Figure 3. Sampling error due of a periodic signal with N=0.05
ratio.
The L1-norm and the L2-norm based sampling errors are shown in Figure 4
for a range of \(N\) ratios in the interval of [0.01, 0.5]. The
limits were chosen considering practical aspect. The tested finest
resolution was 0.01 (equivalent to 10 samplings per each period), which
has resulted in negligible, 0.03% and 0.04% errors using the L1-norm
and the L2-norm, respectively. The tested largest ratio was chosen in
accordance with the Nyquist criterion, which says that meaningful
frequency components of the properly sampled periodic signal exist below
the half of the period of the signal, i.e. the Nyquist frequency (see
e.g. Leis, 2011). For this extreme case, the sampling error was found to
be 63.7% and 70.7% for the L1-norm and the L2-norm, respectively.