Today's lecture Continuous and discrete-time signals The sequence Distinction between discrete and digital Examples The sequence Continuous and discrete-time systems Notations Transformation of the independent axis Time Shifting Time Reversal Time Scaling Example Sinusoids

Continuous-time signals A value of signal exists at every instant of time Independent variable Independent variable

Discrete-time signals The value of signal exists only at equally spaced discrete points in time Independent variable Independent variable

Discrete-time signals Why to discretize How to discretize How closely spaced are the samples Distinction between discrete & digital signals How to denote discrete signals Is the image a discrete or continuous signal The image is generally considered to be a continuous variable Sampling can however be used to obtain a discrete, two dimensional signal (sampled image)

Continuous and discrete signals A continuous-time signal is represented by enclosing the independent variable (time) in parentheses () A discrete-time signal is represented by enclosing the independent variable (index) in square brackets []

Continuous and discrete signals Examples of continuous signals Speech, video, image The variation of atmospheric pressure, wind speed and temperature with altitude Examples of discrete signal Demographic data, weekly stock position of a company

Continuous and discrete time system Like signals we have continuous and discrete-time systems as well system system

Continuous and discrete time system Examples of continuous and discrete-time systems Squaring System Differentiator System Accumulator System

Transformations Transformations of the independent variable Time Shift

Transformations Time reversal

Transformations Time scaling

Transformations Example

A is the maximum amplitude of the sinusoidal signal Sinusoidal signals x(t) = A cos(ωt + Φ) A is the maximum amplitude of the sinusoidal signal ω is the radian frequency  is the phase shift