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This brief introduces a new method for sampling of transient analog waveforms based on the parallel exponential filters. The signal is fed to the parallel network consisting of resistor-capacitor (RC) circuits, outputs of which are simultaneously sampled. We show that N previous samples of the input signal can be reconstructed from single output samples of N parallel RC circuits. The parallel sampling method increases the sampling rate of the data acquisition system by a factor of N. In particular, the method is useful in increasing the sampling rate of the Flash-type analog-to-digital VLSI circuits. We present the parallel RC network, develop the reconstruction algorithm, and briefly describe a variety of applications such as measurement and reconstruction of pulses produced by ultrawideband transmitters, radiation detectors, and pulse lasers.