<p>As the harmonic analysis associated with the modified Whittaker transform has been extensively investigated and has witnessed a remarkable development, it is natural to study several aspects of the time-frequency analysis associated with the Whittaker convolution operators (WCO). Knowing the fact that the study of the time-frequency analysis is both theoretically interesting and practically useful, this article aims to explore two other aspects of time-frequency analysis associated with WCO, namely spectral analysis associated with concentration operators and spectrogram analysis. As an application, we obtain some results concerning the Whittaker heat operator and the Whittaker Poisson integral.</p>