This paper investigates the problem of estimating the spectral power parameters of random analog sources using numerical measurements acquired with minimum digitization complexity. Therefore, spectral analysis has to be performed with binary samples of the analog sensor output. Under the assumption that the structure of the spectral power density of the analog sources is given, we investigate the achievable accuracy for power level estimation with likelihood-oriented processing. The discussion addresses the intractability of the likelihood with multivariate hard-limited samples by exploiting advances on probabilistic modeling and statistical processing of hard-limited multivariate Gaussian data. In addition to estimation-theoretic performance analysis, the results are verified by running an iterative likelihood-oriented algorithm with synthetic binary data for two exemplary sensing setups.