Filter Bank Multicarrier (FBMC) is emerging as a better alternative to the Orthogonal Frequency Division Multiplexing (OFDM) in next generation wireless multicarrier systems. For robust performance under doubly dispersive channels, the prototype filter in FBMC systems must be isotropic and orthogonal in time and frequency. The existing design methods for prototype filter design are the Extended Gaussian Function (EGF) design based on Zak transform and Weighted HermitePulse (WHP) design. In this paper, it is attempted to design the prototype filter by performing time frequency analysis on the Ambiguity function of isotropic Hermite pulses. The Filter coefficients are obtained as the weighted sum of the Hermite pulses and constrained optimization is performed to find out the weights. An alternative objective function and optimization procedure is used in the present study which yield better results compared to conventional WHP problem. The orthogonality and isotropic conditions of the designed filter is compared with the conventional filters using Ambiguity plots. © 2013 IEEE.