This paper presents a nonparametric method for estimating waveforms of event-related signals embedded in additive noise. The signals have transient character with varying shapes and arrival times. The estimation method is based on a series expansion of the signal by a set of basis functions. Using a template that contains a priori information, two sets of basis functions are designed by means of one uniform and one nonuniform bandpass filter bank. Then, signal-dependent basis functions are obtained. When no a priori information about the signal is available, signal-independent basis functions are constituted by the impulse responses of the subfilters. Delayed copies are created for each basis function with which time jitter in arrival time of the signal can be handled. The method gives a robust estimate of the waveform of transient signals having unknown waveforms and arrival times since no model assumptions are needed. One application is discussed through examples and compared with the estimate, which is obtained by the Karhunen-Loeve expansion.