The emergence of cognitive radar has led to a considerable amount of research into optimizing a radar's waveform to achieve better performance for a desired task. Specifically, optimizing a waveform's energy spectrum to take advantage of interference, noise, and a target's scattering characteristics has led to a number of approaches for design. Noise radar has emerged as a desirable candidate for radar operation in a tactical environment due to its low probability of interception and detection (LPI/LPD) characteristics, along with the ease of wideband waveform generation. This paper attempts to take a step towards the development of a cognitive noise radar by combining these two areas of research. This is studied by looking at adaptive spectral shaping of noise radar pulses to achieve performance gains in the system. Techniques traditionally applied to stochastic process modeling are utilized to derive a pulse shaping filter that takes advantage of the at spectrum of a white noise pulse to shape it to the desired spectral mask.