proportional to the highest signal frequency. This time step is much smaller than the length Tsim of the entire simulation interval. As a consequence, the presence of widely spaced time constants forces SPICE- like simulation algorithms to take an enormous number of simulation steps. Hence, to cover the entire simulation interval, a SPICE-like simulator needs to take (2.5) finfo steps. With fcarrier/ finfo often being over 1000 and with, for bit error rate simulations, N being a million in order of magnitude, SPICE-like simulators are forced to take over a billion steps to complete a single simulation run. As a result, the simulation of a complete system architectures may take days or even weeks to complete. Both chapters 3 and 5 present methods that cope with this problem by means of models that keep slow-and fast-varying behavior explicitly separated. In this way, the situation in Fig. 2.8 is avoided. Wide separation of carrier and settling time constants is even a necessary condition for the oscillator modeling methods in chapter 5 to work properly. It is an excellent example on how building block characteristics that at first seem hamper efficient analysis, can be exploited to speed up simulation. 2.2.2.3 Stochastic behavior All physical systems, and, therefore, all telecom systems and their building blocks, have in common that they produce noise. For example, both thermal and 1/f noise occur in a wide variety of applications. Noisy signals, also called stochastic processes, are disturbances about which little information is available. Hence, they cannot be compensated for and, as a consequence, they cause data transmission errors. As it is the case for signal components due to nonlinear intermodulation, it is important to keep their magnitude small. Contrary to deterministic signals, the shape of a stochastic process n(t) is never known exactly. There is only a certain probability that a particular shape will occur. Stochas- tic processes are therefore characterized by probability density functions that quan