HIGH SPEED REALISATION OF DIGITAL FILTERS

Transcription

1 HIGH SPEED REALISATION OF DIGITAL FILTERS A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF PHILOSOPHY IN ELECTRICAL AND ELECTRONIC ENGINEERING AT THE UNIVERSITY OF HONG KONG BY TSIM TS1M MAN-TAT, JIMMY DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING UNIVERSITY OF HONG KONG JANUARY, 1989

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3 ABSTRACT A B S T RAe T Abstract of thesis entitled "High Speed Realisation of Digital Abstract of thesis entitled "High Speed Realisation of Digital Filters" submitted by Tsim Man-Tat, Jimmy for the degree of Master of Philosophy at the University of Hong Kong in January Filters" submitted by Tsim Man-Tat, Jimmy for the degree of Master of Philosophy at the University of Hong Kong in January In this thesis, systematic methods for realising high speed digital In this thesis, systematic methods for realising high speed digital filters using multiprocessing techniques shall be described. Two filters using multiprocessing techniques shall be described. Two classes of design methodologies for the realisation of one-dimensional classes of design methodologies for the realisation of one-dimensional (1-0) and two-dimensional (2-D) finite impulse response (FIR) digital (1-D) and two-dimensional (2-D) finite impulse response (FIR) digital filters, namely (i) linear or cyclic convolution in polynomial ring with filters, namely (i) linear or cyclic convolution in polynomial ring with the application of short convolution algorithms or transforms, and the application of short convolution algorithms or transforms, and (ii) block level systolic delayed multipath, are presented. block level systolic delayed multipath, are presented. Both classes of digital filter structures possess a high degree of parallelism and regularity and is therefore suitable for VLSI or multiprocessor implementation. The number of processing elements that can be incorporated-in the structure are greatly increased. Thus, high throughput ~hroughput improvement and multiprocessing efficiency can be achieved. (ii) Both classes of digital filter structures possess a high degree of parallelism and regularity and is therefore suitable for VLSI or multiprocessor implementation. The number of processing elements that can be incorporated. in the structure are greatly increased. Thus, high improvement and multiprocessing efficiency can be achieved. For the realisation of infinite impulse response (IIR) digital For the realisation of infinite impulse response (IIR) digital filters, direct application of the above high speed FIR digital filter filters, direct application of the above high speed FIR digital filter structures presents difficulty because of the inherent timing constraint structures presents difficulty because of the inherent timing constraint in the recursive loop of an IIR digital filter. With the efficient in the recursive loop of an IIR digital filter. With the efficient transformation method introduced in this thesis, the allowable transformation method introduced in this thesis, the allowable processing delays in the recursive loop of an IIR digital filter is processing delays in the recursive loop of an IIR digital filter is - i 1-

4 Abstract increased and hence relaxing the aforementioned timing constraint. increased and hence relaxing the aforementioned timing constraint. Using this transformation, the above high speed FIR digital filter Using this transformation, the above high speed FIR digital filter structures can then be applied to the realisation of both 1-0 and 2-D structures can then be applied to the realisation of both 1-D and 2-D IIR digital filters. The resulting IIR digital f'ilter structures also IIR digital filters. The resulting IIR digital filter structures also possess characteristics of high degree of parallelism and regularity, possess characteristics of high degree of parallelism and regularity, and high throughput improvement and multiprocessing efficiency. and high throughput improvement and multiprocessing efficiency. - iii i

5 REFERENCE [1] V. Cappellini, A.G. constantinides and P. Emiliani, Digital Digita7 filters fi7ters and their applications. app7ications. Academic Press, [2] K. Hayashi, K.K. Dhar, K. Sugahara and K. Hirano, "Design of high-speed digital filters suitable for multi-dsp implementation," IEEE Trans. Circuit and System, vol. CAS-33, pp , Jan [3] R.C. Agarwal and J.W. Cooley, "New algorithms for digital convolution," IEEE Trans. Acoustics, Speech and Signal Processing, vol. ASSP-25, pp , Oct [4] R.C. Agarwal and C.S. Burrus, "Fast one-dimensional digital convolution by multidimensional techniques," IEEE Trans. Acoustics, Speech and Signal Processing, vol. ASSP-22, pp. 1-10, Feb [5] H.T. Kung, "Why systolic architectures?", IEEE Computer Magazine, pp , Jan R.l -

6 Reference Reference [6] R.C. Agarwal and C.S. Burrus, "Number theoretic transforms to implement fast digital convolution," Proc. IEEE, vol. 63, pp , April [7] H.J. Nussbaumer, Fast Fourier transform and convolution algorithms. New York: Springer-Verlag, [8] R.E. Blahut, Fast algorithms for digital signal processing. Addison-Wesley Publishing Company, [9] S. Winograd, "On computing the discrete Fourier transform," Math. of Computation, vol. 32, pp , Jan [10] S. Winograd, "Arithmetic complexity of computations," CMS-NSF CBMS-NSF Regional Conf. Series Applied Math., Siam Publications #33, [11] R.E. Crochiere and L.R. Rabiner, Multirate Digital Signal Processing, Prentice Hall, Englewood Cliffs, NJ, [12] K.K. Dhar and K.Hirano, "A digital filter design algorithm suitable for multi-dsp implementation," Workshop digest of IEEE international workshop on digital signal processing, Kyoto, Japan, pp. 2g-1 to 2g-7, June R.2 -

7 Reference [13] W.D. W.O. Stanley, G.R. Dougherty and R. Dougherty, Digital Signal Processing. Reston Publishing Co. Ltd., 2nd edn, 1984, ch. 5, pp [14] S.K. Mitra and K. Hirano, "All digital N-path filter," Proc European Conf. on Circuits Theory and Design, pp , Sept [15] K. Sugahara, K. Hayashi, K. Hirano, and S.K. Mitra, "N-path digital filters," Proc. IEEE Int. Conf. on Acoust., Speech, and Signal Processing, March [16] R.C. Agarwal and C.S. Burrus, "Fast convolution using Fermat number transforms with applications to digital filtering," IEEE Trans. on Acoust., Speech, and Signal Processing, Vol. ASSP-22, pp , April [17] I.S Reed and T.K. Truong, "The use of finite fields to compute convolutions," IEEE Trans. on Information Theory, Vol. IT-21, pp , March [18] H.J. Nussbaumer, "Digital filtering using complex Mersenne transforms," IBM Journal of Research and Development 20, pp , Sept R.3 -