Multicore DSP

4Numerical issues

CHAPTER MENU

1. 4.1 Introduction
2. 4.2 Fixed‐ and floating‐point representations
   1. 4.2.1 Fixed‐point arithmetic
      1. 4.2.1.1 Unsigned integer
      2. 4.2.1.2 Signed integer
      3. 4.2.1.3 Fractional numbers
   2. 4.2.2 Floating‐point arithmetic
      1. 4.2.2.1 Special numbers for the 32‐bit and 64‐bit floating‐point formats
3. 4.3 Dynamic range and accuracy
4. 4.4 Laboratory exercise
5. 4.5 Conclusion
6. References

4.1 Introduction

The majority of digital signal processing (DSP) algorithms are based on the dot product (dotp; ). The dotp is an approximation of , which means that by moving to the digital domain we have already started introducing errors. These errors come from the sampling rate, and that is not a problem if the application’s bandwidth can be handled by the processor and the other errors come from the fact that numbers cannot be represented with an infinite number of bits. Depending on the application, the dotp function can be implemented in fixed‐ or floating‐point arithmetic. For applications that require high dynamic precision and accuracy, floating‐point arithmetic is the best choice. However, it is important to note that even with floating‐point arithmetic, calculation errors are unavoidable since processors have a limited number of bits. When dealing with multicores, the effect of parallelising ...