Lecture 2 Data and Signals

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Presentation transcript:

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

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.

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.

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.

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.

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

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.

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

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

Table 1 Units of period and frequency but different frequencies

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:

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).

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.

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.

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

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

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

EXAMPLE of SINUSOID Given the Formula Make a plot

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

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

EXAMPLE of SINUSOID Given the Formula Make a plot

Basic properties of the sine and cosine functions

Some basic trigonometric identities