Related papers: Accurate Power Spectrum Estimation toward Nyquist …
Efficient estimators of Fourier-space statistics for large number of objects rely on Fast Fourier Transforms (FFTs), which are affected by aliasing from unresolved small scale modes due to the finite FFT grid. Aliasing takes the form of a…
abridged] A method to rapidly estimate the Fourier power spectrum of a point distribution is presented. This method relies on a Taylor expansion of the trigonometric functions. It yields the Fourier modes from a number of FFTs, which is…
Because of mass assignment onto grid points in the measurement of the power spectrum using the Fast Fourier Transform (FFT), the raw power spectrum $\la |\delta^f(k)|^2\ra$ estimated with FFT is not the same as the true power spectrum…
Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model…
There has been a growing interest in wideband spectrum sensing due to its applications in cognitive radios and electronic surveillance. To overcome the sampling rate bottleneck for wideband spectrum sensing, in this paper, we study the…
Estimators for $n$-point clustering statistics in Fourier-space demand that modern surveys of large-scale structure be transformed to Cartesian coordinates to perform Fast Fourier Transforms (FFTs). In this work, we explore this…
The growing scarcity of spectrum resources, wideband spectrum sensing is required to process a prohibitive volume of data at a high sampling rate. For some applications, spectrum estimation only requires second-order statistics. In this…
This paper studies two spectrum estimation methods for the case that the samples are obtained at a rate lower than the Nyquist rate. The first method is the correlogram method for undersampled data. The algorithm partitions the spectrum…
Poisson distributed shot noise is normally considered in the Gaussian limit in cosmology. However, if the shot noise is large enough and the correlation function/power spectrum conspires, the Gaussian approximation mis-estimates the errors…
This paper studies a spectrum estimation method for the case that the samples are obtained at a rate lower than the Nyquist rate. The method is referred to as the correlogram for undersampled data. The algorithm partitions the spectrum into…
We present a new and highly efficient algorithm for computing a power spectrum made from evenly spaced data which combines the noise-reducing advantages of the weighted fit with the computational advantages of the Fast Fourier Transform…
The limited availability of spectrum resources has been growing into a critical problem in wireless communications, remote sensing, and electronic surveillance, etc. To address the high-speed sampling bottleneck of wideband spectrum…
Precision measurements of the galaxy power spectrum P(k) require a data analysis pipeline that is both fast enough to be computationally feasible and accurate enough to take full advantage of high-quality data. We present a rigorous…
In many applications of frequency estimation, the frequencies of the signals are so high that the data sampled at Nyquist rate are hard to acquire due to hardware limitation. In this paper, we propose a novel method based on subspace…
This note considers the problem of approximating the locations of dominant spikes for a probability measure from noisy spectrum measurements under the condition of residue signal, significant noise level, and no minimum spectrum separation.…
Context: Fourier transform (or lag) correlators in radio interferometers can serve as an efficient means of synthesising spectral channels. However aliasing corrupts the edge channels so they usually have to be excluded from the data set.…
We present two related techniques to measure the two-point correlation function and the power spectrum with edge correction in any spatial dimensions. The underlying algorithm uses fast Fourier transforms for calculating the two-point…
We introduce a new compressive power spectrum estimation approach in both frequency and direction of arrival (DOA). Wide-sense stationary signals produced by multiple uncorrelated sources are compressed in both the time and spatial domain…
Sampling a signal below the Shannon-Nyquist rate causes aliasing, meaning different frequencies to become indistinguishable. It is also well-known that recovering spectral information from a signal using a parametric method can be ill-posed…
We show how to estimate the covariance of the power spectrum of a statistically homogeneous and isotropic density field from a single periodic simulation, by applying a set of weightings to the density field, and by measuring the scatter in…