Characterizing neuronal responses to natural stimuli remains a central goal in sensory neuroscience. In auditory cortical neurons, the stimulus selectivity of elicited spiking activity is summarized by a spectrotemporal receptive field (STRF) that relates neuronal responses to the stimulus spectrogram. Though effective in characterizing primary auditory cortical responses, STRFs of non-primary auditory neurons can be quite intricate, reflecting their mixed selectivity. The complexity of non-primary STRFs hence impedes understanding how acoustic stimulus representations are transformed along the auditory pathway. Here, we focus on the relationship between ferret primary auditory cortex (A1) and a secondary region, dorsal posterior ectosylvian gyrus (PEG). We propose estimating receptive fields in PEG with respect to a well-established high-dimensional computational model of primary-cortical stimulus representations. These ``cortical receptive fields'' (CortRF) are estimated greedily to identify the salient primary-cortical features modulating spiking responses and in turn related to corresponding spectrotemporal features. Hence, they provide biologically plausible hierarchical decompositions of STRFs in PEG. Such CortRF analysis was applied to PEG neuronal responses to speech and temporally orthogonal ripple combination (TORC) stimuli and, for comparison, to A1 neuronal responses. CortRFs of PEG neurons captured their selectivity to more complex spectrotemporal features than A1 neurons; moreover, CortRF models were more predictive of PEG (but not A1) responses to speech. Our results thus suggest that secondary-cortical stimulus representations can be computed as sparse combinations of primary-cortical features that facilitate encoding natural stimuli. Thus, by adding the primary-cortical representation, we can account for PEG single-unit responses to natural sounds better than bypassing it and considering as input the auditory spectrogram. These results confirm with explicit details the presumed hierarchical organization of the auditory cortex.