1. A process variable transmitter, comprising: a process variable sensor configured to sense a process variable of an industrial process and responsively provide a sensor signal representative of the sensed process variable; an analog-to-digital (A/D) converter receiving the sensor signal provided by the process variable sensor that senses the process variable and converts the sensor signal to a digital signal at a conversion rate; a processor that receives the digital signal and provides a measurement output indicative of the process variable based upon the digital signal; and a noise detector that receives the sensor signal at a refresh rate that is greater than the conversion rate, and generates a first value indicative of a number of positive noise events relative to a positive threshold value, and a second value indicative of a number of negative noise events relative to a negative threshold value, the processor evaluating the positive noise events and the negative noise events and generating a noise output that is indicative of detected noise based on the first and second values, wherein the noise detector comprises: a positive noise threshold generator that receives the sensor signal and generates the positive threshold value as a positive voltage threshold; and a negative noise threshold generator that receives the sensor signal and generates the negative threshold value as a negative voltage threshold.