Digital Signal Processing Reference
In-Depth Information
Figure 3.2
Spectra of a signal before and after periodic and random sampling: (a) spectrum
of the analog signal; (b) spectrum of the periodically sampled signal; (c), (d) expectations of
the spectrum estimates when the signal is sampled randomly; (e) overlapping base and image
bands
where
S
x
(
f
) is the spectrum of the respective original signal and
S
x
(
f
)isthe
complex of the conjugate of
S
x
(
f
).
Figures 3.2(a) and (b) illustrate the result. It is well known, but is not always
interpreted correctly. It can be seen that the spectra of the periodically sampled
signals are also periodic in the frequency domain and the sampling process is
responsible for that. However, it would be wrong to conclude that this periodicity
of sampled signal spectra is unavoidable. It is not the sampling itself but its
periodicity in the time domain that produces this negative effect.
