A method of identifying a first peak signal corresponding to a first part of a sample from among other peak signals of other parts of the sample, the method comprising, at a computer system: receiving a data signal from a polymerase chain reaction experiment involving the sample, the data signal having an amplitude that varies over time, wherein the data signal comprises a plurality of overlapped peaks at different times; transforming the data signal to obtain a two-dimensional array of coefficients corresponding to localized functions, wherein transforming the data signal to obtain a coefficient in the two-dimensional array comprises computing a convolution of the data signal and a respective localized function having a time location and a time scale factor; identifying a first time region corresponding to a first peak of the first peak signal, wherein a first boundary of the first time region is a local minimum between the first peak and a second peak; removing the coefficients of the two-dimensional array corresponding to localized functions with time locations within the first time region; calculating parameters of a cut function by: creating an artificial data signal from a first set of overlapping predetermined peak signals; for each of the overlapping predetermined peak signals, computing a recovered peak by computing an artificial background signal and subtracting the artificial background signal from the artificial data signal; determining differences between the recovered peaks and the overlapping predetermined peak signals; and using the differences in a regression analysis to determine the parameters of the cut function; determining new coefficients for the two-dimensional array using the cut function; using the new coefficients to obtain an altered two-dimensional array; performing an inverse transform of the altered two-dimensional array to obtain a background signal; and subtracting the background signal from the data signal to obtain the first peak signal corresponding to the first part of the sample in the PCR experiment. receiving a data signal from a polymerase chain reaction experiment involving the sample, the data signal having an amplitude that varies over time, wherein the data signal comprises a plurality of overlapped peaks at different times; transforming the data signal to obtain a two-dimensional array of coefficients corresponding to localized functions, wherein transforming the data signal to obtain a coefficient in the two-dimensional array comprises computing a convolution of the data signal and a respective localized function having a time location and a time scale factor; identifying a first time region corresponding to a first peak of the first peak signal, wherein a first boundary of the first time region is a local minimum between the first peak and a second peak; removing the coefficients of the two-dimensional array corresponding to localized functions with time locations within the first time region; calculating parameters of a cut function by: creating an artificial data signal from a first set of overlapping predetermined peak signals; for each of the overlapping predetermined peak signals, computing a recovered peak by computing an artificial background signal and subtracting the artificial background signal from the artificial data signal; determining differences between the recovered peaks and the overlapping predetermined peak signals; and using the differences in a regression analysis to determine the parameters of the cut function; creating an artificial data signal from a first set of overlapping predetermined peak signals; for each of the overlapping predetermined peak signals, computing a recovered peak by computing an artificial background signal and subtracting the artificial background signal from the artificial data signal; determining differences between the recovered peaks and the overlapping predetermined peak signals; and using the differences in a regression analysis to determine the parameters of the cut function; determining new coefficients for the two-dimensional array using the cut function; using the new coefficients to obtain an altered two-dimensional array; performing an inverse transform of the altered two-dimensional array to obtain a background signal; and subtracting the background signal from the data signal to obtain the first peak signal corresponding to the first part of the sample in the PCR experiment.