ATPG patterns of a digital sequential circuit contain temporally and spatially ordered bits as well as random (or don't care) bits. We synthesize BIST hardware that mimics these characteristics by controlled mixing of spectral components and noise. A Hadamard digital wave generator circuit produces all required spectral sequences and a weighted pseudorandom bit generator provides random bits. While these two blocks serve the entire circuit under test, specific to each primary input are two small blocks, one that combines the required Hadamard sequences in proper proportions and the other a randomizer that adds the required amount of noise if necessary. As an example, the FlexTest ATPG produced 55110 patterns for s38417, detecting 15472 of 31180 stuck-at faults. Sixty four-thousand of our BIST patterns detected 17020 faults as compared to 4244 detected by a previously reported spectral BIST method utilizing similar hardware overhead.