Unit1_Signals - EE3210 Signals and Systems Unit 1 Basic...

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EE3210 Signals and Systems Unit 1 Basic Concepts of Signals
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Unit 1: Basic Concepts of Signals 2 Classification of Signals Continuous-Time and Discrete-Time Signals Real-Valued and Complex-Valued Signals Periodic and Aperiodic Signals Even and Odd Signals Energy and Power Signals
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Unit 1: Basic Concepts of Signals 3 Continuous vs. Discrete Signals x( t ) t x[ n ] n Discrete-time Signal (independent variable: n, an integer ) Continuous-time Signal (independent variable: t, a real number ) x[n] is also referred as a sequence . Any particular one in x[n] is called a sample . (a). (b).
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Unit 1: Basic Concepts of Signals 4 Real and Complex Signals Examples of real signals: cos t t 2 Examples of complex signals: 2 t 2 –3tj cos t + j sin t Euler’s formula: e jt = cos t + j sin t Very Important! Remember it.
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Unit 1: Basic Concepts of Signals 5 Periodic and Aperiodic Signal IF x(t) is periodic with period T, then x(t) = x(t+T) for all t IF x[n] is periodic with period N, then x[n] = x[n+N] for all n ( N: integer ) Fundamental period (T 0 or N 0 ) : the smallest positive values of periods for which the above equations hold.
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Unit 1: Basic Concepts of Signals 6 Fundamental Frequency For a periodic signal, its fundamental frequency is defined as f 0 = 1/T 0 . Its fundamental radian frequency is defined as ω 0 = 2 π f 0 = 2 π / T 0 . For brevity, radian frequency is often referred to as frequency.
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7 Example Consider the continuous-time signal sin t . Is it periodic? If yes, what is its fundamental period? what is its fundamental frequency?
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This note was uploaded on 11/22/2009 for the course ELECTRONIC EE3210 taught by Professor Sungchiwan during the Spring '09 term at École Normale Supérieure.

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Unit1_Signals - EE3210 Signals and Systems Unit 1 Basic...

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