response were explored: convolution kernel methods and a windowed fast Fourier transform (FFT) algorithm similar to techniques used in and . Preflight Monte-Carlo simulations testing on synthetic data suggested that convolution in the time domain generated fewer spectral artifacts in the calibrated time series than a windowed FFT algorithm. Compensation filters are developed using the inverse FFT of the response function on an abscissae of 2048 frequencies, corresponding to a 2048 tap (all zero) linear time invariant (LTI) finite impulse response (FIR) filter [@OppenheimSchafer]. The filters are non-causal, such that real time merging of data (e.g. on the spacecraft) is not possible; the future development of causal FIR filters for on-board merging presents an opportunity to increase scientific returns from telemetry limited missions.

Merging {#sec:merging}
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Many algorithms for merging data from multiple sensors, occasionally referred to as data fusion, were initially developed in the context of radio system engineering as a method to optimize signal to noise ratios and correct for signal loss due to stochastic fluctuations impacting transmission, [@Kahn1954; @Brennan1959]. Recent research has demonstrated the applicability of data fusion in merging magnetic field measurements from multiple sensors onboard a single spacecraft: [@Alexandrova2004; @Kiyani2009; @Chen2010]. However, not until MMS 