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This paper proposes a method of digital predistortion suitable for wideband high crest factor applications such as those encountered in DAB, DVB-T and WCDMA transmitters. The proposed method is advantageous for four main reasons. Firstly, it utilizes a reliable frequency domain measure of transmitter output nonlinearity, specifically the Weighted Adjacent Channel Power (WACP), as the objective for predistortion filter parameter estimation. This is in direct contrast to traditional approaches which utilize a time domain measure obtained via a full feedback path and potentially corrupted by gain and phase compensation error as well as ADC distortion. Secondly, the method models predistortion filter parameter estimation as a generic nonlinear mathematical optimization problem. This model assumes a nonconvex objective function and therefore utilizes both global and local optimization algorithms to achieve true global convergence. This is once again in direct contrast to traditional approaches which model predistortion filter parameter estimation as a linear regression problem. Such a model incorrectly assumes a convex error surface and therefore restricts itself to inadequate local optimization algorithms which unfortunately cannot guarantee true global convergence. Thirdly, the method's predistortion filter is a pruned Volterra Series with memory which utilizes a hybrid pruning strategy in order to keep high order kernels to a practically manageable size, suitable for optimization parameter estimation. Predistortion filter memory ultimately makes the method highly suited to wideband applications. Finally, predistortion filter parameter estimation does not require known test signals to be injected into the transmitter and therefore the technique is on-air adaptive. This means any transmitter using this method of digital predistortion will be both on-air and optimally linearized for its entire operational life. Preliminary results obtained from actual hardware are pres- nted.