1. Statistical Parameters
Table 11.1

2. In-Class Example
Determine the mean and variance of x(t) = 3sin(4pt) for one period
and 1.5 periods.
What is the period of 3sin(4pt) ?
one period equals one cycle → determine the time for one cycle
frequency = 4p radians/s = (x cycles/s) • (2p radians/cycle)
→ x = 2 cycles/s → 0.5 s/cycle
So, one period = 0.5 s and 1.5 periods = 0.75 s.
Mean:
for one period:

3. In-Class Example for 1.5 periods: Variance: for one period:

4. The Root-Mean-Square (rms)
For a continuous waveform:
For a discrete waveform:
Figure 11.8

5. In-Class Example
Determine the rms for 3 cycles of the ramp function y(t) = At/T. A
y(t) t T 2T 3T
What kind of signal is this?
periodic
How many periods must be considered for this waveform?
ONE

6. In-Class Example for t1 = 0 and t2 = T What is the mean value of y(t)?

7. In-Class Example
Determine the rms of x(t) = 3sin(4pt) for one period.