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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