Astrophysical phenomena such as self-annihilation of primordial black holes (PBHs), gamma ray bursts (GRBs), and supernovae are expected to produce single dispersed pulses detectable in the low end of the radio spectrum. Analysis of these pulses could provide valuable information about the sources, and the surrounding and intervening medium. The Eight-meter-wavelength Transient Array (ETA) is a radio telescope dedicated to the search for these pulses in an 18 MHz bandwidth centered at 38 MHz. ETA consists of 10 dual-polarized active dipoles providing an all-sky field of view. This thesis describes the results of a search campaign using ETA, namely, a Crab giant pulse (CGP) search. CGPs are already known to exist, and thus provide an excellent diagnostic for system performance. We found 11 CGP candidates in 14 hours of data. Although there has not been a single compelling detection (signal-to-noise ratio > 6), our analysis shows that at least a few of these candidates may be CGPs. We also explain the analysis preparation for PBH and GRB searches. Additionally, we describe the instrument and a software "toolchain" developed for the analysis of data that includes calibration, radio frequency interference (RFI) mitigation, and incoherent dedispersion. A dispersed pulse simulation code was developed and used to test the toolchain. Finally, improvements are suggested.