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The Alpha Magnetic Spectrometer (AMS-02) has provided unprecedented precision measurements of the electron and positron cosmic-ray fluxes and the positron fraction spectrum. At the higher energies, sources as energetic local pulsars, may contribute to both cosmic-ray species. The discreteness of the source population, can result in features both on the positron fraction measurement and in the respective electron and positron spectra. For the latter, those would coincide in energy and would contrast predictions of smooth spectra as from particle dark matter. In this work, using a library of pulsar population models for the local part of the Milky Way, we perform a power-spectrum analysis on the cosmic-ray positron fraction. We also develop a technique to cross-correlate the electron and positron fluxes. We show that both such analyses, can be used to search statistically for the presence of spectral wiggles in the cosmic-ray data. For a significant fraction of our pulsar simulations, those techniques are already sensitive enough to give a signal for the presence of those features above the regular noise, with forthcoming observations making them even more sensitive. Finally, by cross-correlating the AMS-02 electron and positron spectra, we find an intriguing first hint for a positive correlation between them, of the kind expected by a population of local pulsars.