Cross-Terms and Spectral Leakage Minimization in Time-Frequency Distribution

Non-stationary signals in several applications appear sparse in the time-frequency (TF) domain. In this letter, we optimize a quadratic TF distribution (QTFD) versus its kernel by exploiting this property by maximizing power per nonzero components in the TFD domain. This approach reduces the number of large cross-terms (CTs) values while preserving auto-terms. This optimization is conducted by introducing an efficient approximation of l(0) and l(1) norm without any assumption about auto-terms' locations and CTs in the TF domain. The proposed TFD exhibits superior performance in instantaneous frequency (IF) estimation and fewer CTs than the state-of-the-art TFDs.