High energy physics experiments require on-the-fly processing of signals from many particle detectors. Such signals contain a high and fluctuating rate of pulses. Pulse shape hints particle type, and the amplitude relates to energy of the particle, while pulse occurrence times are needed for event reconstruction. Traditionally, these parameters have been extracted with the help of complete racks of dedicated electronics. Our FPGA design on a general-purpose DAQ card does real-time pulse detection and high-precision curve fitting. It greatly shrinks required equipment in terms of form factor, cost, power usage, and setup time. Unlike traditional systems, we can handle bursts of back-to-back pulses, pulses as narrow as 6 ns and at rates over 1M pulses per second. We have a novel scalable architecture that combines pipelining and parallelism. Moreover, the parallel part of the architecture uses loop pipelining in each of its interleaved identical parallel processors (IIPPs). An IIPP is a specialized CPU, which executes nested loops, with number of iterations that varies from pulse to pulse. IIPPs are fed data from a FIFO by a priority encoder based dispatcher. Number of IIPPs can be calculated to meet any pulse rate and average pulse width. The architecture is flexible enough to work with a variety of curve fitting algorithms.