Spectral Characteristics of Random Processes - Random Signals and Processes Primer with MATLAB - page 502

7.7 Questions

Q.7.1. Is it possible for a process X ( t ), which is at least WS stationary, to have an
autocorrelation function given as:

R XX ðtÞ¼ sin ðo 0 tÞ; (7.201)

where o 0 is a constant.
Q.7.2. Does the Fourier transform of a random process give the phase information
of a random process?
Q.7.3. Does the PSD represents a spectral characteristic of the process or only of a
particular realization of a process?
Q.7.4. The Fourier transform of deterministic signals can be viewed as a decom-
position of the signal into sinusoids of different frequencies with determin-
istic amplitudes and phases. Is there such decomposition in the case of a
random process?
Q.7.5. Due to duality in time and frequency, the constant in frequency
corresponds to a delta in time and vice versa, as shown in Table 7.1

Table 7.1 Duality of time and frequency
Time Frequency

R xx ( t ) S xx ( f )