Interval Arithmetic Requirements for Digital Signal Processor

1. Interval Arithmetic Requirements for Digital Signal Processor William Edmonson Hampton University Winser Alexander NC State University Esther Hughes Virginia Commonwealth University Clay Gloster Howard University

2. Outline • Digital Signal Processing • Applications • Digital Signal Processors • Importance of Interval Method • Interval - Digital Signal Processors • Conclusion Workshop on Reliable Engineering

3. Digital Signal Processing • Definition • Extraction of useful information carried by the signal • Transformation • Filtering • Estimation Workshop on Reliable Engineering

4. Digital Signal Processing • Applications • Transformation • Time-Frequency Analysis • Music/Video Coding • Filtering • Active Noise Cancellation • Speech Synthesis • Estimation • Direction of Arrival • Medical Imaging Workshop on Reliable Engineering

5. Digital Signal Processors • Definition • Special purpose processor designed to efficiently perform convolution and correlation operations, and fast I/O. • Multiply-Accumulate (MAC) where Workshop on Reliable Engineering

6. Digital Signal Processors • Important Features • Real-time operation of repetitive arithmetic operations • Reduced footprint • Reduced power • Examples • Cell phones • Audio equipment • Hearing aids Workshop on Reliable Engineering

7. General Purpose Processor • von Neumann Architecture • Single access to memory during each instruction cycle • Shared data and program memory Workshop on Reliable Engineering

8. Digital Signal Processor • Harvard Architecture • Multiple bus structure • Separate memory for data and program • Reduced optimized instruction set • Addition, Subtraction, Logical • Multiply-accumulate operation Workshop on Reliable Engineering

9. Digital Signal Processor • Modified Harvard Architecture Workshop on Reliable Engineering

10. Importance of Interval Methods to DSP • The control and analysis of numerical errors • Filtering • Estimation • Implementation of optimization methods that produce guaranteed estimates. • Large problem set of nonlinear estimation • Direction of Arrival (Sonar, RADAR) • Spectral Estimation (Harmonic Retrieval) • Neural Networks • Medical Image Reconstruction (PET) Workshop on Reliable Engineering

11. Importance of Interval Methods to DSP • Slow software implementation • General purpose processors • DSP’s • Lack of dedicated interval arithmetic based HW • Embedded computing • Wireless communication • Space exploration vehicles Workshop on Reliable Engineering

12. Interval Digital Signal Processor • Requirements • Modified Harvard Architecture • Interval multiply-accumulate in 1 instruction cycle • Directed rounding • Fixed-point arithmetic • Memory access of interval numbers in 1 instruction cycle Workshop on Reliable Engineering

13. Interval Digital Signal Processor • Arithmetic Logic Unit/Multiply Accumulator • 2 data busses • Simultaneous fetches of operands • B bits wide • 4 input data registers • X = [xlb,xub] Y = [ylb,yub] • 2 accumulators • Upper and lower interval results • 2 B bits wide Workshop on Reliable Engineering

14. Interval Digital Signal Processor • Saturation arithmetic • Overflow conditions • Directed rounding • Round towards + ∞ • Interval instruction set • Addition, subtraction, multiplication, multiply-accumulate • Logical operations Workshop on Reliable Engineering

15. Interval Digital Signal Processor • Interval Multiplication Workshop on Reliable Engineering

16. Interval Digital Signal Processor Workshop on Reliable Engineering

17. Conclusion • Outlined HW requirements for a fixed-point DSP • Future work is to implement on a FPGA • Initial work for full acceptance by signal processing community • Technology key across all areas of reliable engineering • Civil Engineering • Active Vibration Control • Mechanical/Aerospace Engineering • Robotic Vision and Guidance • Acknowledgements • Funding of this work is through a NASA-FAR grant. Workshop on Reliable Engineering