Spectral Characteristics of Random Processes - Random Signals and Processes Primer with MATLAB - page 482

The PSD is shown in Fig. 7.23b .
Note that the delta function at o ¼ 0 indicates that the process has a DC
component. The same can be observed from the autocorrelation function ( 7.148 )
which has a constant term of 0.25 (see Sect. 6.5 and Fig. 7.23a ).
Exercise E.7.6 Find the PSD of a process X ( t ) that is at least WS stationary, and
show that the process has neither a DC component nor a periodic component, if the
autocorrelation function is given as (Fig. 7.24a ):

R XX ðtÞ¼ 4e 3 jtj :

(7.150)

a

AUTOCORRELATION FUNCTION

4

3.5

3

2.5

2

1.5

1

0.5

0

− 3 − 2 − 1 0 1 2 3

τ

b

PSD

3.5

3

2.5

2

1.5

1

0.5

0

− 20 − 15 − 10 − 5 0 5 10 15 20

ω

Fig. 7.24 Exercise E.7.6: ( a ) ACF and ( b ) PSD