Cellular standards evolve to support increasingly higher bandwidths which results in strict in-and out-of-band requirements such as lower error vector magnitude (EVM) and/or adjacent channel leakage ratio (ACLR). Digital polar transmitters, which are showing the best performance in terms of power consumption, are challenged to fulfill these requirements. This work will show that even in case of ideal analog components and infinite digital resources, there are principle limitations in terms of out-of-band noise for digital polar transmitters. A typical polar modulation will be compared to a theoretical signal with continuous amplitude modulation. The analysis of the resulting error signal suggests a decomposition into two components which can be partially compensated in the amplitude and phase modulation paths. Based on that decomposition a compensation algorithm has been developed and evaluated with a 400 MHz 5G New Radio (NR) signal for Band n257 on Frequency Range 2 with carrier frequency of 26.5 GHz. The compensation results in an out-of-band noise reduction of 44 dB close to the carrier frequency. Furthermore, EVM improvements for NR signals are demonstrated.