Is it possible to sketch a bode plot for a discrete-time transfer function?
In linear, time-invariant, continuous time systems, the transfer function \$H(s) \$ is a broken rational function in s. We obtain the complex frequency response through the substitution \$s=j\cdot \omega\$. In this case it is rather easy to find the asymptotic behaviour of the system and to sketch the bode diagram.

In linear, time-invariant, discrete time systems, the transfer function \$H(z) \$ is a broken rational function in z. We obtain the complex frequency response through the substitution \$s=e^{j\cdot \omega \cdot T_S}\$. Since this relationship is non-linear, there are no straight lines as asymptotes.

However, if one examines the zeros and poles of the time-discrete system, it is possible to predict the behavior of the system for frequencies between 0 and \$\frac{f_S}{2}\$ (or rather between \$-\frac{f_S}{2}\$ and \$+\frac{f_S}{2}\$) . Imagine the poles as very high mountains in the complex z-plane and the zeros as deep valleys, and then take a walk along the unit circle. This should give you a good feeling for how the system behaves.