Interpolation and Sampling - Signal Processing for Communications - page 254

In the periodized spectrum, the copies do overlap and the resulting discrete-
time spectrum is an aliased version of the original, which is similar to the
original; however, the original spectrum cannot be reconstructed from the
sampled signal. In a practical sampling scenario, the correct design choice
would have been to lowpass filter (in the continuous-time domain) the orig-
inal signal so as to eliminate the spectral tails beyond

l g r , y i d . , © , L s

± Ω N .

1

0

− 2 Ω − Ω − Ω 0 Ω Ω 2 Ω

s s N N s s

1

0

− 2 Ω s − Ω s − Ω N 0 Ω N Ω s 2 Ω s

1

0

- π -2 π/ 3 - π/ 3 0 π/ 3 2 π/ 3 π

Figure 9.12 Sampling of a non-bandlimited signal.