1. 1 Signals Signal  a transmitted effect conveying a message  A essential characteristic of a signal is that of change, since it must be capable of carrying information.  The change must be partly unpredictable.  It is also necessary to discuss the sinusoidal or pulse waveforms because they can be modulated to carry information. Signal can be: Temporal (function of time) Spatial (function of space) Spatial-temporal We use f(t) for all such signals

2. 2 Power and Energy The instantaneous power in a signal f(t) is defined as Because signal is usually represented by voltage or current, the corresponding units will be mean squares volts of mean squares amperes. (not Watts). The energy in small time interval δt is The total energy over all time: The mean power :

3. 3 Example: The rectangular pulse of height A and width θ, shown in the figure below has instantaneous power and energy It has zero mean power.

4. 4 Example: Repetitive pulses So the pulses have finite mean power Mean power is

5. 5 Signal types in terms of energy of power: (i)Transient signals: finite energy, zero mean power, usually last for a finite of time (ii)Continuous signals: finite mean power but infinite energy, last for all time repetitive random --- noise The signal in above example (repetitive pulses) is a finite mean power signal.

6. 6 Basic time and frequency average (i) Time domain average (a) Finite power signals

7. 7 The average of f(t) over the interval T is defined as

8. 8

9. 9 Example: Find the mean value, mean square value and variance for a sine wave

10. 10 Type of signalTime domain Finite power continuous (random) repetitive Finite energyArea, total energy E A summary

11. 11 T0T0 02θ Voltage A time Homework (p44, Sec 2.2.4, Question 1, Solution: p227—228) The Figure below shows a repetitive triangular waveform. (i)Find the area and total energy of one pulse of the waveform. (ii)Find the mean, mean square and variance of the repetitive waveform.