Linear interpolation: more information?

Consider a time series representing a signal plus noise. Generating additional data points through linear interpolation increases the sig of the signal peak, although the power spectrum remains practically unchanged. This provides the possibility to boost signal sigs artificially, although the amount of information contained by the time series does not increase. Does this make sense?

Figure 41: Grey graphs: sig (left) and power (squared amplitude, logarithmic scale) spectrum (right) of a synthetic time series ($100$ equidistant data points) containing a sinusoidal signal without noise. Black graphs: same for a new time series generated by inserting $9$ additional linearly interpolated points such that the result is an equidistantly sampled dataset consisting of $991$ points.

Fig.41 displays the sig (left) and power (squared amplitude, right) spectrum of an equidistantly sampled time series consisting of $100$ data points and representing a sinusoidal signal with a frequency of $0.075832\,\mathrm{d}^{-1}$ and an amplitude of $1$ in black colour. No noise is added. Based on this time series, a new dataset is generated: between each pair of data points, $9$ additional, equidistant data points are inserted. The observables are assigned by linear interpolation. The number of data points in this new time series is thus $991$. The corresponding spectra are shown in grey colour. The longer dataset generates a peak significance that is roughly ten times higher than the initial one, whereas the power spectrum remains practically unchanged. Only the fact that the linear interpolation does not reveal the ``true'' observables that would be generated by the signal exactly is responsible for a small deviation of the black graph from the grey one.

The explanation for this behaviour is quite similar to the previous section ``The effect of binning'', p., and correspondingly, the effect is mitigated for very noisy signals. Therefore in practical applications, it will be impossible to enhance the capability of a frequency analysis by artificially introducing new data points.