EECS20N: Signals and Systems

Mixed Systems

Mixed systems combine time-based signals with event sequences where time-based and event-based systems interact as peers.

For example, the classic moving average cross-over method, popular on Wall Street, tells when to buy and sell stocks by comparing short-term and long-term trends. A short-term moving average might detect short-term trends, while a long-term moving average might detect long term trends. This method compares them, and if the short-term trend is more sharply upward than the long term trend, a buy signal is generated. If the short term trend is more sharply downward than the long term trend, a sell signal is generated. A system implementing this is shown below:

The input is a discrete-time signal

price: IntegersReals

The input to the state machine is a tuple of discrete-time signals

(x, y) ∈ [IntegersReals] × [IntegersReals]

The output is an event sequence

action: Integers → {buy, sell, absent}

Notice that the guards on the transitions represent rather large sets, since the input alphabet is very large. A typical execution of this system is shown below: