1. ECE 1100: Introduction to Electrical and Computer Engineering David R. Jackson Professor, ECE Dept. Spring 2008 Notes 9 Sinusoidal Signals t v(t)v(t)

2. Basic Facts Sinusoidal waveforms (waves that vary sinusoidally in time) are the most important types of waveforms encountered in physics and engineering.  Most natural sources of radiation (the sun, etc.) emit sinusoidal waveforms.  Most human-made systems produce sinusoidal waveforms (AC generators, microwave oscillators, etc.)  Most communications is done via sinusoidal waveforms that have been modulated, either in an analog fashion (such as AM or FM) or digitally.

3. General Sinusoidal Waveform A = amplitude of sinusoidal waveform  = “radian frequency” of sinusoidal waveform [radians/s]  = phase of sinusoidal signal [radians] t v (t)v (t) A -A

4. Period of Sinusoidal Wave T = period (cycle) of wave [s] = time it takes for the waveform to repeat itself. In this example, T = 0.5 [ s ]. t [s] v (t)v (t) T 0.5 1.0 1.5

5. Frequency of Sinusoidal Wave f = frequency = # cycles (periods) / s Units: Hz = cycle/s In this example, f = 2 Hz f = 1/T [Hz] cycles/s = 1 / (s/cycle) t [s] v (t)v (t) 1.0 0.5 1 [s] 1.5

6. Radian Frequency Since the cosine function repeats after 2 , we have t v (t)v (t) T

7. Radian Frequency (cont.)  = 2  f [rad/s] Hence: or

8. Summary t v(t)v(t) A -A  = 2  f [rad/s] f = 1/T [Hz]