Waveforms need to be quantitatively defined in many different ways.
Peak value: maximum instantaneous value
Peak to peak value: difference between maximum and minimum instantaneous values throughout the entire range
RMS value: room-mean-square. Provides power equivalent value as if the waveform was DC.
\(RMS = \sqrt{\frac{1}{T}\int^T_0 x^2(t)dt}\)
Frequency: repetition rate per second of a periodic waveform
Period: duration in seconds of a repetitive waveform
$$x(t + T) = x(t)$$
Power and Energy
Instantaneous power is always given by:
$$p(t) =v(t) i(t)$$
This result is simple but when discussing power consumption it is the average power that is needed.
To calculate average we first obtain the total energy used:
$$E = \int^T_0 v(t) i(t)dt$$
Then we simply divide by the time interval to obtain average power:
$$P = \frac{E}{T}$$
For DC voltage and current the integration simplifies into a multiplication, with the familiar:
$$E = VIT, P = VI$$
For a resisitive device one can use Ohm’s Law:
$$P = \frac{1}{T}\int^T_0 \frac{v^2(t)}{R}dt$$
This is the origin of the RMS value, such that:
$$P = \frac{V^2_{RMS}}{R}$$