1. Area-Effective FIR Filter Design for Multiplier-less Implementation Tay-Jyi Lin, Tsung-Hsun Yang, and Chein-Wei Jen Department of Electronics Engineering National Chiao Tung University, Taiwan {tjlin, thyang, cwjen}@twins.ee.nctu.edu.tw

2. In this paper We propose a complexity-aware quantization algorithm of FIR filters, which enables designers to explicitly trade quantization error for simpler implementations The proposed algorithm precisely distributes a pre-defined addition budget among the filter coefficients with successive approximation and common subexpression elimination

3. Outline Preliminary  Quantization by Successive Coefficient Approximation  Common Subexpression Elimination Complexity-Aware Coefficient Quantization Simulation Result Conclusion

4. Quantization by Successive Approximation* * D. Li, Y. C. Lim, Y. Lian, and J. Song, “A polynomial-time algorithm for designing FIR filters with power-of-two coefficients,” IEEE Trans. Signal Processing, vol.50, pp.1935-1941, Aug 2002

5. Constant Multiplications Consider a 4-tap FIR filter with the coefficients: h 0 =0.0111011, h 1 =0.0101110, h 2 =1.0110011, and h 3 =0.0100110 Common Subexpression across Coefficients (CSAC)

6. Common Subexpression Elimination Tabular form CSAC CSWC

7. Steepest-descent CSE Heuristic* * M. Mehendale, S. D. Sherlekar, VLSI Synthesis of DSP Kernels - Algorithmic and Architectural Transformations, Kluwer Academic Publishers, 2001

8. Outline Preliminary Complexity-Aware Coefficient Quantization Simulation Result Conclusion

9. Complexity-Aware Quantization Complexity-aware allocation of non-zero terms (with CSE) Improved SF Exploration (next page)

10. Improved SF Exploration Instead of the fixed 2 -w stepping from the lower bound, the next SF is calculated as denotes the magnitude of a coefficient denotes the distance to its next quantization level as the SF increases, which depends on the approximation scheme (e.g. rounding to the nearest value, toward 0, or toward -∞, etc).

11. Simulation Result For 16-bit wordlength and ±3dB acceptable gain, the improved SF exploration has 14,986 to 20,429 candidates depending on the coefficients, instead of 45,875 for all. CSE Improved SF Search

12. Conclusion Successive approximation with appropriate scaling can significantly reduce the addition complexity The proposed algorithm controls the CSE to incur the minimum additions during the successive approximation The improved SF exploration finds better or identical (but never worse) results with only 1/3 candidates The proposed complexity-aware quantization algorithm allows designers to explicitly trade quantization error for simpler implementations, which can also be easily  modified for goals other than small area (e.g. low power, etc), or  adapted to other implementation styles (e.g. FIR code generation for programmable processors)