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High peak-to-average power ratio (PAPR) of the transmitted signal is one of the limitations to employing orthogonal frequency division multiplexing (OFDM) system. In this paper, we propose a new nonlinear companding algorithm that transforms the OFDM signals into the desirable statistics form defined by a linear piecewise function. By introducing the variable slopes and an inflexion point in the target probability density function, more flexibility in the companding form and an effective trade-off between the PAPR and bit error rate performances can be achieved. A theoretical performance study for this algorithm is presented and closed-form expressions regarding the achievable transform gain and signal attenuation factor are provided. We also investigate the selection criteria of transform parameters focusing on its robustness and overall performance aspects. The presented theoretical analyses are well verified via computer simulations.