EECS20N: Signals and Systems

Data and Event Sequences

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. The file is a function

File: {1, 2, ... , N} → Binary

An English text with N words is a sequence w1, w2, ..., wN . The text is a function

EnglishText: {1, 2, ... , N} → EnglishWords

A data sequence is a signal

Data: {1, 2, ... , N} → SymbolSet

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

An event stream 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 stream is a function

EventStream: {1, 2, ... , N} → EventSet

The behavior of state machines is described by event streams.

In general a data sequence is a function

Data: Indices → SymbolSet

and an event stream is a function

EventStream: Indices → EventSet

where Indices is an ordered set of indices eg. {1, 2, 3, ... }