A process variable transmitter with diagnostics based on power spectral density (PSD) analysis of a process variable sensor signal is provided. In one embodiment, the process variable transmitter is a pressure transmitter and the diagnostics are used to diagnose impulse line obstruction or impending obstruction. Other diagnostics are also useful such as diagnosing primary element degradation. The sensor signal is digitized and the digitized signal is transferred into the frequency domain. The power of the frequencies on the sensor signal is examined to provide the enhanced diagnostics. In one aspect diagnostics are generated directly with the sensor PSD data. In another aspect, the PSD analysis is used to tune a filter in order to enhance traditional diagnostic algorithms.