Here is another perspective of the quite obvious signal detection algorithm that Mann casually dismissed. This is simple in that it is a straightforward Fourier series of the ENSO signal. Can take either the Sine expansion or the Cosine expansion as it will give complementary symmetries. Below is the Cosine series, with the frequencies between 0.5 and 1/year mirror-folded back and then compared to the spectrum between 0 and 0.5 /year.
The arrows indicate the mirror-image folding and the gray rectangular box is a guide-to-the-eye in how to compare the amplitudes.
This deconstruction is called double-sideband suppressed carrier modulation and it has never been described for climate dipoles according to the research literature. All the frequencies below half the carrier frequency constitute the lower sideband while the frequencies above half the carrier frequency are the upper sideband.
The spectrum is symmetrical with a Cosine series and polarity-reversed anti-symmetrical with a Sine series. What gets suppressed is the carrier frequency, which amounts to an annual impulse that likely drives the ENSO behavior but is not seen directly in the spectrum because the underlying modulated signal is purely sinusoidal, i.e. there is no DC component.