Desired order continuous polynomial time window functions for harmonic analysis

An approach for the construction of a family of desired order continuous polynomial time window functions is presented without self-convolution of the parent window. The higher order of continuity of the time window functions at the boundary of the observation window helps in suppressing the spectral leakage. Closed-form expressions for window functions in the time domain and their corresponding Fourier transform are derived. The efficacy of these new window functions in discerning the weak signal is demonstrated by computer simulations.