The subject of this paper is the direct identification of continuous-time autoregressive moving average (CARMA) models. The topic is viewed from the frequency domain perspective which then turns the reconstruction of the continuous-time power spectral density (CT-PSD) into a key issue. The first part of the paper therefore concerns the approximate estimation of the CT-PSD from uniformly sampled data under the assumption that the model has a certain relative degree. The approach has its point of origin in the frequency domain Whittle likelihood estimator. The discrete- or continuous-time spectral densities are estimated from equidistant samples of the output. For low sampling rates the discrete-time spectral density is modeled directly by its continuous-time spectral density using the Poisson summation formula. In the case of rapid sampling the continuous-time spectral density is estimated directly by modifying its discrete-time counterpart.