chap 2. signals and spectra: useful wave characteristic

useful wave characteristic are the DC value, average power, and RMS value.


DC value

• the DC value of a wave
  
   is given by its time average, thus

• for any physical wave, we are actually interested in evaluating the DC value only over a finite interval of interest. in such a case, the DC value is

power

• for physics, power는 energy을 단위시간으로 나눈 물리양이다. 이러한 기본개념을 바탕으로 여러 다양한 분야에서 각 학문영역에 적용되어 활용되고 있다. electrical field의 경우 voltage와 current에 의해서 power와 energy를 정의한다.

it is known that power is defined as work per unit time, voltage is work per unit charge, and current is charge per unit time. this is the basic for the definition of power in terms of electrical quantities.

• the instantaneous power is given by

• the average power is

• if a load is resistive (i.e. with unity power factor), the average power is

• using RMS value concept,

RMS (root-mean square) value of

 is

for the case of district function, formula become

, and
for the case of continuous function, formula become

.

• computing average (normalized) power of sinusoidal waveform
  using RMS value concept, RMS value of sinusoidal waveform is
  
  .

• concept of normalized power is assuming that
  
   is
  
  .

instantaneous normalized power is
average normalized power is