Cone-kernel representation versus instantaneous power spectrum

The Cone-kernel representation (CKR) and the instantaneous power spectrum (IFS) are two time-frequency representations (TFRs) where the cross-terms are localized in the region of auto-terms. Exploring their relationship for discrete sequences, we show that the IFS kernel is only two extreme terms of the CKR kernel. Further comparing other properties of these two TFRs, viz., invertibility, aliasing, and noise robustness, we show that there is aliasing in some transform domains for signals sampled at Nyquist rate and that the CKR has better noise robustness than the IFS.