Part 1-Signals

Part 1-Signals - Introduction to Signals Signals 1-1 What...

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Signals 1-1 Introduction to Signals

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Signals 1-2 What is a signal? A signal is a physical phenomenon, a physical process, or a set of data, represented mathematically as a function of one or more independent variables. For this reason, we typically write a signal as x(t), where t in most of cases is interpreted as time. Examples: Closing prices of a stock market A function of time Music A function of time Picture A function of space Video A function of (…?)
Signals 1-3 An Example of a Signal Example 1: Stock Price

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Signals 1-4 More Examples Example 2: Picture
Signals 1-5 Continuous vs. Discrete Signals x( t ) t x[ n ] n Discrete-time signal (independent variable takes a discrete set of values: n, an integer ) Examples: computer data stream, time reading of a digital watch. Continuous-time signal (independent variable varies continuously: t, a real number ) Examples: voltage across a resistor, car Speed as a function of pedal pressure. x [ n ] is also referred as a sequence . Any particular one in x [ n ] is called a sample . (a). (b).

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Signals 1-6 Signals of Main Interest Periodic signals Polynomial signals
Signals 1-7 Periodic and Aperiodic Signal A continuous-time signal x(t) is said to be periodic with period T, if for all t, x(t) = x(t+T) holds for T>0. A discrete-time signal x[n] is said to be periodic with period N, if for all n, x[n] = x[n+N] for N>0 ( N: integer ).

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