This paper develops representations of the "ideal" band-pass filter for nonstationary time series. The approach ties together frequency domain perspectives that involve periodicity and gain functions with a statistical modeling framework. The approximating filter has several advantages compared to existing methods; it has a more attractive gain profile that more accurately matches the targeted pass-band of the "ideal" filter when this is the desired gain. Also, our proposed filter addresses the sample endpoint problem associated with previous representations and allows for evaluation of the "ideal" filter’s implicit assumptions about trend-cycle dynamics. Further, it reveals how filtering errors can result from the indiscriminate use of the "ideal" filter and allows one to quantify such errors. A more flexible approach is to use a modeling framework to design band-pass filters that adapt to series’ properties - consistent with how the trend and cycle components evolve and relate to each other - rather than emulating a given gain function. Computer code is freely available for implementing the methodology in a way that avoids the need for an expert operator. An application to cyclical fluctuations in macroeconomic time series is presented, showing how plausible and intuitive cycles are estimated via the ideal filter or with an adaptive framework.