Abstract
In the above article <xref ref-type="bibr" rid="ref1">[1]</xref>, the authors introduced a Generalized Adaptive Polynomial (GAP) window function and presented examples of how GAP-based window functions outperform existing window functions. Claims in <xref ref-type="bibr" rid="ref1">[1]</xref> need clarification, and more importantly, do not hold in all cases.
Highlights
The first example where the claims do not hold is for Hann, known as Hanning, window function
Hann window belongs to a class of Generalized Cosine Window (GCW) functions of the form w(t) = (−1)mam cos(2πmt), for 0 ≤ t ≤ T. (1)
In [1] authors compare Hann window with "Optimized Hann" in Fig. 3, and present that main lobe width has been reduced from 1.46 bins to 1.25 bins, while keeping the sidelobe level at -31.5 dB
Summary
The first example where the claims do not hold is for Hann, known as Hanning, window function. In [1] authors compare Hann window with "Optimized Hann" in Fig. 3, and present that main lobe width has been reduced from 1.46 bins to 1.25 bins, while keeping the sidelobe level at -31.5 dB. Giving up on a steeper roll-off rate is equivalent to removing the second equation from (2), which leaves one degree of freedom to improve the sidelobe suppression - but it is not a Hann window anymore.
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