1. A method of digital signal decomposition to identify components of a source signal from one or more musical instruments comprising: obtaining a first representation of the source signal, during a first time period, which is a mixture of a first active signal and one or more second active signals, wherein the first active signal and second active signal are audio signals from the one or more musical instruments; calculating a time-frequency transformation of the first representation; obtaining a second representation of the source signal, during a second time period, which comprises the first active signal captured in isolation of at least one of the one or more second active signals present in the first representation; calculating a time-frequency transformation of the second representation, wherein the first and second time periods do not overlap; appending the time-frequency transformation of the second representation to the time-frequency transformation of the first representation to form an extended time-frequency transformation; applying a decomposition technique to the extended time-frequency transformation to extract decomposed components of the source signal; and audibly outputting a combination of one or more time domain signals related to the decomposed components of the source signal.