where represents the scale parameter and represents the delay parameter, each from the left to right channel, for some source . We refer to and together as the

After collecting many such estimates, the DUET system prepares a two-dimensional histogram whose peaks in space should reveal the mixing parameters for each of the sources. To demix the sources, DUET considers the set of parameter estimates a second time after the source mixing parameters are estimated from the histogram. It then assigns each point in time-frequency space to the source whose mixing parameters are closest to that estimated for the time-frequency point. To do this, a variety of matching schemes may be used. We have presented delay and scale subtraction scoring (DASSS) [2], which is similar to a method presented recently by the original DUET authors in [1]. In DASSS, we define a set of functions such that:

and the mixing parameters are always treated as known quantities. If in fact exactly one source, , is active at a given frequency bin in a given frame, it may be shown that our model predicts:

where

We now observe that we may similarly predict the DASSS function values when two sources and are active:

We now make an important observation. If we know how and are distributed, we then know how , , and are distributed. (In general, we will see that distributions on and may be practically estimated from knowledge about a musical or speech source, such as its range and loudness. Distributions on and are not informative, and thus we will use the set , rather than the sets or as our DASSS data.) Below, we will exploit our knowledge of the DASSS data in a Bayesian context to determine if (and which) two sources are most likely active. Much as we know how the DASSS data functions will behave for the two source case, it may also be shown [6] that we can predict the values for the DUET data given by equation 3 in the same case. It is not practical, however, to exploit this data, as logistics and computation quickly become prohibitive [6]. We therefore focus our efforts on DASSS data below.