1. 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

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

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

4. 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)

5. 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 []

6. 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

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

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

9. Transformations
Transformations of the independent variable
Time Shift

10. Transformations
Time reversal

11. Transformations
Time scaling

12. Transformations
Example

13. 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