Spectral Characteristics of Random Processes - Random Signals and Processes Primer with MATLAB - page 472

Fig. 7.16 Multiplication of random process with sinusoidal signal

Fig. 7.17 Power spectral densities: ( a ) Input ( b ) Output

The obtained expression can be rewritten as (see Appendix D ):

:

U 0

e jo 0 t þ e jo 0 t

R YY ðtÞ¼

4 R XX ðtÞ

(7.109)

Using the shifting property of the Fourier transform (see Appendix E ), we
arrive at:

U 0
4

S YY ðoÞ¼ ½ S XX ðo o 0 ÞþS XX ðo þ o 0 Þ : (7.110)

As a result, the output PSD has two symmetrical power spectral components
around the frequencies o 0 and o 0 , which are scaled by U 0 2 /4, as shown in Fig. 7.17b .