One of the biggest challenges in FPGA programming is the process of quantizing mathematical operations to fixed-point for more efficient implementation.

This session teaches the fundamentals of the fixed-point number system and fixed-point arithmetic, along with considerations for targeting popular FPGA devices. These concepts are then reinforced through practical demonstrations, capped by walking through the process of quantizing a signal processing design.

Topics include:

• Fixed-point theory
  • Fixed-point number system
  • Mathematical range
  • Quantization error in the time and frequency domains
• Common functions
  • Arithmetic: square root, reciprocal, log2
  • Trigonometry: cosine, sine, atan2
  • Signal processing: FIR, FFT
• FPGA considerations
  • Targeting Xilinx and Intel devices
  • Maintaining precision
  • Using native floating point for full-precision calculations
• Example: communications packet detection
  • Matched filter
  • Peak detection
  • FPGA optimizations