More Like this

1. Graphon Signal Processing

   https://doi.org/10.1109/TSP.2021.3106857  

   Ruiz, Luana; Chamon, Luiz F.; Ribeiro, Alejandro (August 2021, IEEE Transactions on Signal Processing)
2. Bayesian topological signal processing

   https://doi.org/10.3934/dcdss.2021084  

   Oballe, Christopher; Cherne, Alan; Boothe, Dave; Kerick, Scott; Franaszczuk, Piotr J.; Maroulas, Vasileios (January 2021, Discrete & Continuous Dynamical Systems - S)

   Topological data analysis encompasses a broad set of techniques that investigate the shape of data. One of the predominant tools in topological data analysis is persistent homology, which is used to create topological summaries of data called persistence diagrams. Persistent homology offers a novel method for signal analysis. Herein, we aid interpretation of the sublevel set persistence diagrams of signals by 1) showing the effect of frequency and instantaneous amplitude on the persistence diagrams for a family of deterministic signals, and 2) providing a general equation for the probability density of persistence diagrams of random signals via a pushforward measure. We also provide a topologically-motivated, efficiently computable statistical descriptor analogous to the power spectral density for signals based on a generalized Bayesian framework for persistence diagrams. This Bayesian descriptor is shown to be competitive with power spectral densities and continuous wavelet transforms at distinguishing signals with different dynamics in a classification problem with autoregressive signals. 

   more » « less
3. Infinite quantum signal processing

   https://doi.org/10.22331/q-2024-12-10-1558  

   Dong, Yulong; Lin, Lin; Ni, Hongkang; Wang, Jiasu (December 2024, Quantum)

   Quantum signal processing (QSP) represents a real scalar polynomial of degree $d$using a product of unitary matrices of size $2\times 2$, parameterized by $(d+1)$real numbers called the phase factors. This innovative representation of polynomials has a wide range of applications in quantum computation. When the polynomial of interest is obtained by truncating an infinite polynomial series, a natural question is whether the phase factors have a well defined limit as the degree $d\to \mathrm{\infty }$. While the phase factors are generally not unique, we find that there exists a consistent choice of parameterization so that the limit is well defined in the ${\ell }^1$space. This generalization of QSP, called the infinite quantum signal processing, can be used to represent a large class of non-polynomial functions. Our analysis reveals a surprising connection between the regularity of the target function and the decay properties of the phase factors. Our analysis also inspires a very simple and efficient algorithm to approximately compute the phase factors in the ${\ell }^1$space. The algorithm uses only double precision arithmetic operations, and provably converges when the ${\ell }^1$norm of the Chebyshev coefficients of the target function is upper bounded by a constant that is independent of $d$. This is also the first numerically stable algorithm for finding phase factors with provable performance guarantees in the limit $d\to \mathrm{\infty }$. 

   more » « less
4. Empowering the Growth of Signal Processing: The evolution of the IEEE Signal Processing Society

   https://doi.org/10.1109/MSP.2023.3262905  

   Petropulu, Athina; Moura, José M.F.; Ward, Rabab Kreidieh; Argiropoulos, Theresa (June 2023, IEEE Signal Processing Magazine)
5. Signal Processing On Product Spaces

   https://doi.org/10.1109/ICASSP49357.2023.10095735  

   Roddenberry, T. Mitchell; Grande, Vincent P.; Frantzen, Florian; Schaub, Michael T.; Segarra, Santiago (June 2023, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP))