# ATSFFT: A Novel Sparse Fast Fourier Transform Enabled With Sparsity Detection

## TL;DR

This paper introduces ATSFFT, an adaptive sparse Fourier transform algorithm that detects signal sparsity dynamically, outperforming existing methods and FFT libraries in efficiency and error control.

## Contribution

The paper presents ATSFFT, a novel sparse FFT algorithm with sparsity detection and adaptive tuning, enhancing reliability and performance over previous SFFT implementations.

## Key findings

- ATSFFT outperforms traditional SFFT in efficiency and error control.
- ATSFFT achieves an order of magnitude faster performance than FFTW.
- The method reliably detects sparsity without prior knowledge.

## Abstract

The Fast Fourier Transform(FFT) is a classic signal processing algorithm that is utilized in a wide range of applications. For image processing, FFT computes on every pixel's value of an image, regardless of their properties in frequency domain. The Sparse Fast Fourier Transform (SFFT) is an innovative algorithm for discrete Fourier transforms on signals that possess characteristics of the sparsity in frequency domain. A reference implementation of the algorithm has been proven to be efficient than modern FFT library in cases of sufficient sparsity. However, the SFFT implementation has a critical drawback that it only works reliably for very specific input parameters, especially signal sparsity $k$, which hinders the extensive application of SFFT. In this paper, we propose an Adaptive Tuning Sparse Fast Fourier Transform (ATSFFT), which is a novel sparse fast fourier transform enabled with sparsity detection. In the case of unknown sparsity $k$, ATSFFT is capable of probing the sparsity $k$ via adaptive dynamic tuning and completing the sparse Fourier transform. Experimental results show that ATSFFT outperforms SFFT while it is able to control the computation error better than SFFT. Furthermore, ATSFFT achieves an order of magnitude of performance improvement than the state-of-the-art FFT library, FFTW.