Spatial and temporal spectra of periodic functions for spectrum analysis

Both the spatial and the temporal spectra of reference signals used in interferometric spectrum analyzers affect the system performance. We define a class of bandlimited reference signals that have N discrete frequency components of equal magnitude. We show that the system performance is primarily determined by the aperture weighting function and is much less dependent on the specific signal waveform. The aperture weighting function can be used to match the spectral shape to the photodetector size, which then optimizes the dynamic range. Further, since the spatial aperture weighting is converted to an equivalent temporal weighting, this function can also be used to control spurious temporal modulation products. The analysis is extended to include results for periodic chirp signals such as those produced by VCO or SAW devices and shows that the results are not affected by using a reduced duty cycle. We also find that the effect of using finite as opposed to point photodetectors is to introduce an additional factor to the aperture weighting function. Control of both the spatial and temporal modulation products introduced by the periodic reference is necessary to achieve the expected dynamic range.