Final answer:
To show properties of a random binary wave X(t) where '1' is a pulse of amplitude A and '0' is zero volts, we calculate statistical measures like mean and power based on probabilities and use wave motion principles to model the signal's change over time.
Step-by-step explanation:
To analyze the new random binary wave X(t) where the symbol 1 is represented by a pulse of amplitude A volts and symbol 0 by zero volts, we would define the statistical properties of the signal, such as its mean, power, and autocorrelation function, taking into account that the value of the signal is either A or 0 at any given time.
For instance, if the probability of symbol 1 is p1 and the probability of symbol 0 is p0, the mean value of the signal X(t) is A × p1 since the contribution when the signal is 0 is of course 0. The power of the signal can be calculated using the square of the amplitude (as power is proportional to the square of amplitude) weighted by the probability of symbol 1 occurring.
Additionally, the autocorrelation function would depend on the probabilities p1 and p0 as well as characteristics of the pulse shape and timing. To describe wave movement and properties in terms of position and time, we apply the principle that the motion of a pulse or wave at a constant velocity can be modeled with positional terms replaced by vt, where v is the velocity and t is the time.