audio signal engineers

Abstract: The short-time Fourier transform (STFT) computes the Fourier transform of a short-duration window of a longer signal, which characterizes how a frequency changes over time. While the Fourier transform algorithms, particularly the Fast Fourier Transform (FFT) algorithm, has been well developed to take advantage of parallel computing, there is limited work on understanding the performance of parallel short-time Fourier transform algorithms. In this study, two parallel short-time Fourier transform algorithms, one is FFT-based and the other a quasi-parallel feedforward algorithm, are implemented and analyzed in comparison with each other. It is found that while the quasi-parallel algorithm outperforms in runtime under low concurrency settings, the FFT-based algorithm scales better and has lower memory usage. For each algorithm, three parallel approaches, shared-memory, distributed-memory and hybrid distributed-shared-memory, are tested. Profiling results show that all implementations are compute bound except for the hybrid feedforward algorithm, and that the distributed-memory variants incur significantly higher communication cost. Overall, this study presents a deeper and more comprehensive analysis and demonstrates the defining characteristics of different families of parallel short-time Fourier transform algorithms, in which the FFT-based approach uses less memory while the quasi-parallel feedforward algorithm has lower runtime but higher serial fraction.

Abstract: The short-time Fourier transform (STFT) characterizes the local frequency content of time-varying signals by evaluating the discrete Fourier transform over a sliding analysis window. The STFT is governed by a fundamental resolution trade-off: a short window localizes rapid transients in time at the cost of frequency resolution, whereas a long window resolves closely spaced harmonics at the expense of temporal resolution. The Universal Short-Time Fourier Transform (U-STFT) resolves this trade-off sequentially by modeling the analysis window duration as a data-adaptive state variable that indexes the number of hops included in the current observation interval. At each frame, a bank of candidate window durations is scored using normalized order-three Rényi entropy to quantify joint time-frequency concentration. A window length trellis aggregates the resulting $\mathcal{O}(3^M)$ candidate window schedules with linear complexity per frame, guaranteeing a cumulative mix-loss regret bound of $\mathcal{O}((k+1)\log M)$ relative to any hindsight window schedule with $k$ resolution changes over $M$ frames. By linearity of the Fourier transform, posterior expectation across the candidate bank yields a single spectrum equivalent to an STFT evaluated with a data-adaptive effective window, while an envelope-normalized synthesis stream guarantees exact overlap-add reconstruction. Evaluations on synthetic and marine bioacoustic signals demonstrate adaptive resolution tracking, enhanced spectral concentration, and exact time-domain invertibility.

Abstract: Dense self-attention treats all token pairs as equally plausible before learning, an interaction-isotropic prior that can be mismatched to structured signals. For structured, low signal-to-noise ratio (SNR) signals such as EEG, dependencies are organized along the electrode and time axes, and this uniform prior exposes each token to many irrelevant interactions. We introduce Adaptive Anisotropic Attention (AAA), which splits attention into two paths: a temporal path, where each token attends to the tokens of its own electrode across time, and a spatial path, where it attends to the tokens of the other electrodes at the same time step. A small gate predicts, for every token, a convex combination of the two path outputs: two non-negative weights that sum to one. On six EEG downstream tasks, the resulting model, AXON (AXis-factorized Operator Network), improves mean balanced accuracy over a dense baseline under both linear probing and full fine-tuning. We show that both paths (temporal and spatial) are necessary and that the weighted sum beats a hard choice of one path; most of the benefit comes from the gate learning a different temporal/spatial balance at each layer of the network. Controlled audio spectrogram experiments show that axis factorization transfers beyond EEG. These results suggest that aligning attention with the natural axes of structured signals provides a useful inductive bias.