Wigner cross-products encode relative phases
James B. Lee · The Journal of the Acoustical Society of America · 2016
Two distinct kinds of elements comprise the Wigner time-frequency distribution. First are elements occurring at the actual times and frequencies present in the signal: call these “actual” elements. Second are elements occurring at the arithmetic mean of the actual elements: call these “ephemeral” elements. The actual elements essentially are a power spectrum resolved in time and frequency; always they are positive. The ephemeral elements, sometimes called “cross-products,” can be positive, negative, both, or zero, depending on the relative phases of the actual elements; they encode phase information necessary to complete time-frequency representation of all information in the original signal.