EECS20N: Signals and Systems

Discrete events

  • Information is often represented as a sequence of symbols. A binary file of length n is a sequence b1, b2, , bn, where each bi is a binary symbol, 0 or 1. An English text of length n is a sequence of words w1, w2, , wn . The file is a function

    filename: {1, 2, , n} → Bin

    The text is a function

    text: {1, 2, , n} → EnglishWords

    A data signal is a sequence

    data: {1, 2, , n} → SymbolSet

    where SymbolSet is an appropriate set of symbols eg. Bin, EnglishWords. Data signals arise in computer storage, computer communication networks.

  • An event stream or event trace is a record of the significant events that occur in a system of interest. The trace of events in a phone call might be

    LiftHandset, HearDialTone, DialDigits, HearTelephoneRing,

    or, if the other phone is busy, the trace might be

    LiftHandset, HearDialTone, DialDigits, HearBusyTone,

    An event trace is a sequence

    trace: {1, 2, , n} → EventSet

    The behavior of state machines is described by event traces.