# What is the relationship between a NIZK protocol and a digital signature scheme?

I am reading about the Fiat-Shamir heuristic to take a $\Sigma$-protocol into a non-interactive zero-knowledge proof (NIZK). I am now wondering whether there is a relationship between a NIZK proof and a digital signature scheme?

Specifically, can we take a NIZK proof obtained from applying Fiat-Shamir to a $\Sigma$-protocol and turn it into a digitial signature scheme? (Are there specific requirements for the underlying $\Sigma$-protocol?)