The frequency-domain Prony method (FDPM) [Ando, IEEE Trans. Signal Process. 68, 3461-3470 (2020)] provides a novel and exact short-time, frequency-decomposed scheme for autoregressive model identification and sinusoidal parameter estimation with a superior statistical performance. By using it as localized estimation elements, we construct the time-frequency representation (TFR) of signals as the frequency-reassigned map of the damped sinusoidal parameters of their components. The FDPM for both single and multiple sinusoids is based on a small number of windowless Fourier coefficients of sampled sequence. Thus, a unified and flexible construction of resolution and decomposition structures including linear and log-linear frequency arrays and their combination is possible, and dense analysis along the time axis can be implemented without a significant increase in computational cost. Conditions for constructing the frequency-variant arrays are formulated. Two cooperative behaviors in the TFR are considered to find stable traces of frequencies and rapidly time-varying incidences and components. Several experiments are shown to confirm extended features and performances of the proposed TFR using musical, speech, and natural sound signals.