Time-frequency kernel design for sparse joint-variable signal representations

Highly localized quadratic time-frequency distributions cast nonstationary signals as sparse in the joint-variable representations. The linear model relating the ambiguity domain and time-frequency domain permits the application of sparse signal reconstruction techniques to yield high-resolution time-frequency representations. In this paper, we design signal-dependent kernels that enable the resulting time-frequency distribution to meet the two objectives of reduced cross-term interference and increased sparsity. It is shown that, for random undersampling schemes, the new adaptive kernel is superior to traditional reduced interference distribution kernels.