Signal Metrics for a Sinusoidal Signal

• It is relatively easy to analytically determine the signal metrics for a continuous-time sinusoidal signal of the form:
  $$x(t) = A \sin(\omega t + \phi),$$
  as defined in an earlier section of these notes.

• The peak amplitude is $A$.

• Over one period of a sinusoid, the signal mean is zero.

• The signal power of a sinusoid can be determined by integrating over one period:
  $$\int^{2\pi}_0 \frac{1}{2\pi} \sin^2(\theta) d\theta = \int^{2\pi}_0 \frac{1}{4\pi} \left[ 1 - \cos(2 \theta) \right] d\theta = \frac{1}{2}$$

• The plot below shows the signal metrics calculated for a discrete-time sinusoidal signal. Note that these values were calculated over the entire signal length, which is not an exact integer number of periods.

  Figure 7: Signal metrics for a sinusoidal signal.