Systems and methods for analysing a time-domain signal are described. The method comprising: in a mixer (150), mixing the time-decay signal (115) with a local oscillator signal (122) generated by a local oscillator (120), resulting in a mixed signal from which a Fourier transformed time-decay signal is generated comprising a fundamental transformed time decay signal at the fundamental frequency of the local oscillator signal (122) and a plurality of transformed time-decay signals at a plurality of frequencies; and determining the magnitude of each of the transformed time-decay signals at the fundamental frequency and at a frequency other than the fundamental frequency.