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Lecture #1. Introduction to signals. 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. Independent variables.
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Lecture #1 Introduction to signals signals & systems
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 signals & systems
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 signals & systems
Continuous time (CT) signal Most of the signals in the physical world are CT signals—E.g. voltage & current, pressure, temperature, velocity, etc. signals & systems
Discrete time (DT) signal • Examples of DT signals in nature: • DNA base sequence • Population of the nth generation of certain species signals & systems
Continuous-time analog signal Sampling Discrete-time analog signal Quantizing & encoding Discrete-time digital signal 0001 signals & systems
Classification of signals • Continuous-time and discrete-time signals • Even and odd signals • Periodic and nonperiodic signals • Deterministic and random signals Periodic signals signals & systems
Even signal odd signal signals & systems
Elementary signals • Exponential signals • Sinusoidal signals • Step function • Rectangular pulse • Impulse function • Derivatives of the impulse • Ramp function signals & systems
Exponential signals signals & systems
Step function Shift a signals & systems
Rectangular pulse signals & systems
Amplitude width Impulse function signals & systems
Derivatives of the impulse signals & systems
Ramp function signals & systems
simple operation signals & systems
Basic operations on signals • Operations performed on dependent variables • Amplitude scaling, Addition, Multiplication, differentiation • Operations performed on independent variables • Time scaling • Reflection • Time shifting signals & systems
Time scaling signals & systems
Reflection signals & systems
Time shifting signals & systems
Precedence rule for time shifting and time scaling Example 1.5 find y(t)=x(2t+3) signals & systems
Precedence rule for discrete-time signal signals & systems
