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Register a new userUnifying Probabilistic Models for Time-Frequency Analysis
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In audio signal processing, probabilistic time-frequency models have many benefits over their non-probabilistic counterparts. They adapt to the incoming signal, quantify uncertainty, and measure correlation between the signals amplitude and phase information, making time domain resynthesis straightforward. However, these models are still not widely used since they come at a high computational cost, and because they are formulated in such a way that it can be difficult to interpret all the modelling assumptions. By showing their equivalence to Spectral Mixture Gaussian processes, we illuminate the underlying model assumptions and provide a general framework for constructing more complex models that better approximate real-world signals. Our interpretation makes it intuitive to inspect, compare, and alter the models since all prior knowledge is encoded in the Gaussian process kernel functions. We utilise a state space representation to perform efficient inference via Kalman smoothing, and we demonstrate how our interpretation allows for efficient parameter learning in the frequency domain.
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To handle time series with complicated oscillatory structure, we propose a novel time-frequency (TF) analysis tool that fuses the short time Fourier transform (STFT) and periodic transform (PT). Since many time series oscillate with time-varying frequency, amplitude and non-sinusoidal oscillatory pattern, a direct application of PT or STFT might not be suitable. However, we show that by combining them in a proper way, we obtain a powerful TF analysis tool. We first combine the Ramanujan sums and $l_1$ penalization to implement the PT. We call the algorithm Ramanujan PT (RPT). The RPT is of its own interest for other applications, like analyzing short signal composed of components with integer periods, but that is not the focus of this paper. Second, the RPT is applied to modify the STFT and generate a novel TF representation of the complicated time series that faithfully reflect the instantaneous frequency information of each oscillatory components. We coin the proposed TF analysis the Ramanujan de-shape (RDS) and vectorized RDS (vRDS). In addition to showing some preliminary analysis results on complicated biomedical signals, we provide theoretical analysis about RPT. Specifically, we show that the RPT is robust to three commonly encountered noises, including envelop fluctuation, jitter and additive noise.
A typical audio signal processing pipeline includes multiple disjoint analysis stages, including calculation of a time-frequency representation followed by spectrogram-based feature analysis. We show how time-frequency analysis and nonnegative matrix factorisation can be jointly formulated as a spectral mixture Gaussian process model with nonstationary priors over the amplitude variance parameters. Further, we formulate this nonlinear models state space representation, making it amenable to infinite-horizon Gaussian process regression with approximate inference via expectation propagation, which scales linearly in the number of time steps and quadratically in the state dimensionality. By doing so, we are able to process audio signals with hundreds of thousands of data points. We demonstrate, on various tasks with empirical data, how this inference scheme outperforms more standard techniques that rely on extended Kalman filtering.
This study presents PRISM, a probabilistic simplex component analysis approach to identifying the vertices of a data-circumscribing simplex from data. The problem has a rich variety of applications, the most notable being hyperspectral unmixing in remote sensing and non-negative matrix factorization in machine learning. PRISM uses a simple probabilistic model, namely, uniform simplex data distribution and additive Gaussian noise, and it carries out inference by maximum likelihood. The inference model is sound in the sense that the vertices are provably identifiable under some assumptions, and it suggests that PRISM can be effective in combating noise when the number of data points is large. PRISM has strong, but hidden, relationships with simplex volume minimization, a powerful geometric approach for the same problem. We study these fundamental aspects, and we also consider algorithmic schemes based on importance sampling and variational inference. In particular, the variational inference scheme is shown to resemble a matrix factorization problem with a special regularizer, which draws an interesting connection to the matrix factorization approach. Numerical results are provided to demonstrate the potential of PRISM.
A novel photonic approach to the time-frequency analysis of microwave signals is proposed based on the stimulated Brillouin scattering (SBS)-assisted frequency-to-time mapping (FTTM). Two types of time-frequency analysis links, namely parallel SBS link and time-division SBS link are proposed. The parallel SBS link can be utilized to perform real-time time-frequency analysis of microwave signal, which provides a promising solution for real-time time-frequency analysis, especially when it is combined with the photonic integration technique. A simulation is made to verify its feasibility by analyzing signals in multiple formats. The time-division SBS link has a simpler and reconfigurable structure, which can realize an ultra-high-resolution time-frequency analysis for periodic signals using the time segmentation and accumulation technique. An experiment is performed for the time-division SBS link. The multi-dimensional reconfigurability of the system is experimentally studied. An analysis bandwidth of 3.9 GHz, an analysis frequency up to 20 GHz, and a frequency resolution of 15 MHz are demonstrated, respectively.
Sensor-based time series analysis is an essential task for applications such as activity recognition and brain-computer interface. Recently, features extracted with deep neural networks (DNNs) are shown to be more effective than conventional hand-crafted ones. However, most of these solutions rely solely on the network to extract application-specific information carried in the sensor data. Motivated by the fact that usually a small subset of the frequency components carries the primary information for sensor data, we propose a novel tree-structured wavelet neural network for sensor data analysis, namely emph{T-WaveNet}. To be specific, with T-WaveNet, we first conduct a power spectrum analysis for the sensor data and decompose the input signal into various frequency subbands accordingly. Then, we construct a tree-structured network, and each node on the tree (corresponding to a frequency subband) is built with an invertible neural network (INN) based wavelet transform. By doing so, T-WaveNet provides more effective representation for sensor information than existing DNN-based techniques, and it achieves state-of-the-art performance on various sensor datasets, including UCI-HAR for activity recognition, OPPORTUNITY for gesture recognition, BCICIV2a for intention recognition, and NinaPro DB1 for muscular movement recognition.
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