Todays lecture Continuous and discretetime signals Distinction between

Today's lecture − Continuous and discrete-time signals § Distinction between discrete and digital § Examples − The sequence − Continuous and discrete-time systems § Notations § Examples − 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 2

Discrete-time signals − The value of signal exists only at equally spaced discrete points in time 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 6

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

Continuous and discrete time system − Examples of continuous and discrete-time systems Squaring System Differentiator System Accumulator System 8

Transformations − Transformations of the independent variable § Time Shift

Transformations § Time reversal

Transformations § Time scaling

Transformations § Example

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