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Fixed-point refinement of digital signal processing systems

Fixed-point refinement of digital signal processing systems

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For the digital signal processing (DSP) part of mixed-signal systems, fixed-point arithmetic is favoured due to its high efficiency in terms of implementation cost, namely energy consumption, area and latency. Fixed-point arithmetic provides low-cost operators at the expense of an unavoidable error between the ideal precision values and the finite precision ones. With a careful data word-length (WL) optimisation process, the designer can safely profit from the inherent trade-off between implementation cost and computation accuracy. In this chapter, we describe in detail the different stages comprising the fixed-point conversion process (i.e. dynamic range evaluation, WL optimisation, and accuracy evaluation) and propose practical solutions to address each stage.

Chapter Contents:

  • 8.1 Introduction
  • 8.2 Fixed-point arithmetic
  • 8.2.1 Fixed-point representation
  • 8.2.2 Format propagation
  • 8.2.2.1 Addition–subtraction
  • 8.2.2.2 Multiplication
  • 8.2.2.3 Division
  • 8.2.3 Quantisation process and rounding modes
  • 8.2.3.1 Truncation
  • 8.2.3.2 Conventional rounding
  • 8.2.3.3 Convergent rounding
  • 8.2.4 Overflow modes
  • 8.3 Architecture support for fixed point
  • 8.3.1 Fine-grained word-length operators
  • 8.3.2 Mid and coarse-grained word-length operators
  • 8.3.2.1 Multi-precision operations
  • 8.3.2.2 Exploitation of sub-word parallelism with SIMD
  • 8.4 Fixed-point conversion process
  • 8.5 Integer-part word-length selection
  • 8.5.1 Dynamic range evaluation
  • 8.5.1.1 Interval-based methods
  • 8.5.1.2 Statistical methods
  • 8.5.1.3 Stochastic methods
  • 8.5.2 IWL determination and insertion of scaling operations
  • 8.6 Fractional-part word-length determination
  • 8.6.1 Word-length optimisation
  • 8.6.1.1 Optimisation algorithms
  • 8.6.1.2 Comparison of optimisation techniques
  • 8.6.2 Accuracy evaluation
  • 8.6.2.1 Simulation-based approaches
  • 8.6.2.2 Analytical approaches
  • 8.7 Conclusion
  • References

Inspec keywords: digital signal processing chips; fixed point arithmetic; mixed analogue-digital integrated circuits; optimisation

Other keywords: digital signal processing systems; dynamic range evaluation; mixed-signal systems; fixed-point conversion process; energy consumption; fixed-point arithmetic; data word-length optimisation; fixed-point refinement

Subjects: Optimisation techniques; Digital signal processing chips; Digital signal processing chips; Digital arithmetic methods; Optimisation techniques

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