In this report spectral estimation, using Poisson distributed time samples which have been time quantized, is considered. An expression for the probability density function for the time quantized Poisson samples is derived. For a large class of nonbandlimited spectral density functions the bias of the spectral estimates is determined and an asymptotic bound on the variance is also derived. Numerical analysis of the bias and variance bound is performed and graphs of the bias as a function of frequency are presented. Finally, examples of spectral estimates are given with varying degress of time quantization. Results show small amount of bias introduced into estimates and variance remains almost unaffected. The chief advantage of Poisson sampling theory is that it eliminates spectral aliasing on nonbandlimited and undersampled time series data. Time quantized Poisson data results from sampling constraints due to hardware implementation.