Recent work has developed a modeling method applicable to certain types of signals having a "finite rate of innovation" (FRI). Such signals contain a sparse collection of time- or frequency-limited pulses having a restricted set of allowable pulse shapes. A limitation of past work on FRI is that all of the pulses must have the same shape. Many real signals, including electrocardiograms, consist of pulses with varying widths and asymmetry, and therefore are not well fit by the past FRI methods. We present an extension of FRI allowing pulses having variable pulse width (VPW) and asymmetry. We show example results for electrocardiograms and discuss the possibility of application to signal compression and diagnostics.