A Flexible Window Function for Spectral Analysis
Butterworth Window, Tae Hyun Yoon, Eon Kyeong Joo · 2010
resolution of the estimated PSD can be obtained if we reduce a window’s 3-dB bandwidth. The sidelobe attenuation means the difference between magnitude of the mainlobe and the maximum magnitude of the sidelobes. The sidelobe roll-off rate is the asymptotic decay rate of sidelobe peaks. Undesirable spectral leakage [4]–[6] can be reduced by increasing sidelobe attenuation and roll-off rate. Therefore, an ideal window for PSD estimation has zero bandwidth and infinite sidelobe attenuation such as an impulse function in frequency domain. The conventional windows are able to control 3-dB bandwidth or sidelobe attenuation by only one parameter in general [1], [7]–[12]. Thus, they cannot control these two characteristics independently. In other words, if we reduce a window function’s 3-dB bandwidth, the sidelobe attenuation is also reduced, and vice versa [5], [6]. This behavior is the cause of the tradeoff problem between good frequency resolution and acceptable spectral leakage in the estimated PSD. The Butterworth window does not have this problem because it allows control of the 3-dB bandwidth and sidelobe attenuation independently. Butterworth windows are used as antialiasing filters to reduce the noise in the reconstructed image in previous research [13]. They are also used to remove the edge effect of the matched filter output in pattern matching algorithm [14]. The transfer function of a Butterworth filter is adopted as a window in those applications. However, in this article, a portion of the impulse response of a Butterworth filter is called the Butterworth window and its characteristics in PSD estimation are analyzed.