Harmonic Aliasing
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Consider three periodic signals:
- x_1(t) with period T_1={1\over11},seconds
- x_2(t) with period T_2={1\over12},seconds
- x_3(t) with period T_3={1\over13},seconds
Each of these signals contains a fundamental component (at frequency \omega given by 2\pi divided by its period) as well as harmonics 2, 3, 4, and 5, but not other frequencies.
Each of these continuous-time signals is sampled 40 times per second to generate corresponding discrete-time signals:
- x_1[n] = x_1(n/40)
- x_2[n] = x_2(n/40)
- x_3[n] = x_3(n/40)
Each of these discrete-time signals contains exactly five discrete-time sinusoidal components with frequencies in the range 0\le\Omega\le\pi.
Each plot on the facing page shows the frequencies found in one of these DT signals. In the circle next to each plot, write the name of the corresponding signal (either x_1, x_2, or x_3).
Each of the DT frequency components is associated with one of the harmonics in
the original CT signal. For each DT frequency, write the number of the
associated CT harmonic (1-5) in the box above that frequency.
If none of these harmonics could have produced a given frequency, enter an X in its box instead.
