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Orthogonal frequency division multiplexing (OFDM) is an attractive technique for wireless communication applications. However, an OFDM signal has a large peak-to-mean envelope power ratio, which can result in significant distortion when passed through a nonlinear device, such as a transmitter power amplifier. We investigate, through extensive computer simulations, the effects of clipping and filtering on the performance of OFDM, including the power spectral density, the crest factor, and the bit-error rate. Our results show that clipping and filtering is a promising technique for the transmission of OFDM signals using realistic linear amplifiers.