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Table 11 Average absolute errors attained in sparse scenarios with the SFFTv1, SFFTv2, SFFTv3, and DFTCOMM algorithms for N = {213, 214,…, 218} and k s = L o  = 50

From: Unified commutation-pruning technique for efficient computation of composite DFTs

L i  = N

k s = L o

SFFTv1

SFFTv2

SFFTv3

DFTCOMM

AbsError

AbsError

AbsError

AbsError

213

50

5.6162 × 10−5

5.0689 × 10−5

2.4973 × 10−5

2.7642 × 10−10

214

50

7.0000 × 10−4

6.3012 × 10−4

4.9943 × 10−5

1.8228 × 10−9

215

50

2.8526 × 10−4

2.5407 × 10−4

9.9883 × 10−5

1.6704 × 10−8

216

50

3.7305 × 10−4

3.6885 × 10−4

1.9976 × 10−4

1.5567 × 10−7

217

50

4.9801 × 10−7

4.8631 × 10−7

1.5437 × 10−7

2.6652 × 10−10

218

50

0.0023

0.0023

7.9905 × 10−4

8.2515 × 10−6