A new signal-processing technique based on analytic wavelet transform has been developed for detecting and differentiating temporally overlapped ultrasonic pulse trains that carry spatially distributed pressure information across an injection mold cavity. Compared to conventional wavelets that have a constant relative bandwidth at all the scales, the analytic wavelets investigated in this paper feature variable relative bandwidth, making it possible to simultaneously match the frequency characteristics of the ultrasonic pulse trains transmitted from the mold-embedded pressure sensors. As a result, more accurate detection and differentiation of the temporal and spectral information embedded within the ultrasonic pulse trains could be achieved. Theoretical framework for the analytic wavelet transform was established, and a multichannel ultrasonic pulse detector based on the complex Morlet wavelet was designed and experimentally investigated. The results have confirmed the effectiveness of the new signal-processing technique for on-line pressure sensing for injection molding process monitoring.