[Paper Review] Digital Signal Processing in Cosmology

Jens Jasche, Francisco-Shu Kitaura+1 more|ArXiv.org|Jan 20, 2009

Computational Physics and Python Applications3 citations

TL;DR

This paper introduces a supersampling technique from 3D computer graphics to reduce aliasing artifacts in cosmological signal processing, particularly for power spectrum estimation using Fast Fourier Transforms (FFTs). By oversampling the continuous galaxy distribution at sub-grid resolution and averaging, the method suppresses aliasing more effectively and efficiently than standard filter approximations like CIC or TSC, enabling more accurate cosmological inference without excessive computational cost.

ABSTRACT

We address the problem of discretizing continuous cosmological signals such as a galaxy distribution for further processing with Fast Fourier techniques. Discretizing, in particular representing continuous signals by discrete sets of sample points, introduces an enormous loss of information, which has to be understood in detail if one wants to make inference from the discretely sampled signal towards actual natural physical quantities. We therefore review the mathematics of discretizing signals and the application of Fast Fourier Transforms to demonstrate how the interpretation of the processed data can be affected by these procedures. It is also a well known fact that any practical sampling method introduces sampling artifacts and false information in the form of aliasing. These sampling artifacts, especially aliasing, make further processing of the sampled signal difficult. For this reason we introduce a fast and efficient supersampling method, frequently applied in 3D computer graphics, to cosmological applications such as matter power spectrum estimation. This method consists of two filtering steps which allow for a much better approximation of the ideal sampling procedure, while at the same time being computationally very efficient.Thus, it provides discretely sampled signals which are greately cleaned from aliasing contributions.

Motivation & Objective

• To address the fundamental challenge of discretizing continuous cosmological signals—such as galaxy distributions—for FFT-based analysis.
• To reduce sampling artifacts, especially aliasing, introduced by conventional particle assignment schemes like NGP, CIC, and TSC.
• To develop a computationally efficient alternative to ideal low-pass filtering that maintains high fidelity in sampled signals.
• To provide a practical, scalable solution for accurate power spectrum and higher-order spectrum estimation in large-scale structure cosmology.

Proposed method

• Adopting a supersampling approach from 3D computer graphics, the method samples the continuous signal at a higher resolution than the target grid.
• The signal is first assigned to a super-resolution grid using standard particle assignment (e.g., CIC), then downsampled by averaging over sub-pixels to produce the final low-resolution output.
• The method inherently includes pass-band attenuation correction, eliminating the need for separate post-processing corrections.
• It leverages the fact that high-frequency components are naturally suppressed in the averaging step, reducing aliasing effects.
• The approach avoids the need for large, computationally expensive filter kernels by using oversampling instead of increasing filter support.
• The technique is compatible with existing FFT pipelines and can be combined with other filter approximations to further improve accuracy.

Experimental results

Research questions

• RQ1 How can aliasing artifacts in FFT-based power spectrum estimation be reduced without incurring prohibitive computational costs?
• RQ2 To what extent can supersampling outperform standard particle assignment schemes (e.g., CIC, TSC) in suppressing sampling artifacts in cosmological data?
• RQ3 Can a supersampling method that includes pass-band attenuation correction be efficiently integrated into existing cosmological signal processing pipelines?
• RQ4 Is there a practical trade-off between computational cost and accuracy improvement when using supersampling over traditional low-pass filter approximations?
• RQ5 Can this method be generalized to higher-order statistics like the bispectrum, where standard methods fail due to mode coupling and aliasing?

Key findings

• The supersampling method significantly reduces aliasing artifacts in the power spectrum estimation by oversampling the signal at sub-grid resolution before averaging.
• The method achieves better suppression of aliasing than conventional filter approximations like CIC or TSC, even with minimal increase in computational cost.
• Pass-band attenuation is naturally corrected during the downsampling process, eliminating the need for additional correction steps.
• The approach remains computationally efficient compared to increasing the spatial support of ideal low-pass filter approximations, which become impractical as filter size grows.
• The method is particularly effective for high-accuracy power spectrum estimation and can be extended to higher-order statistics where standard FFT techniques fail due to sampling artifacts.
• The technique is complementary to existing filter-based approaches and can be combined with them to further improve signal fidelity.