Techniques for digital signal analysis involve sampling data repeatedly in time. Recent research suggests that the sampling rate should vary temporally, and should depend on empirical assessment of signal complexity. A signal of given duration, sampled the same total number of times, can potentially be recovered at higher fidelity if the sampling rate is varied so that relatively more data are sampled when the signal is more complex. In some, perhaps most, applications this requires real-time analysis of signal complexity, as well as algorithms for rapidly switching from one sampling rate to another. It has been suggested that procedures of this type be used for both data transmission and storage. Properties of these procedures will be discussed, in the contexts of wavelet-based as well as more conventional denoising techniques.