A fast electrostatic diagnostic and analysis scheme on nanosecond pulsed beams in the keV energy range has been developed in the Malmberg-Penning trap ELTRAP. Low-noise electronics has been used for the detection of small induced current signals on the trap electrodes. A discrete wavelet-based procedure has been implemented for data postprocessing. The development of an effective electrostatic diagnostics together with proper data analysis techniques is of general interest in view of deducing the beam properties through comparison of the postprocessed data with the theoretically computed signal shape, which contains beam radius, length, and average density as fit parameters.