  In the frequency-domain multiplexing (FDM) scheme, transition-edge sensors
(TES) are individually coupled to superconducting LC filters and AC biased at
MHz frequencies through a common readout line. To make efficient use of the
available readout bandwidth and to minimize the effect of non-linearities, the
LC resonators are usually designed to be on a regular grid. The lithographic
processes however pose a limit on the accuracy of the effective filter
resonance frequencies. Off-resonance bias carriers could be used to suppress
the impact of intermodulation distortions, which nonetheless would
significantly affect the effective bias circuit and the detector spectral
performance. In this paper we present a frequency shift algorithm (FSA) to
allow off-resonance readout of TES's while preserving the on-resonance bias
circuit and spectral performance, demonstrating its application to the FDM
readout of a X-ray TES microcalorimeter array. We discuss the benefits in terms
of mitigation of the impact of intermodulation distortions at the cost of
increased bias voltage and the scalability of the algorithm to multi-pixel FDM
readout. We show that with FSA, in multi-pixel and frequencies shifted on-grid,
the line noises due to intermodulation distortion are placed away from the
sensitive region in the TES response and the X-ray performance is consistent
with the single-pixel, on-resonance level.
