol. CAS-39 , pp. 90-98, Feb . 1992. 4. J .L. Sanz-Gonzalez, J .c. Herranz-Tores and F. L6pezFerreras, "Fixed and floating point realizations for low roundoff noise digital filters" Proc. IEEE 1992 International Symposium on Circuits and Systems (lSCAS'9 2), San Diego , California, May 1992. 5. J. L. Sanz-Gonzdlez, F. L6pez-Ferreras andD . Andina "Floating-point realizations for minimu m roundoff noise digital f il ters" Proc. European Association for Signal Processing Conference (EUSIPCO-92), Brussels. Aug. 1992. 6. J .L. Sanz-Gonzalez, J. C.Herr anz-Tort s and E. CaleroPerez . "Optimal structures for high speed and low roundoff noise digital filters" . Proc. IEEE 1991 International Conference on Acoustics, Speech andSignal Processing (ICASSP·9 1). Vol. 3 pp. 1897-1900 . Toronto, Canada , May 1991. 7. J.L. Sanz-Gonzalez, F. L6pez-Ferreras and D. Andina "Roundoff noise results on optimal and block-optimal digital filter structures ". 1993 IEEE Intern ational Symposium on Circuits and Systems (lSC AS'93), Chicago, lIIinois, May 3-6. 1993.
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