Virtual analog synthesis requires bandlimited source signal algorithms. An efficient methodology for the task expresses the traditionally used source waveforms or their time-derivatives as a sequence of bandlimited impulses or step functions. Approximations of the ideal bandlimited functions used in these quasi-bandlimited oscillator algorithms are typically linear-phase functions. In this paper, a general nonlinear-phase approach to the task is proposed. The discussed technique transforms an analog prototype filter to a digital filter using a modified impulse invariance transformation method that enables the impulse response to be sampled with arbitrary sub-sample shifts. The resulting digital filter is a set of parallel first- and/or second-order filters that are excited with short burst-like signals that depend on the offset of the waveform discontinuities. The discussed approach is exemplified with a number of design cases, illustrating different trade-offs between good alias reduction and low computational cost.