In this article, we optimize the kernel of a time-frequency distribution (TFD) for a specific class of signals with some instantaneous frequency (IF) patterns, such as linear frequency modulated (LFM) and sinusoidal frequency modulated (SFM) signals. We introduce an IF estimator of such patterns by maximizing the integration of the local signal-to-noise ratio (LSNR) in the time-frequency (TF) domain over the curves of possible patterns by using an initial kernel. We then maximize the integrated LSNR by optimizing the kernel function by using the estimated IF. This approach provides a signal-dependent kernel in the time-delay domain (TDD), which can be used to reestimate the IF more accurately. Our experimental results for linear and sinusoidal frequency modulation reveal that our optimized signal-dependent TFD kernel significantly outperforms well-established TFDs in the IF estimation, while significantly reducing the number and impacts of the cross-terms (CTs), especially for crossing component signals.