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**Introduction to signals**

Lecture #1 Introduction to signals meiling chen signals & systems

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**signals Electrical signals Acoustic signals Video signals**

Signals are functions of independent variables that carry information. Electrical signals Voltages and currents in a CKT Acoustic signals Audio or speech signals Video signals Intensity variations in an image meiling chen signals & systems

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**Independent variables**

Can be continuous Can be discrete Can be 1-dimension, 2-D, …N-D For this course we focus on a signal 1-D independent variable which we called “time” Continuous time x(t) , t– continuous values Discrete time x[k], k– Integer values only meiling chen signals & systems

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**Continuous time (CT) signal**

Most of the signals in the physical world are CT signals—E.g. voltage & current, pressure, temperature, velocity, etc. meiling chen signals & systems

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**Discrete time (DT) signal**

Examples of DT signals in nature: DNA base sequence Population of the nth generation of certain species meiling chen signals & systems

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**Sampling Quantizing & encoding Continuous-time analog signal**

Discrete-time analog signal Quantizing & encoding Discrete-time digital signal 0001 meiling chen signals & systems

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**Classification of signals**

Continuous-time and discrete-time signals Even and odd signals Periodic and nonperiodic signals Deterministic and random signals Periodic signals meiling chen signals & systems

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Even signal odd signal meiling chen signals & systems

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**Elementary signals Exponential signals Sinusoidal signals**

Step function Rectangular pulse Impulse function Derivatives of the impulse Ramp function meiling chen signals & systems

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Exponential signals meiling chen signals & systems

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meiling chen signals & systems

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Step function Shift a meiling chen signals & systems

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Rectangular pulse meiling chen signals & systems

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Impulse function Amplitude width meiling chen signals & systems

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**Derivatives of the impulse**

meiling chen signals & systems

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meiling chen signals & systems

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Ramp function meiling chen signals & systems

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simple operation meiling chen signals & systems

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**Basic operations on signals**

Operations performed on dependent variables Amplitude scaling, Addition, Multiplication, differentiation Operations performed on independent variables Time scaling Reflection Time shifting meiling chen signals & systems

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Time scaling meiling chen signals & systems

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Reflection meiling chen signals & systems

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Time shifting meiling chen signals & systems

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**Precedence rule for time shifting and time scaling**

Example 1.5 find y(t)=x(2t+3) meiling chen signals & systems

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**Precedence rule for discrete-time signal**

meiling chen signals & systems

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