This research is on numerical methods for digital logic synthesis based on spectral information of the logic description. The approach is to use the BDD description of the circuits to develop efficient methods for computing the spectral coefficients. Because of the numerical nature of the algorithms, design optimizations can be included in the synthesis process, rather than later. Theoretical results are being derived and used to implement a new class of synthesis algorithms that are suitable for incorporation into existing design environments. The algorithms are being tested on industry benchmarks.