Given that the Walsh transform performs operations with the boolean function and a Walsh matrix, how can the Walsh spectrum be interpreted? Specifically, if I were to use the Walsh function for searching non-random sequences, how would I be able to determine that the sequence is non-random given the Walsh spectrum? Is there an analogous result such as what the Fourier transform does to decompose signals that can be visibly seen in the Fourier spectrum?
Let us say you are given this dot product, how would I be able to interpret the result? Only answer the last question.