A communications device includes a signal input that receives an orthogonal frequency division multiplexed (OFDM) communications signal. A demodulator is connected to the signal input for receiving the OFDM communications signal and demodulating the OFDM communication signal. It includes at least one memory element for storing the at least one sine/cosine basis waveform approximation as complex exponential functions. A logic circuit performs logical shifts in additions and multiples of +/−2n and extracts amplitude and phase values from a plurality of N data subcarriers within the OFDM communications signal. The demodulator includes efficient implementation of the FFT for use as an OFDM demodulator where the complex exponentials are approximated by multi-level complex sinusoids and optionally oversampled to increase SNR of the FFT output.