Tree rings are the most widely-used proxy records for reconstructing Common Era temperatures. Tree-ring records correlate strongly with temperature on an interannual basis, but studies have found discrepancies between tree rings and climate models on longer timescales, indicating that low-frequency noise could be prevalent in these archives. Using a large network of temperature-sensitive tree-ring records, we partition timeseries variance into a common (i.e., “signal”) and non-climatic (i.e., “noise”) component using a frequency-resolved signal-to-noise ratio (SNR) analysis. We find that the availability of stored resources from prior years (i.e., biological “memory”) dampens the climate signal at high-frequencies, and that independent noise reduces the SNR on long timescales. We also find that well-replicated, millennial-length records had the strongest common signal across centuries. Our work suggests that low-frequency noise models are appropriate for use in pseudoproxy experiments, and speaks to the continued value of high-quality data development as a top priority in dendroclimatology.