Kernel-based estimators for the Kirkwood-Rihaczek time-frequency spectrum

In this paper, we examine kernel-based estimators for the Kirkwood-Rihaczek time-frequency spectrum of harmonizable, nonstationary processes. Based on an inner product consideration, we propose and implement an estimator for the Kirkwood-Rihaczek spectrum. The estimator is constructed from a combination of the complex demodulate with a short-time Fourier transform. Our proposed estimator is less computationally intensive than a theoretically equivalent, known estimator. We compare and test the results of the proposed estimator with an existing estimator from a Matlab time-frequency toolbox on simulated and real-world data. We demonstrate that the proposed estimator is less sensitive to unwanted cross-terms, and less affected by edge effects than the Matlab time-frequency toolbox estimator.