On Performance of Sparse Fast Fourier Transform Algorithms Using the Flat Window Filter

The problem of computing the Sparse Fast Fourier Transform(sFFT) of a <inline-formula> <tex-math notation="LaTeX">K </tex-math></inline-formula>-sparse signal of size <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-fo...

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Vydáno v:IEEE access Ročník 8; s. 79134 - 79146
Hlavní autoři: Li, Bin, Jiang, Zhikang, Chen, Jie
Médium: Journal Article
Jazyk:angličtina
Vydáno: Piscataway IEEE 2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Aliasing
Buckets
Complexity
Complexity theory
Computation
computational complexity
Dirichlet problem
Discrete Fourier transforms
Fast Fourier transformations
flat window filter
Fourier transforms
Frequency-domain analysis
Kernel
Microsoft Windows
Performance evaluation
Run time (computers)
Runtime
Sampling
Signal processing algorithms
Sparse fast Fourier transform (sFFT)
sub-linear algorithms
ISSN:2169-3536, 2169-3536
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Shrnutí:The problem of computing the Sparse Fast Fourier Transform(sFFT) of a <inline-formula> <tex-math notation="LaTeX">K </tex-math></inline-formula>-sparse signal of size <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> has received significant attention for a long time. The first stage of sFFT is hashing the frequency coefficients into <inline-formula> <tex-math notation="LaTeX">B(\approx {K}) </tex-math></inline-formula> buckets named frequency bucketization. The process of frequency bucketization is achieved through the use of filters: Dirichlet kernel filter, aliasing filter, flat filter, etc. The frequency bucketization through these filters can decrease runtime and sampling complexity in low dimensions. It is a hot topic about sFFT algorithms using the flat filter because of its convenience and efficiency since its emergence and wide application. The next stage of sFFT is the spectrum reconstruction by identifying frequencies that are isolated in their buckets. Up to now, there are more than thirty different sFFT algorithms using the sFFT idea as mentioned above by their unique methods. An important question now is how to analyze and evaluate the performance of these sFFT algorithms in theory and practice. In this paper, it is mainly discussed about sFFT algorithms using the flat filter. In the first part, the paper introduces the techniques in detail, including two types of frameworks, five different methods to reconstruct spectrum and corresponding algorithms. We get the conclusion of the performance of these five algorithms, including runtime complexity, sampling complexity and robustness in theory. In the second part, we make three categories of experiments for computing the signals of different SNR, different <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula>, and different <inline-formula> <tex-math notation="LaTeX">K </tex-math></inline-formula> by a standard testing platform and record the run time, percentage of the signal sampled, and <inline-formula> <tex-math notation="LaTeX">L_{0},L_{1},L_{2} </tex-math></inline-formula> error both in the exactly sparse case and general sparse case. The result of experiments is consistent with the inferences obtained in theory. It can help us to optimize these algorithms and use them correctly in the right areas.
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ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2020.2989327