A new discrete-time analytic signal for reducing aliasing in discrete time-frequency distributions

The commonly used discrete-time analytic signal for discrete time-frequency distributions (DTFDs) contains spectral energy at negative frequencies which results in aliasing in the DTFD. A new discrete-time analytic signal is proposed that approximately halves this spectral energy at the appropriate discrete negative frequencies. An empirical comparison shows that aliasing is reduced in the DTFD using the proposed analytic signal rather than the conventional analytic signal. The time domain characteristics of the two analytic signals are compared using an impulse signal as an example, where the DTFD of the conventional signal produces more artefacts than the DTFD of the proposed analytic signal. Furthermore, the proposed discrete signal satisfies two important properties, namely the real part of the analytic signal is equal to the original real signal and the real and imaginary parts are orthogonal.