Charge sharing and migration of scattered and fluorescence photons in photon counting detector (PCD) degrade the detector's energy response and cause a single photon to be potentially counted as multiple events in neighboring pixels, leading to correlations of signal and noise. Signal and noise correlations in conventional linear, space-invariant imaging can be usefully characterized by the frequency dependent detective quantum efficiency, DQE(f). The situation is complicated in the PCDs by the spectral dimension. We analyze DQE(f) of CdTe PCDs using a spatial domain method starting from a previously described computation of spatio-energetic cross talk. DQE(f) is estimated as the squared signal-to-noise ratio of the estimate of the amplitude of a small-signal sinusoidal modulation in the object at a frequency f by a given system compared to that with an ideal detector. DQE(f) for spectral and effective monoenergetic imaging are estimated using a multi-pixel Cramer-Rao lower bound for CdTe detectors of different pixel pitch. For a 120 kVp incident spectrum, DQE(0) for a spectral task was ~18%, 25% and 34% for 250 μm, 500 μm and 1 mm pixels, respectively. Positive correlation between same basis material estimates in neighboring pixels from the spatio-energetic cross-talk causes this effect to have least impact at the detector's Nyquist frequency. For effective monoenergetic imaging, DQE(0) at the optimal energy is relatively tolerant of spectral degradation (85-92% depending on pixel size), but is highly dependent on effective energy, with maximum variation (in 250 μm pixels) of 25-85% for effective energies between 30 to 120 keV.