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The linearity of an efficient polar transmitter architecture, with a 1 bit oversampled delta sigma (DeltaSigma) modulating the envelope signal, depends, to a high degree, on low-pass envelope filtering. This filter is compulsory to attenuate the DeltaSigma quantisation noise. A high cut-off frequency results in more noise being included. In contrast, using a filter with a low cut-off frequency results in attenuation of the information content of the envelope signal. Either way, the result is unwanted spectral regrowth. By pre-emphasising the envelope signal, the filter s attenuation of the information is mitigated. The pre-emphasis is implemented by a digital pseudo-derivative high-pass filter, with inverse magnitude characteristics of the analogue low-pass filter, within a limited interest band. Consequently, the low-pass filter can be designed with a lower cut-off frequency to attenuate more of the DeltaSigma modulator noise, and the modulator can switch at lower frequencies. With this technique, the WLAN output spectrum, at the critical 30 MHz offset corner frequency, is improved by 12.5 dB, considering a second order DeltaSigma sampling at 1.28 GHz. The technique was verified with an experimental setup and the behaviour agrees well with simulations.