Incorporation of the linear time-varying filter and, its Zadeh's generalized transfer function concepts to the derivation of the Capon's minimum-variance spectral estimator leads to a new, bilinear, cross-term suppressed and alias-free time-frequency representation (TFR) that has a higher resolution than the spectrogram with the same window width. Time-variant autocorrelation function of the nonstationary signal of interest is employed in this proposed TFR. By adopting an approximation for time-variant autocorrelation functions, we obtain another new, bilinear, parameterized TFR related to the spectrogram, the frequency resolution of which can be adjusted by varying its parameter for a fixed window width. We compare resolution and cross-term suppression properties of these proposed TFR's with other basic bilinear TFR's, via simulations on synthesized signals. Then, by incorporating polynomial-phase kernel functions to the Capon's estimator, we propose new bilinear signal representations for the analysis of constant-Amplitude polynomial-phase signals and apply them to interference excision in direct-sequence spread-spectrum communications. (C) 2002 Elsevier Science B.V. All rights reserved.