Everything about Polyspectra
Higher-order frequency analysis
Polyspectra, also known as higher-order spectra, are frequency-domain statistical quantities that generalize the spectral density to higher orders. Polyspectra of a given signal can reveal non-Gaussian behavior, time-inversion asymmetries, and phase correlations between different frequency contributions to the signal. While a standard power spectrum quantifies the distribution of intensity across frequencies, polyspectra characterize higher-order phase and amplitude correlations between frequency components. Higher-order spectra include the third-order bispectrum, the fourth-order trispectrum, and their multivariate generalizations. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: PolyspectraA 5-minute orientation
- Skim a recent paper: Quantum polyspectra approach to the dynamics of blinking quantum emitters at low photon rates without binning: Making every photon countInfluential work since 2022
- Pick up a classic book: Volterra-type systems and polyspectraThe most-reprinted book on the subject
- Read the landmark paper: An Introduction to PolyspectraCited 442 times
- Go sideways: Multidimensional spectral estimationA closely related topic
- Go sideways: Spectral density estimationA closely related topic
📖 Definitions
Noun plural of polyspectrum
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
An Introduction to Polyspectra
Polyspectra searches for sharp oscillatory features in cosmic microwave sky data
Stochastic system identification with noisy input-output measurements using polyspectra
A theory of polyspectra for nonstationary stochastic processes
Strongly scale-dependent polyspectra from curvaton self-interactions
On the limiting behaviour of needlets polyspectra
Multitaper estimators of polyspectra
Efficient Parallel Algorithm for Estimating Higher-order Polyspectra
🆕 Influential since 2022
Quantum polyspectra approach to the dynamics of blinking quantum emitters at low photon rates without binning: Making every photon count
Revealing hidden states in quantum dot array dynamics: Quantum polyspectra versus waiting time analysis
Fluctuations of polyspectra in spherical and Euclidean random wave models
Parity-odd polyspectra of spatial point processes
Robust fingerprint recognition approach based on diagonal slice of polyspectra in the polar space
📚 Books worth reading
- 📕Volterra-type systems and polyspectraSaleh Abdalla Alshebeili · 1992
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Multidimensional spectral estimation Multidimension spectral estimation is a generalization of spectral estimation, normally formulated for one-dimensional signals, to multidimensional signals…
- Spectral density estimation In statistical signal processing, the goal of spectral density estimation (SDE) or simply spectral estimation is to estimate the spectral density (also…
- Spectral density In signal processing, the power spectrum Sxx(f) of a continuous time signal x(t) describes the distribution of power into frequency components f composing…
- Discrete-time Fourier transform In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of discrete values. The DTFT…
- Multitaper In signal processing, multitaper analysis is a spectral density estimation technique developed by David J. Thomson. It can estimate the power spectrum…
- Bispectrum In mathematics, in the area of statistical analysis, the bispectrum is a statistic used to search for nonlinear interactions. It is the third-order Polyspectrum…
- Bicoherence In mathematics and statistical analysis, bicoherence (also known as bispectral coherency) is a squared normalised version of the bispectrum. The bicoherence…
- Estimation theory Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component…