Asymmetric transmission of waves has received considerable attention in the last few decades, inspired by numerous applications in the domains of optics and wave communications. A possible way to achieve such asymmetry in wave propagation is through the violation of reciprocity. We explore asymmetric propagation in an acoustic diode (AD) made of two segments of equal sphere sizes but different elastic properties, in which both chains obey Hertzian's contact law. In the forward configuration, the first chain acts as the nonlinear medium, ensuring the suitable generation of a self-demodulated signal, while the second chain, made of soft spheres, provides the low-pass filter. It is shown that both large nonlinearity and low dispersion cause the smallest distortion of the wave envelope, therefore optimizing the transmission of information through the system.