Fast recursive filtering with multiple slow processing elements

This paper describes systolic realizations of FIR and IIR digital filters with sample rates much higher than the speed of a single "arithmetic unit" or "processing element." The architecture trades increased throughput for increased latency. For IIR filters, the technique is based on block-state filter descriptions in which the state update matrix is converted to triangular or "quasi-triangular" form via a unitary or orthogonal similarity transformation. The effect of this transformation on the roundoff noise is examined in the Appendix. The latency, complexity, and suitability to VLSI implementations are considered, as well as an attractive application to interpolation and decimation.

[1]  Charles M. Rader,et al.  Effects of parameter quantization on the poles of a digital filter , 1967 .

[2]  B. Gold,et al.  A note on digital filter synthesis , 1968 .

[3]  L. Jackson.  Roundoff-noise analysis for fixed-point digital filters realized in cascade or parallel form , 1970 .

[4]  H. Voelcker,et al.  Digital filtering via block recursion , 1970 .

[5]  Leland B. Jackson,et al.  On the interaction of roundoff noise and dynamic range in digital filters , 1970, Bell Syst. Tech. J..

[6]  C. Burrus.  Block implementation of digital filters , 1971 .

[7]  G. Stewart.  Introduction to matrix computations , 1973 .

[8]  L. Rabiner,et al.  Some comparisons between fir and iir digital filters , 1974 .

[9]  C. Sidney Burrus,et al.  A unified analysis of multirate and periodically time-varying digital filters , 1975 .

[10]  S. Hwang.  Roundoff noise in state-space digital filtering: A general analysis , 1976 .

[11]  C. Burrus,et al.  Design and implementation of multirate digital filters , 1976 .

[12]  Clifford T. Mullis,et al.  Synthesis of minimum roundoff noise fixed point digital filters , 1976 .

[13]  L. Rabiner,et al.  Further considerations in the design of decimators and interpolators , 1976 .

[14]  S. Hwang.  Minimum uncorrelated unit noise in state-space digital filtering , 1977 .

[15]  Sudhir Ahuja,et al.  Effective Pipelining of Digital Systems , 1978, IEEE Transactions on Computers.

[16]  S. Mitra,et al.  Block implementation of recursive digital filters--New structures and properties , 1978 .

[17]  Allen G. Lindgren,et al.  Optimal synthesis of second-order state-space structures for digital filters , 1979 .

[18]  C. Barnes,et al.  Block-shift invariance and block implementation of discrete-time filters , 1980 .

[19]  C. Barnes,et al.  Finite word effects in block-state realizations of fixed-point digital filters , 1980 .

[20]  Allen G. Lindgren,et al.  Fast state-space decimator with very low round-off noise , 1981 .

[21]  J. Zeman,et al.  Fast Digital Filters with Low Round-Off Noise , 1981 .

[22]  Jean-Marc Delosme,et al.  Highly concurrent computing structures for matrix arithmetic and signal processing , 1982, Computer.

[23]  H. T. Kung.  Why systolic architectures? , 1982, Computer.

[24]  Chrysostomos L. Nikias,et al.  Fast block data processing via a new IIR digital filter structure , 1984 .

[25]  T. Barnwell,et al.  Increasing the parallelism of filters through transformation to block state variable form , 1984, ICASSP.

[26]  Thomas Kailath,et al.  Orthogonal digital filters for VLSI implementation , 1984 .

[27]  Edward A. Lee,et al.  On quantization effects in state-variable filter implementations , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.