Known apparatus for measuring jitter in a signal under test employ narrowband filters and limiters that have technological limitations when the bit rate of the signal under test is around 40 Gbps. The present invention avoids the use of the above-mentioned elements by firstly wideband filtering an extracted clock signal and mixing the filtered clock signal down to baseband using a quadrature demodulator to yield a complex baseband signal. Prior to conversion of the complex baseband signal to the digital domain, the quadrature components of the complex baseband signal are low-pass filtered. Subsequently, digitized signals are converted to a polar form having an amplitude and phase, the phase being weighted by the amplitude prior to measurement of the phase in order to incorporate a measure of confidence in the phase relating to a density of transitions in the signal under test.