Neural networks frequently waste capacity on learning transformations (like scale changes in time series) that are irrelevant to the main classification or identification task. Current invariance approaches, whether architecture- or data-centric, remain computationally expensive, need careful tuning, and generalize poorly; moreover, none achieves online scale invariance without prior knowledge of the amplitude. To address this gap, it is here proposed a general time-series framework that imposes online scale invariance via an explicit, non-learned functional transformation: a covariance-based filter. This filter is first benchmarked against standard offline normalizers using real seismic signals, demonstrating preservation of waveform shape and frequency content (Fréchet distance 1.9×10-4 spectral correlation >0.99). The invariant filter is then used as the initial layer of a Long Short-Term Memory (LSTM) network for frequency estimation. A comparative evaluation with amplitude-varying sinusoidal signals, using the Sum of Squared Errors (SSEs) as the metric, shows notable gains: a conventional 10-unit LSTM with data augmentation needed 50,000 training epochs to reach an SSE of 686 rad2/s2, while the invariant LSTM achieved the same error with only 4 units in 30,766 epochs. The contributions of this work are threefold: theoretical, by proposing a deterministic, non-learned invariant function; methodological, by designing a generalizable preprocessing filter; and applied, by showing faster convergence and lower model complexity for LSTM-based time-series analysis.
