1. Lecture 2 Data and Signals
Soutenance de thèse vendredi 24 novembre 2006, Lorient
Lecture 2
Data and Signals

2. ANALOG AND DIGITAL
Data can be analog or digital. The term analog data refers to information that is continuous; digital data refers to information that has discrete states. Analog data take on continuous values. Digital data take on discrete values.

3. Analog and Digital Data
Data can be analog or digital.
Analog data are continuous and take continuous values.
Digital data have discrete states and take discrete values.

4. Comparison of analog and digital signals
Signals can be analog or digital. Analog signals can have an infinite number of values in a range; digital signals can have only a limited number of values.

5. Periodic and aperiodic Signals
Both analog and digital signals can be of two forms: periodic and aperiodic (non-periodic) signals.
A periodic signal consists a continuously repeated pattern.
The completion of one full pattern is called a cycle.
A period is defined as the amount of time (expressed in seconds) required to complete one full cycle.

6. Periodic and aperiodic Signals
An aperiodic signal changes constantly without exhibiting a pattern or cycle that repeats over the time.

7. Analog Signals
Analog signals can be classified as simple or composite.
A simple analog signal or sine wave, cannot be decomposed into simpler signals.
A composite analog signal is composed of multiple sine waves.

8. SINUSOIDAL SIGNAL FREQUENCY AMPLITUDE PERIOD (in sec) PHASE
Radians/sec
Hertz (cycles/sec)
PERIOD (in sec)
AMPLITUDE
Magnitude
PHASE

9. Figure 1 Two signals with the same amplitude and phase, but different frequencies

10. Table 1 Units of period and frequency but different frequencies

11. Example 1
The power we use at home has a frequency of 60 Hz. The period of this sine wave can be determined as follows:

12. The period of a signal is 100 ms. What is its frequency in kilohertz?
Example 2
The period of a signal is 100 ms. What is its frequency in kilohertz?
Solution
First we change 100 ms to seconds, and then we calculate the frequency from the period (1 Hz = 10−3 kHz).

13. Frequency
Frequency is the rate of change with respect to time.
Change in a short span of time means high frequency.
Change over a long span of time means low frequency.

14. If a signal does not change at all, its frequency is zero.
Note
If a signal does not change at all, its frequency is zero.
If a signal changes instantaneously, its frequency is infinite.

15. Phase describes the position of the waveform relative to time 0.
Note
Phase describes the position of the waveform relative to time 0.

16. Figure 2 Three sine waves with the same amplitude
and frequency, but different phases

17. We know that 1 complete cycle is 360°. Therefore, 1/6 cycle is
A sine wave is offset 1/6 cycle with respect to time 0. What is its phase in degrees and radians?
Solution
We know that 1 complete cycle is 360°. Therefore, 1/6 cycle is

18. EXAMPLE of SINUSOID
Given the Formula
Make a plot

19. Formula defines A, w, and f
PLOT COSINE SIGNAL
Formula defines A, w, and f

20. PLOTTING COSINE SIGNAL from the FORMULA
Determine period:
Determine a peak location by solving
Zero crossing is T/4 before or after
Positive & Negative peaks spaced by T/2

21. EXAMPLE of SINUSOID
Given the Formula
Make a plot

22. Basic properties of the sine and cosine functions

23. Some basic trigonometric identities