Complex heterodyne for undersampled chirped sinusoidal signals

Abstract

We describe a method for analyzing frequency-chirped sinusoidal signals using a complex heterodyne, sometimes also known as complex demodulation on the digitized waveform. This method allows one to use prior knowledge of the signal to reduce the effective bandwidth of the signal. The method can be used to extract a frequency-chirped signal even when it is sampled well below the Nyquist criterion. Accordingly, the method facilitates the use of less-expensive data acquisition and signal processing hardware than has traditionally been used for these applications. This technique is particularly useful for high-precision (parts in 10(9)) interferometer applications in which there exists a differential acceleration between the two arms (commonly found in absolute gravity meters or gradiometers).

Comment on 'Simultaneous gravity and gradient measurements from a recoil-compensated absolute gravimeter'

“…The paper [10] reports the bias of 29 µGal, obtained by the non-linear fitting of the fringe signal. The same nonlinear model implemented in the laboratory testing of the complex heterodyne revealed a bias equivalent to 7 µGal [11]. Another paper [12] reports the bias in the gradient of at least 3000 E, obtained by the model similar to that used in the paper [1].…”

Prospects for Precise Measurements with Echo Atom Interferometry

“…Atoms will also be selected in the magnetically "insensitive" m F = 0 state to avoid systematic effects due to magnetic interactions. A reduction in measurement time will be realized by using techniques for under-sampling fringe patterns [134] developed for commercial corner-cube gravimeters. We now discuss the layout of the improved apparatus.…”

Gravimetric Methods – Absolute and Relative Gravity Meter: Instruments Concepts and Implementation

“…It is possible to digitize the entire chirped waveform (not just the zero-crossings) and analyze these data using a nonlinear leastsquares fit using parameters that can be determined in the time domain (Parker et al, 1995) and/or the frequency domain (Niebauer et al, 2006). This approach is becoming more and more popular as the speed of digitizing electronics and computation is increasing and memory has become much less expensive.…”