  In this work, the optimization of the analog transmit waveform for joint
delay-Doppler estimation under sub-Nyquist conditions is considered. Based on
the Bayesian Cram\'er-Rao lower bound (BCRLB), we derive an estimation
theoretic design rule for the Fourier coefficients of the analog transmit
signal when violating the sampling theorem at the receiver through a wide
analog pre-filtering bandwidth. For a wireless delay-Doppler channel, we obtain
a system optimization problem which can be solved in compact form by using an
Eigenvalue decomposition. The presented approach enables one to explore the
Pareto region spanned by the optimized analog waveforms. Furthermore, we
demonstrate how the framework can be used to reduce the sampling rate at the
receiver while maintaining high estimation accuracy. Finally, we verify the
practical impact by Monte-Carlo simulations of a channel estimation algorithm.
