Did you know we can use formal mathematical proofs to verify a complex DSP design, from its ideal equation all the way down to the hardware gate level? It’s a powerful way to tackle the subtle but critical bugs that plague our work: unexpected overflows, cascading quantisation errors, and other finite wordlength effects that simulations can easily miss.
As engineers, we often rely on simulation to validate our designs, but this comes with limitations. A paper from IEEE Transactions explores that simulation provides only partial verification. This is especially true when some simulation software uses floating-point implementation, whereas actual DSP implementation is fixed-point. This means they can’t exhaustively prove that the FXP version correctly mirrors the FP algorithm for all possible inputs.
This is where the paper proposes an alternative: the formal verification of DSP designs using Higher-Order Logic (HOL). This framework models the entire DSP design flow as a series of mathematical theorems. It allows you to begin with the ideal algorithm using infinite-precision real numbers, formally analyse the transition to finite-precision arithmetic (both FP and FXP), and finally prove that the hardware implementation at the Register Transfer Level (RTL) correctly matches the specification.
You can formally prove the correctness of each translation step and, most importantly for anyone in acoustics or signal processing, create a mathematical proof that quantifies and bounds the roundoff errors introduced by the move from ideal numbers to finite hardware.
It’s an interesting reminder that formal methods can be a helpful tool for building robust and reliable systems where precision and correctness are non-negotiable.
Be sure to check the original paper at IEEE.