On "A Flexible Window Function for Spectral Analysis" [Letter to Editor]

a windowing function that is based on the well-known Butterworth filters was proposed [1] with the claim that it can solve " the tradeoff problem between the frequency resolution and spectral leakage in the estimated power spectral density, unavoidable with the conventional windows. " That claim is a consequence of not considering the available time duration in the window design for which we provide an illustration in this comment correspondence. The Butterworth window is defined as the truncated impulse response of a Butterworth filter constituted by the initial positive part of the impulse response from the beginning until the first zero crossing [1]. The shortcoming in the claim is that the proposed window does not maintain a constant time duration; however this constraint on the window duration is crucial in window design, and it is the reason for the mentioned classical tradeoff between spectral leakage and frequency resolution. After realizing this constant duration constraint, one can easily deduce that the proposed benefit of the Butterworth window in controlling the " 3-dB bandwidth and sidelobe attenuation independently " disappears, and it becomes only a regular window design choice as long as the mainlobe-width versus side-lobe attenuation tradeoff allows. As the article suggests, for some windows , such as Hanning or Hamming, the sidelobe attenuation is fixed. If the constraint on the window duration, or length, is removed, it will be possible to adjust the mainlobe width, or the frequency resolv-ability, of these windows by increasing the window duration. This means that the independently adjustable 3 dB-bandwidth of the Butterworth window proposed in [1] is nothing special. On the contrary, this property is shared by any conventional window function once they are granted a freely adjustable window length. Considering a more common case, if we assume that the window duration is fixed, which is the case for power spectrum estimation of some time sequence, the ultimate limit of frequency resolution of these discrete Fourier transform-based estimation methods is set by the rectangular window and it corresponds to the smallest 3 dB-bandwidth of the mainlobe. This limit is approximately 1/NT, where N and T denote the number of samples used to define the window and the sampling time, respectively. The resulting minimum sidelobe attenuation is 13.3 dB. Any attempt to increase sidelobe attenuation by a smoother window will increase the mainlobe width [2]. That is why the tabulated classical window functions specify the …