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A Frequency Position Modulation system for encoding signals for transmission. A signal's discrete frequency support is used to represent symbols. The signal can be non-uniformly spread over many GHz of instantaneous bandwidth, resulting in a communications system that is resilient to interference and difficult to intercept. The FPM symbols are recovered using adaptive projections that use an analog polynomial nonlinearity paired with an analog-to-digital converter that is sampling at a rate at that is only a fraction of the instantaneous bandwidth of the signal. In the presence of partial band interference, nonlinearities generated by the transmitter are exploited by the receiver to help unambiguously recover tones that could otherwise be lost. The nonlinearities are generated by driving the power amplifier of the transmitter into saturation to induce distortions at a desired level.