What are some good tools which will simplify the process of designing and modeling analog signals? I am currently using Mathematica for modeling signal behavior, but that requires me to define a new model for every new piece of functionality (e.g. a low-pass filter). Are there any tools that could help me out?
SPICE (or any derivative of it) would be the best choice if you are doing circuit simulation as part of the process, also take a look at MATLAB with Simulink.
Does CircuitLab have the functionality you need? You can use voltages from ground to model analog signals. We've got arbitrary Laplace transform blocks to handle your linear filter needs, and furthermore we have arbitrary behavioral sources if you want to apply nonlinearities anywhere in your signal chain. Piecewise-linear and step functions for inputs, plus time domain and frequency domain analysis modes.
Take a look at this circuit for a closed-loop multi-domain simulation, including a thermal model (modeled as R and Cs) plus a controller with nonlinearities:
If not, let us know what features you'd need!