This article develops a class of multivariate filters for extracting related signals from multiple nonstationary time series affected by noisy fluctuations. Many such applications are possible for the statistical data available in various sciences. For instance, in the bivariate case, the filters can be used for signal analysis where one series is of prime interest and is related to a second series with higher signal-content; the formulas show exactly how much weight should be placed on the auxiliary data at different leads and lags. The multivariate class generalizes the widely used Butterworth class, which has the limitation of being applicable only separately to each individual series, even in multivariate applications. The new filters provide the same flexibility in design - with minimal complexity of form - as basic Butterworth filters. In the multiple series case, there are similarly compact gain functions that now account for inter-relationships among series. The filter parameters, which may have important effects on conclusions based on the extracted signals, may be guided by the dataset at hand to help ensure consistency with observed properties. An application to U.S. petroleum consumption is presented, where more precise trends are estimated by making use of the related time series of OPEC oil imports.